JP6019585B2 - Terminal device - Google Patents

Description

The present invention relates to an end terminal device.

  In recent years, a three-dimensional magnetic sensor that is mounted on a mobile device such as a mobile phone, a PDA (Personal Digital Assistant) terminal, a PND (Portable Navigation Device), or a mobile body such as an automobile and detects geomagnetism has been developed. In general, a three-dimensional magnetic sensor includes three magnetic sensor modules for decomposing magnetic field vectors into three orthogonal components and detecting them as scalar quantities. The three magnetic sensor modules each output a scalar quantity. Outputs three-dimensional vector data as three components.

  A terminal device such as a mobile phone on which a three-dimensional magnetic sensor is mounted is often provided with various components having magnetic properties, such as various metals having magnetism, and an electric circuit. In this case, the vector data output from the three-dimensional magnetic sensor is a value including a vector representing a magnetic field generated by a component mounted on the terminal device in addition to a vector representing geomagnetism. Therefore, in order to accurately obtain the direction of geomagnetism, a correction process for removing the vector representing the internal magnetic field generated by the components of the terminal device from the vector data output from the three-dimensional magnetic sensor is required. Thus, in order to obtain an accurate value of the geomagnetism that is the detection target, a component that is removed from the data output from the three-dimensional magnetic sensor in the correction process is referred to as an offset.

The internal magnetic field is a magnetic field generated by a component of the terminal device, and is directed in a certain direction with respect to the terminal device and has a certain magnitude. When viewed from the three-dimensional magnetic sensor mounted on the terminal device, the internal magnetic field is a vector having a certain direction and a certain magnitude, regardless of the posture of the terminal device. expressed.
On the other hand, the geomagnetism is a magnetic field having a horizontal component toward the north of the magnetic pole and a vertical component in the dip direction, and is a uniform magnetic field having a certain direction and a certain magnitude with respect to the ground. Therefore, when changing the attitude of the terminal device with respect to the ground, the direction of geomagnetism viewed from the terminal device also changes. That is, when viewed from a three-dimensional magnetic sensor mounted on the terminal device, the geomagnetism is expressed as a vector having a certain magnitude that changes its direction with a change in the attitude of the terminal device.
When a plurality of magnetic data is acquired while rotating the three-dimensional magnetic sensor in the vertical and horizontal directions to greatly change the posture three-dimensionally, a plurality of coordinates indicated by a plurality of vector data sequentially output by the three-dimensional magnetic sensor are Distributed around a spherical surface with the coordinates of the vector representing the magnetic field as the center point and the magnitude of the vector representing the geomagnetism as the radius.

  In Patent Document 1, by utilizing such properties of the geomagnetism and the internal magnetic field, based on a plurality of magnetic data acquired while changing the attitude of the three-dimensional magnetic sensor, a certain direction and magnitude representing the internal magnetic field are disclosed. There is disclosed a method for calculating an accurate geomagnetic direction by calculating a vector having a thickness and performing a correction process for removing the vector representing the internal magnetic field from the output data as an offset.

By the way, when the component of the terminal device on which the three-dimensional magnetic sensor is mounted has a soft magnetic material, a plurality of coordinates indicated by vector data sequentially output from the three-dimensional magnetic sensor are obtained as a result of the soft magnetic material being magnetized. Due to the influence of the generated magnetic field, it is not distributed near the spherical surface but distributed near the elliptical surface. That is, if there is no influence of the magnetic field generated by the soft magnetic material, the plurality of coordinates that should be distributed in the vicinity of the spherical surface move so as to expand and contract in the principal axis direction of the ellipsoid due to the influence of the magnetic field generated by the soft magnetic material. It is distributed in the vicinity of an ellipsoid having the same center point as the spherical surface. In this way, a phenomenon in which a plurality of coordinates indicated by vector data sequentially output from a three-dimensional magnetic sensor due to the influence of a magnetic field generated as a result of magnetizing a soft magnetic material is distributed near the ellipsoid is called a soft iron effect. It is.
When the soft iron effect is generated, it is not possible to calculate the correct direction of geomagnetism based on the coordinates existing in the vicinity of the ellipsoid. In order to calculate the correct orientation of the geomagnetism, coordinate transformation to move the coordinates on the ellipsoid to coordinates on the sphere, that is, to expand and contract in the principal axis direction of the ellipsoid starting from the center point of the ellipsoid It is necessary to perform coordinate transformation to move. Such a process of converting the coordinates on the ellipsoid into coordinates on the sphere is called ellipse correction. The direction of geomagnetism can be calculated by subtracting the coordinate indicated by the center point of the spherical surface from the coordinate after coordinate conversion calculated by performing ellipse correction.

  In Non-Patent Document 1 and Non-Patent Document 2, when the soft iron effect occurs, the coordinates on the ellipsoid indicated by the vector data output from the three-dimensional magnetic sensor are converted into coordinates on the sphere. Therefore, a method for calculating a coordinate transformation matrix is disclosed.

JP 2007-240270 A

JF Vasconcelos, G. Elkaim, C. Silvestre, P. Oliveira, and B. Cardeira, “A Geometric Approach to Strapdown Magnetometer Calibration in Sensor Frame”, in IFAC Workshop on Navigation, Guidance and Control of Underwater Vehicles, Killaloe, Ireland, April 2008 C. C. Foster and G. H. Elkaim, “Extension of a Two-Step Calibration Methodology to Include Nonorthogonal Sensor Axes”, IEEE Transactions on Aerospace and Electronic Systems, Vol. 44, No. 3, July 2008

  However, the calculation for calculating an accurate offset value has a large amount of calculation. In addition, the calculation for calculating the coordinate transformation matrix for performing ellipse correction is also computationally intensive. Therefore, when the terminal device performs these calculations, the terminal device needs to include a large-capacity memory and a high-performance CPU. Further, when the terminal device performs these calculations, a large amount of power is consumed. Therefore, when the terminal device is a portable device powered by a battery, there is a problem that it is difficult to use the terminal device for a long time. Were present.

  In view of the circumstances described above, an object of the present invention is to calculate an accurate geomagnetism direction while suppressing a processing load on a terminal device when calculating the geomagnetism direction.

In order to solve the above-described problems, a terminal device according to the present invention is a terminal device that communicates with a server device, detects magnetic components in three directions, and expresses detected values in a three-axis coordinate system. A three-dimensional magnetic sensor that sequentially outputs as magnetic data that is vector data, a storage unit that stores the magnetic data sequentially output from the three-dimensional magnetic sensor, and a first prescribed number of the magnetic data is stored in the storage unit A vector for calibrating the magnetic data, which is calculated based on the first prescribed number of the magnetic data, the first prescribed number of the magnetic data being transmitted to the server device. And a terminal-side transmitting / receiving unit that receives an offset .

  Since the terminal device according to the present invention can calculate the direction of geomagnetism using the offset calculated by the server device, the processing load on the terminal device can be kept small. Therefore, even a simple terminal device that does not include a large-capacity memory or a high-performance CPU can calculate an accurate geomagnetic direction.

In the terminal device described above , each of the second specified number of magnetic data in the coordinate system is stored in the storage unit when the second specified number less than the first specified number is stored in the storage unit. An approximate center point calculation unit that calculates the coordinates of the approximate center point that is the center point of the spherical surface determined by the coordinates indicated by In the case of being larger , it is preferable that the offset is updated with a vector indicating the coordinates of the approximate center point .

  When the magnetization state of the components of the terminal device changes, the direction and magnitude of the internal magnetic field may change. In this case, the accurate geomagnetic direction cannot be calculated unless the offset used for the correction process is updated so as to represent the direction and magnitude of the internal magnetic field after the change. This is because when the offset is calculated based on the magnetic data output from the three-dimensional magnetic sensor before the internal magnetic field changes, the coordinate indicated by the offset and the coordinate indicated by the internal magnetic field are different.
  The coordinates of the approximate center point calculated based on the magnetic data output from the three-dimensional magnetic sensor after the internal magnetic field changes represent the direction and magnitude of the internal magnetic field. When the server device calculates the offset based on the magnetic data output from the three-dimensional magnetic sensor before the internal magnetic field changes, the server device is based on the magnetic data output from the three-dimensional magnetic sensor after the internal magnetic field changes. The coordinates of the approximate center point calculated in this way and the coordinates indicated by the offset are different. Therefore, by determining whether or not the distance between the coordinates indicated by the offset and the coordinates of the approximate center point is equal to or less than a predetermined threshold, it is possible to determine whether or not the internal magnetic field has changed.
  The terminal device according to this aspect calculates the approximate center point based on the second specified number of magnetic data when the second specified number of magnetic data is stored in the storage unit. Then, it is determined whether or not the distance between the coordinates indicated by the offset and the coordinates of the approximate center point is greater than a predetermined threshold. Furthermore, when it is determined that the internal magnetic field has changed, the offset is updated with the approximate center point representing the internal magnetic field after the change. That is, the terminal device according to this aspect can prevent the continuation of the state where the coordinates indicated by the offset deviate from the coordinates indicated by the internal magnetic field, and can always calculate an accurate geomagnetic direction.

In the terminal device described above , each of the second specified number of magnetic data in the coordinate system is stored in the storage unit when the second specified number less than the first specified number is stored in the storage unit. An approximate center point calculation unit that calculates coordinates of an approximate center point that is a center point of a spherical surface defined by the coordinates indicated by It is preferable that accumulation of the first prescribed number of the magnetic data is started when larger than a predetermined threshold value .

  When the magnetization state of the components of the terminal device changes, the direction and magnitude of the internal magnetic field may change. In this case, the accurate geomagnetic direction cannot be calculated unless the offset used for the correction process is updated so as to represent the direction and magnitude of the internal magnetic field after the change. This is because when the offset is calculated based on the magnetic data output from the three-dimensional magnetic sensor before the internal magnetic field changes, the coordinate indicated by the offset and the coordinate indicated by the internal magnetic field are different.
  The coordinates of the approximate center point calculated based on the magnetic data output from the three-dimensional magnetic sensor after the internal magnetic field changes represent the direction and magnitude of the internal magnetic field. When the server device calculates the offset based on the magnetic data output from the three-dimensional magnetic sensor before the internal magnetic field changes, the server device is based on the magnetic data output from the three-dimensional magnetic sensor after the internal magnetic field changes. The coordinates of the approximate center point calculated in this way and the coordinates indicated by the offset are different. Therefore, by determining whether or not the distance between the coordinates indicated by the offset and the coordinates of the approximate center point is equal to or less than a predetermined threshold, it is possible to determine whether or not the internal magnetic field has changed.
  The terminal device according to this aspect calculates the approximate center point based on the second specified number of magnetic data when the second specified number of magnetic data is stored in the storage unit. Then, it is determined whether or not the distance between the coordinates indicated by the offset and the coordinates of the approximate center point is greater than a predetermined threshold. When the distance is larger than the predetermined threshold, accumulation of the first specified number of magnetic data is started after the internal magnetic field is changed, and the offset after the change of the internal magnetic field can be acquired from the server device. That is, the terminal device according to this aspect can prevent the continuation of the state where the coordinates indicated by the offset deviate from the coordinates indicated by the internal magnetic field, and can always calculate an accurate geomagnetic direction.

In the terminal device described above, the server device that communicates with the terminal device described above may receive the first specified number of magnetic data in the coordinate system when the first specified number of magnetic data is supplied from the terminal device. The coordinates of the center point of the optimum ellipsoidal surface determined so as to have the coordinates indicated by each of the magnetic data, and the coordinates on the sphere centered on the center point of the optimum ellipsoidal surface as the coordinates on the optimum ellipsoidal surface An elliptical surface correction unit that calculates an optimal elliptical surface correction matrix for coordinate transformation to, and adopting the central point of the optimal elliptical surface as a response center point, adopting the optimal elliptical surface correction matrix as a response correction matrix, A data control unit that generates response information including the response center point and the response correction matrix; and a server-side transmission / reception unit that transmits the response information to the terminal device. Serial server side transceiver receives the response information transmitted, it is preferably characterized by.

  When the soft iron effect has occurred, the coordinates indicated by the plurality of magnetic data are distributed in the vicinity of the ellipsoid. Therefore, in order to calculate the direction of the geomagnetism, the coordinates distributed in the vicinity of the ellipse are the same as the ellipse. It is necessary to perform coordinate transformation (that is, ellipse correction) for transformation into coordinates distributed in the vicinity of a spherical surface having the center point. In order to calculate a matrix for performing such coordinate transformation, it is necessary to specify the shape of an ellipsoid having a plurality of magnetic data in the vicinity and accurately expressing the distribution shape of the plurality of magnetic data. Become. However, such an operation for specifying the shape of the ellipsoid has a large amount of calculation.
  According to this aspect, the optimal ellipsoid shape that accurately represents the distribution shape of a plurality of magnetic data is specified, and the optimal central point that is the central point of the optimal ellipsoid and the coordinates on the optimal ellipsoid are determined. The server apparatus calculates an optimal ellipsoidal correction matrix that represents coordinate transformation to coordinates on a spherical surface centered at. Then, the coordinates of the optimum center point and the optimum ellipsoid correction matrix are transmitted to the terminal device. Therefore, even when the terminal device is a simple device that does not include a large-capacity memory or a high-performance CPU, the accurate geomagnetic direction is calculated based on the magnetic data detected by the terminal device. It becomes possible.

Further, in the terminal device described above, the server device that communicates with the terminal device described above has a spherical surface determined so as to have the coordinates indicated by each of the first specified number of magnetic data in the coordinate system in the vicinity. A center point calculation unit that calculates the coordinates of the center point, and a distortion evaluation value that indicates a degree of difference between the shape of the solid and the shape of the spherical surface that are determined to have the first specified number of the magnetic data in the vicinity of the surface. A distortion determination unit that calculates and determines whether or not the distortion evaluation value is equal to or less than a distortion allowable value, and when the determination result in the distortion determination unit is affirmative, the data control unit When the center point calculated by the point calculation unit is adopted as the response center point, the unit matrix is adopted as the response correction matrix, and the determination result in the distortion determination unit is negative, the center point of the optimal elliptical surface is set as the response center As a point While adopting, it is preferably characterized in that employing the optimum ellipsoidal correction matrix as a response correction matrix.

  According to this aspect, the distortion determination unit that determines whether or not the distribution shape of the coordinates indicated by the plurality of magnetic data can be regarded as a spherical surface is provided. Therefore, when the soft iron effect occurs, that is, when the coordinates indicated by a plurality of magnetic data are distributed in the vicinity of an ellipsoid having a shape different from the spherical surface, and when the soft iron effect does not occur, that is, a plurality of magnetic data It can be distinguished from the case where the coordinates indicated by the data are distributed near the spherical surface. If the soft iron effect does not occur, the server device can generate response information without calculating the coordinates of the optimum center point and the optimum ellipsoidal correction matrix, so that the processing load of the server device Can be reduced.

It is a block diagram which shows the structure of the geomagnetic measurement system which concerns on 1st Embodiment of this invention. It is a conceptual diagram explaining the magnetic field which a three-dimensional magnetic sensor measures. It is a conceptual diagram explaining a geomagnetism and an internal magnetic field. It is a conceptual diagram explaining a geomagnetism and an internal magnetic field. It is a conceptual diagram explaining a magnetizing magnetic field. It is a conceptual diagram explaining a magnetizing magnetic field. It is a conceptual diagram explaining the soft iron effect. It is a conceptual diagram explaining an ellipse surface correction matrix. It is a block diagram which shows the structure of the geomagnetic measurement system which concerns on 1st Embodiment. It is a functional block diagram for demonstrating the function of the geomagnetic measurement system which concerns on 1st Embodiment. It is explanatory drawing explaining adoption of the offset of the geomagnetism measuring system which concerns on 1st Embodiment. It is a flowchart showing operation | movement of the terminal device which concerns on 1st Embodiment. It is a flowchart showing the detail of operation | movement of the terminal device which concerns on 1st Embodiment. It is a flowchart showing the detail of operation | movement of the terminal device which concerns on 1st Embodiment. It is a flowchart showing operation | movement of the server apparatus which concerns on 1st Embodiment. It is a functional block diagram for demonstrating the function of the ellipsoid initial correction value production | generation part which concerns on 1st Embodiment. It is a conceptual diagram explaining the 1st ellipsoid, the 2nd ellipsoid, and the 3rd ellipsoid. It is a conceptual diagram explaining an initial ellipsoid correction matrix. It is a conceptual diagram explaining the 2nd condition. It is a conceptual diagram explaining the case where rotation generate | occur | produces in ellipse correction. It is a block diagram which shows the structure of the geomagnetism measuring system which concerns on 2nd Embodiment of this invention. It is a functional block diagram for demonstrating the function of the server apparatus which concerns on 2nd Embodiment. It is a conceptual diagram explaining a geomagnetism, an internal magnetic field, a magnetizing magnetic field, and an external magnetic field. It is a conceptual diagram explaining an external magnetic field. It is a conceptual diagram explaining an external magnetic field. It is a flowchart showing operation | movement of the server apparatus which concerns on 2nd Embodiment. It is a conceptual diagram explaining a center point calculation process. It is a conceptual diagram explaining a magnetic data distribution determination process. It is a conceptual diagram explaining a magnetic data distribution determination process. It is a conceptual diagram explaining a distortion determination process. It is a conceptual diagram explaining a distortion determination process. It is a conceptual diagram explaining a distortion determination process. It is explanatory drawing explaining adoption of the offset of the geomagnetic measurement system which concerns on the modification 10. FIG. 14 is a flowchart showing details of an operation of a terminal device according to Modification 10; 14 is a flowchart showing details of an operation of a terminal device according to Modification 10;

<A. First Embodiment>
Hereinafter, the geomagnetic measurement system according to the first embodiment of the present invention will be described. FIG. 1 is a block diagram showing a configuration of a geomagnetism measurement system SYS according to the first embodiment.
As shown in FIG. 1, the geomagnetism measurement system SYS according to the first embodiment includes a plurality of terminal devices 1 and a server device SV. Each of the plurality of terminal devices 1 is connected to the server device SV via the network NW. Each terminal device 1 includes a three-dimensional magnetic sensor that detects a magnetic field and outputs magnetic data (see FIG. 9A). The geomagnetism measurement system SYS calculates the direction of geomagnetism viewed from the terminal device 1 based on the output from the three-dimensional magnetic sensor provided in the terminal device 1.
In the following, first, an outline of a magnetic field detected by a three-dimensional magnetic sensor provided in each terminal device 1 will be described as a premise for explaining a method of calculating the direction of geomagnetism by the geomagnetism measurement system SYS.

[1. Outline of magnetic field detected by 3D magnetic sensor]
In the present embodiment, as the magnetic field detected by the three-dimensional magnetic sensor, it is assumed that there is a magnetic field generated by a component provided in a device on which the three-dimensional magnetic sensor is mounted, in addition to the geomagnetism that is the measurement target. Specifically, the presence of an internal magnetic field and a magnetizing magnetic field is assumed as the magnetic field generated by the component.
Hereinafter, the outline of these three types of magnetic fields assumed in the present embodiment and vector data output from the three-dimensional magnetic sensor when the three-dimensional magnetic sensor detects these magnetic fields will be described with reference to FIGS. Will be described.

  FIG. 2 shows a geomagnetism Bg that is a measurement target of the geomagnetism measurement system SYS according to the present embodiment, an internal magnetic field Bi generated by the component 2 included in the terminal device 1 on which the three-dimensional magnetic sensor is mounted, and a magnetization generated by the component 2. It is a figure explaining magnetic field Bm.

The geomagnetism Bg is a magnetic field having a uniform direction and magnitude toward the magnetic pole north. Strictly speaking, the direction and size of the geomagnetism Bg varies depending on the region, but has a uniform direction and size, for example, when a large movement such as moving to a different city is not performed.
The internal magnetic field Bi is a magnetic field having a certain direction and a certain magnitude as viewed from the terminal device 1 among the magnetic fields generated by the components 2 provided in the terminal device 1. That is, no matter how the attitude of the terminal device 1 changes, the internal magnetic field Bi is detected by the three-dimensional magnetic sensor 60 as a magnetic field having a fixed direction and magnitude.
The magnetizing magnetic field Bm is a magnetic field that changes its direction and magnitude in accordance with a change in the attitude of the terminal device 1 among the magnetic fields generated by the components 2 provided in the terminal device 1. As shown in FIG. 2, the component 2 includes a soft magnetic material 21. The soft magnetic material 21 is magnetized by the influence of a magnetic field (that is, geomagnetism Bg) emitted from an object outside the terminal device 1. As will be described in detail later, the magnetic field generated as a result of the soft magnetic material 21 being magnetized by the geomagnetism Bg changes its orientation and magnitude as the posture of the terminal device 1 changes. Further, the magnetic field generated as a result of the soft magnetic material 21 being magnetized by the geomagnetism Bg is determined in direction and size depending on the material, size, shape, etc. of the soft magnetic material 21 in addition to the attitude of the terminal device 1. It is done. The magnetizing magnetic field Bm is a magnetic field generated by the soft magnetic material 21 as a result of the soft magnetic material 21 being magnetized by the geomagnetism Bg. That is, the magnetizing magnetic field Bm is a magnetic field that changes the direction and magnitude depending on the direction of the geomagnetism Bg viewed from the terminal device 1 and the material, size, shape, and the like of the soft magnetic material 21.

For convenience of explanation, a ground coordinate system Σ _G and a sensor coordinate system Σ _S as shown in FIG. 2 are introduced. Subscript G attached to the upper left of each vector described in Figure 2, it means that the vector is a vector expressed in ground coordinate system sigma _G.
The ground coordinate system Σ _G is a coordinate system fixed on the ground. The origin is an arbitrary point on the ground, and three directions orthogonal to each other, for example, east, north, and vertical upward are respectively represented by the x axis and the y axis. , And the z-axis coordinate system.
The sensor coordinate system Σ _S is a coordinate system fixed to the three-dimensional magnetic sensor 60, and the values output from the three sensor modules of the three-dimensional magnetic sensor 60 are respectively expressed as x-axis (first axis) and y-axis. This is a coordinate system provided to plot on the axis (second axis) and the z-axis (third axis). That is, the magnetic data output from the 3D magnetic sensor 60 is expressed as vector data of the sensor coordinate system sigma _S. Incidentally, the posture μ shown in Figure 2, represents the direction of each axis of the sensor coordinate system sigma _S in ground coordinate system sigma _G (i.e., in the ground coordinate system sigma _G, the three-dimensional magnetic sensor 60 orientation).
In the following, the case of changing the posture mu, in each of the ground coordinate system sigma _G and the sensor coordinate system sigma _S, or explained the direction of the internal magnetic field Bi and magnetizing field Bm how changes.

First, how the internal magnetic field Bi and the geomagnetism Bg are represented in the ground coordinate system Σ _G and the sensor coordinate system Σ _S will be described with reference to FIGS. 3 and 4. 3 and 4, for the sake of simplicity, it is assumed that the terminal device 1 does not include the soft magnetic material 21 and the magnetizing magnetic field Bm does not exist.
3, the direction and magnitude of the internal magnetic field Bi and geomagnetism Bg, a view showing the ground coordinate system sigma _G. Attitude mu terminal device 1, when changing from the posture mu ₁ the posture mu _2, the internal magnetic field ^G Bi, but is the size constant, the orientation is changed along with the change in the attitude mu. On the other hand, it is constant direction and magnitude of the geomagnetism ^G Bg.

4, the direction and magnitude of the internal magnetic field Bi and geomagnetism Bg, a diagram expressing the sensor coordinate system sigma _S. Specifically, FIG. 4 shows N (first specified number) magnetisms output from the three-dimensional magnetic sensor 60 when the magnetic field is measured while changing the attitude μ of the terminal device 1 from μ ₁ to μ _N. the coordinates indicated by the data q ₁ to q _N, is a plot in the sensor coordinate system sigma _S (N is 9 or more natural number representing a prescribed number of measurements of the magnetic data required to derive accurately offset). Here, the subscript S attached to the upper left of each vector described in Figure 4, it means that the vector is a vector expressed in the sensor coordinate system sigma _S.

In the sensor coordinate system Σ _S , the internal magnetic field Bi is expressed as a vector ^S Bi having a constant direction and a constant magnitude (a vector going from the origin of the sensor coordinate system Σ _S to the center point c _OG ). On the other hand, the magnitude of the geomagnetism Bg is constant, but the direction changes with the attitude μ of the three-dimensional magnetic sensor 60. That is, the geomagnetism Bg is expressed as a vector ^S Bg (μ) having a certain size and having an orientation depending on the attitude μ of the terminal device 1. Therefore, when the starting point of the vector ^S Bg (μ) is arranged at the center point c _OG and the posture μ is changed, the end point of the vector ^S Bg (μ) is centered on the center point c _OG and the magnitude of the geomagnetism Bg. the a radius, indicating the coordinates on the sphere S _G.

In the sensor coordinate system sigma _S, each of the coordinate indicated by the plurality of magnetic data _q 1 to q _N is to represent the sum of the internal magnetic field ^S Bi and geomagnetism ^S Bg, coordinates indicated by the plurality of magnetic data _q 1 to q _N is distributed on a spherical surface _{S G.} The measurement values of the three-dimensional magnetic sensor 60, since it has a measurement error, the coordinates indicated by the plurality of magnetic data q ₁ to q _N, strictly speaking, it is stochastically distributed in the vicinity of the sphere S _G.
Therefore, by subtracting the internal magnetic field ^S Bi from the coordinates indicated by the magnetic data q _i, it is possible to calculate the direction and magnitude of the geomagnetism ^S Bg in the sensor coordinate system sigma _S. As described above, in order to obtain the correct orientation of the geomagnetism Bg that is the detection target, the center point c _OG of the spherical surface S _G that represents the internal magnetic field Bi output from the three-dimensional magnetic sensor 60 is determined from the coordinates indicated by the magnetic data q _i . The process of subtracting the indicated coordinates is called a correction process.
A vector removed from the magnetic data q _i in the correction process is referred to as an offset c _OFF . That is, the offset _{c OFF} is a vector ^S Bi representing the internal magnetic field, in the sensor coordinate system sigma _S, expressed as a vector indicating the center point _{c OG} of the spherical _{S G} from the origin.

When the terminal device 1 includes the soft magnetic material 21, the soft magnetic material 21 is magnetized under the influence of the geomagnetism Bg. As a result, the soft magnetic material 21 generates a magnetized magnetic field Bm. FIG. 5 and FIG. 6 show how the orientation and magnitude of the magnetizing magnetic field Bm change in each of the ground coordinate system Σ _G and the sensor coordinate system Σ _S when the attitude μ of the terminal device 1 is changed. Will be described with reference to FIG.

5, in the ground coordinate system sigma _G, it is illustrated FIGS direction and magnitude of the magnetizing magnetic field Bm. 5, the terminal apparatus 1, rectangular soft having parallel long sides 211a and 211b in the x-axis of the sensor coordinate system sigma _S, the short sides parallel 212a and 212b in the y-axis of the sensor coordinate system sigma _S It comprises a material 21, the soft magnetic material 21 exemplifies a case which is arranged so as to be positioned on the x-axis of the sensor coordinate system sigma _S.

As described above, the magnetization magnetic field Bm is a magnetic field generated as a result of the soft magnetic material 21 being magnetized by the geomagnetism Bg, and depends on the orientation μ of the terminal device 1 and the material, size, shape, etc. of the soft magnetic material 21. The magnetic field changes its direction and size. If the attitude mu terminal apparatus 1 is changed from the attitude mu ₁ the posture mu _2, the direction and magnitude of the magnetizing magnetic field ^G Bm ^is changed from G Bm (mu ₁₎ to ^G Bm (μ _2). For example, if the attitude mu of the terminal device 1 is attitude mu _1, the soft magnetic material 21 generates a magnetizing field ^G Bm (mu ₁₎ directed from the short side 212a of the soft magnetic material 21 to the other short side 212b If the attitude mu terminal apparatus 1 posture mu _2, the soft magnetic material 21, the other to generate a magnetizing field ^G Bm towards the long sides 211b (μ ₂₎ from the long sides 211a of the soft magnetic material 21.
Direction and magnitude of the three-dimensional magnetic sensor 60 detects magnetizing field ^G Bm (mu) is dependent and attitude mu, and the position ^S Pm of the soft magnetic material 21 in the sensor coordinate system sigma _S. For example, in the case of FIG. 5, the three-dimensional magnetic sensor 60 detects a magnetic field oriented in the same direction as (in the sensor coordinate system sigma _S), magnetizing field ^G Bm a (mu _1), geomagnetism ^G Bg (mu ₁₎ . Further, the three-dimensional magnetic sensor 60 (in the sensor coordinate system sigma _S), the magnetizing field ^G Bm (mu _2), the geomagnetic ^G Bg (mu ₂₎ is detected as a magnetic field oriented in the direction opposite.
Incidentally, the soft magnetic material 21, in addition to the geomagnetic Bg, is magnetized by the magnetic field of a constant direction and magnitude as viewed from the sensor coordinate system sigma _S to component 2 emitted. Magnetic field the soft magnetic material 21 is emitted as a result when viewed from the sensor coordinate system sigma _S is magnetized by the magnetic field of a constant direction and magnitude, constant direction and magnitude even when the posture μ terminal apparatus 1 is changed Have Among the magnetic fields generated as a result of the soft magnetic material 21 being magnetized, a magnetic field having a fixed direction and magnitude even when the posture μ changes is included in the internal magnetic field Bi described above.

Figure 6 is a diagram terminal device 1 and the magnetic data q ₁ to be measured when the posture mu _1, a magnetic data q ₂ to be measured when the posture mu _2, plotted in the sensor coordinate system sigma _S It is.
Magnetic data _{q 1} is a starting point coordinates indicating the center point _{c OG,} a geomagnetic ^S Bg (μ ₁₎ and magnetizing field ^S Bm having the same orientation (mu _1), geomagnetism ^S Bg (μ ₁₎ and the sum The coordinates indicated by the vector ^S B _E (μ ₁ ). Accordingly, the magnetic data _{q 1} is present outside the sphere _{S G.} On the other hand, the magnetic data _{q 2} is the starting point coordinates indicating the center point _{c OG,} a geomagnetic ^S Bg ^(μ ₂₎ opposite to the magnetizing field ^S Bm ^(μ _2), and a geomagnetism ^S Bg ^(μ ₂₎ This is the coordinate indicated by the added vector ^S B _E (μ ₂ ). Accordingly, the magnetic data _{q 2} is present inside the sphere _{S G.}
That is, the magnetic data _{q 1} and _{q 2} are spherical _{S G,} stretched to the vector ^S Bg ^(μ ₁₎ direction and distributed on an ellipsoid _{V E} obtained by shortening the vector ^S Bg ^(μ ₂₎ Direction To do.
In this way, when the three-dimensional magnetic sensor is incorporated in a device including a soft magnetic material, due to the influence of the magnetization magnetic field generated as a result of the soft magnetic material being magnetized by a magnetic field from the outside of the device such as the geomagnetism, The coordinates indicated by the plurality of magnetic data measured by the three-dimensional magnetic sensor are not distributed near the spherical surface but distributed near the elliptical surface. Such a phenomenon in which coordinates indicated by a plurality of magnetic data are distributed in the vicinity of an ellipsoid due to the influence of a magnetic field generated as a result of magnetizing a soft magnetic material is called a soft iron effect.

The coordinates indicated by the plurality of magnetic data q _{1 to} q _N output from the three-dimensional magnetic sensor 60 when the soft iron effect occurs will be described with reference to FIG.
FIG. 7 shows the magnetic field while changing the attitude μ of the three-dimensional magnetic sensor 60 to μ ₁ to μ _N (N is a natural number of 9 or more representing the specified number of measurement times of magnetic data necessary for accurately deriving the offset). as measured, the coordinates indicated by the N magnetic data q ₁ to q _N output from the 3D magnetic sensor 60 is a diagram plotting the sensor coordinate system sigma _S. 7, the soft iron effect, the coordinates indicated by the plurality of magnetic data q ₁ to q _N is, it is assumed that the distributed on an ellipsoid V _E around the center point c _OG. In FIG. 7, is not considered a measurement error of the 3D magnetic sensor 60, when considering the measurement error, the coordinates indicated by the plurality of magnetic data q ₁ to q _N, distribution on ellipsoidal V _E without the stochastically distributed in the vicinity of the ellipsoidal V _E. In other words, the ellipsoidal V _E is the ellipsoid defined so as to minimize the error between the coordinate indicated by the plurality of magnetic data q ₁ to q _N.

The main axis of the ellipsoidal _{V E,} a long sequence _{L E1, L E2,} and referred to as _{L E3,} the lengths of the three principal axis _{r E1, r E2,} and the _{r E3 (i.e., r E1} ≧ _{r E2} ≧ r _E3 > 0). Further, the radius of the spherical surface S _G is r _G.
At this time, the vector ^S B _E (μ _i ) indicating the coordinates represented by the magnetic data q _i from the center point c _OG has a component parallel to the main axis L _E1 in the vector ^S Bg (μ _i ) representing the geomagnetism r _E1. / _{r G} multiplied by the vector, the vector representing the vector components parallel to the main axis _{L E2} was doubled _r E2 / _{r G,} and the vector sum of the component parallel to the main axis _{L E3} and _r E3 / _{r G} times.
Therefore, the direction of the vector ^S B _E (μ _i ) indicating the coordinates represented by the magnetic data q _i from the center point c _OG is different from the direction of the vector ^S Bg (μ _i ) indicating the geomagnetism. Further, the angle formed by the vector ^S B _E (μ _i ) and the vector ^S B _E (μ _j ) (that is, the coordinates indicated by the two magnetic data q _i and q _j when viewed from the center point c _OG). The angle formed by the vector ^S Bg (μ _i ) and the vector ^S Bg (μ _j ) representing the geomagnetism is different. As described above, when the soft iron effect is generated, the direction of the geomagnetism ^S Bg (μ _i ) cannot be accurately obtained even if the coordinates of the center point c _OG are subtracted from the coordinates of the magnetic data q _i .

Therefore, in this embodiment, as shown in FIG. 8, and calculates the coordinates on the ellipsoid V _E, the ellipsoid correction matrix T _E be converted to coordinates on a spherical surface S _E of radius 1, ellipsoid correction matrix By T _E , the coordinates indicated by the magnetic data q _i are converted into coordinates on the spherical surface S _E represented by the converted magnetic data s _i . The vector ^S Bs (μ _i ) indicating the coordinates represented by the converted magnetic data s _i from the center point c _OG is oriented in the same direction as the vector ^S Bg (μ _i ) representing the geomagnetism. Therefore, the direction of the vector ^S Bg (μ _i ) representing the geomagnetism can be obtained by subtracting the coordinates indicated by the center point c _OG from the coordinates indicated by the converted magnetic data s _i .
As described above, in order to calculate the direction of the geomagnetism Bg, the coordinates indicated by the plurality of magnetic data distributed in the vicinity of the ellipsoid are converted into the plurality of coordinates distributed in the vicinity of the spherical surface of radius 1 having the same center point as the ellipse. The process of converting to is called ellipse correction.

Performed by the ellipsoid correction matrix T _E, the coordinates indicated by the magnetic data q _i on the ellipsoid V _E, the coordinate transformation (ellipse correction) to the coordinates indicated by the converted magnetic data s _i on the sphere S _E is the following It is represented by the formula (1.a).
Here, ellipsoidal correction matrix T _E is a symmetric matrix of 3 rows and three columns represented by the following formula (1.b). The three-dimensional variable vector q shown in the equation (1.c) is a variable vector for representing the coordinates of the magnetic data q _i , and the three-dimensional variable vector s shown in the equation (1.d) is , A variable vector for representing the coordinates of the converted magnetic data s _i , and the three-dimensional variable vector c shown in the equation (1.e) represents the coordinates of the center point c _OG (ie, offset c _OFF ). Is a variable vector for
In the equation (1.a), vector (q-c) represents a coordinate on an ellipsoid obtained by the center point c _OG of ellipsoidal V _E is translated to the origin of the sensor coordinate system sigma _S, vector (s-c) show the coordinates on a sphere of radius 1 centered at the origin of the coordinate system sigma _S.

As described above, the ellipsoidal correction matrix T _E is converted in the coordinate system to the center point c _OG of ellipsoidal V _E as the origin, the coordinates on the ellipsoid V _E, into coordinates on a spherical surface S _E of radius 1 It is a matrix to do. In other words, the ellipsoidal correction matrix T _E includes each of the three eigenvectors are orthogonal to each other, and each of the three principal axes of the ellipsoidal V _E is parallel, and each of the three eigenvalues corresponding to the three eigenvectors, oval the length reciprocal of each of the three principal axes of the plane V _E is determined to be equal.
Here, the three eigenvectors having the ellipsoidal correction matrix _{T E} and _{u T1, u T2,} and _{u T3,} the corresponding eigenvalues lambda _T1, lambda _T2, and lambda _{T3 (where, λ T1 ≧ λ T2 ≧ λ} T3 > 0). At this time, the eigenvector u _T1 is determined to be parallel to the main axis L _E1 , the eigenvector u _T2 is set to be parallel to the main axis L _E2 , and the eigenvector u _T3 is set to be parallel to the main axis L _E3 . The eigenvalue λ _T1 is equal to the reciprocal of the length r _E1 of the main axis L _E1 , the eigenvalue λ _T2 is equal to the reciprocal of the length r _E2 of the main axis L _E2 , and the eigenvalue λ _T3 is equal to the length of the main axis L _E3 . R is determined to be equal to the reciprocal of _E3 . That is, the ellipsoid correction matrix T _E expands or contracts the component in the eigenvector u _T1 direction to the eigenvalue λ _T1 times with respect to an arbitrary vector, expands and contracts the component in the eigenvector u _T2 direction to the eigenvalue λ _T2 times, and the eigenvector u _T3 This is a matrix that expands and contracts the direction component to the eigenvalue λ _T3 times.
Incidentally, the three eigenvalues having the ellipsoidal correction matrix T _E lambda _T1, lambda _T2, and lambda _T3 are both positive values, ellipsoidal correction matrix T _E is a positive definite matrix.

By the way, as shown in FIG. 8, between the vector ^S Bs (μ _i ) indicating the coordinates represented by the converted magnetic data s _i from the center point c _OG and the vector ^S Bg (μ _i ) indicating the geomagnetism. May cause a shift angle ψ. In this case, the correct direction of the vector ^S Bg (μ _i ) cannot be calculated from the converted magnetic data s _i .
However, the deviation angle [psi, a value that depends on the mutual positional relationship between the soft magnetic material 21 and the three-dimensional magnetic sensor 60 (i.e., the direction and magnitude of the vector ^S Pm shown in FIG. 5). Therefore, it is possible to identify the deviation angle ψ from the vector ^S Pm, can from a shift angle ψ identified, a magnetic data s _i after multiple conversion, calculate the direction of the correct geomagnetism Bg is there. Further, by devising the arrangement of the soft magnetic material 21, the shift angle ψ can be suppressed to a small value.

In the following, we determined the shape of the ellipsoid V _E, performs elliptic correction by calculating the ellipsoid correction matrix T _E, describes a method of calculating the direction of the correct geomagnetism Bg.

[2. Device configuration and software configuration]
FIG. 9A is a block diagram showing a configuration of the terminal device 1 according to the first embodiment of the present invention.
The terminal device 1 is connected to various components via a bus and controls the entire device, a RAM 20 that functions as a work area of the CPU 10, a ROM 30 that stores various programs and data such as a terminal-side magnetic data processing program 70, and the like. A communication unit 40 that performs communication, a display unit 50 that displays an image, and a three-dimensional magnetic sensor 60 that detects magnetism and outputs magnetic data are provided.

The three-dimensional magnetic sensor 60 includes an X-axis geomagnetic sensor 61, a Y-axis geomagnetic sensor 62, and a Z-axis geomagnetic sensor 63. Each sensor can be configured using an MI element (magnetoimpedance element), an MR element (magnetoresistance effect element), or the like. The geomagnetic sensor I / F 64 AD-converts the output signal from each sensor and outputs magnetic data q. The magnetic data q are each output from the X-axis geomagnetic sensor 61, Y-axis geomagnetic sensor 62 and the Z-axis geomagnetic sensor 63, representing the x-axis of the sensor coordinate system sigma _S, the three components of the y-axis and z-axis a vector data on the sensor coordinate system sigma _S.
The RAM 20 is used as a work area for the CPU 10. This work area includes storage areas for storing magnetic data output from the three-dimensional magnetic sensor 60 (first storage area Area1 and second storage area Area2), and areas for storing various management information. .
The communication unit 40 is a communication interface for communicating with the server apparatus SV via the network NW. When the CPU 10 executes the terminal-side magnetic data processing program 70, the terminal device 1 starts communication with the server device SV, transmits the magnetic data output from the three-dimensional magnetic sensor 60 to the server device SV, and the server device. Response information transmitted from the SV is received. That is, as the CPU 10 executes the terminal-side magnetic data processing program 70, the terminal device 1 is a part of the geomagnetism measurement system SYS that calculates the direction of the geomagnetism Bg based on the magnetic data output from the three-dimensional magnetic sensor 60. Function.
The display unit 50 displays the direction of the geomagnetism Bg calculated by the geomagnetism measurement system SYS as azimuth information using arrows or the like. The terminal-side magnetic data processing program 70 may be assumed to be linked with a map application or the like, and the display unit 50 displays an arrow or the like, which is direction information indicating the direction of geomagnetism, on the map. Also good.

FIG. 9B is a block diagram showing a configuration of the server apparatus SV according to the first embodiment of the present invention. The server device SV is connected to various components via a bus, controls the entire device, a CPU 910, a RAM 920 that functions as a work area of the CPU 910, a ROM 930 that stores a boot program, etc., and each terminal device 1 via a network NW. A communication unit 940 for communication and a hard disk 950 storing various programs and data such as a server-side magnetic data processing program 960 are provided.
The RAM 920 is used as a work area for the CPU 910. This work area includes a third storage area Area3 for storing magnetic data transmitted from the terminal device 1, and an area for storing various management information. Note that these work areas may be provided on the hard disk 950.

FIG. 10 is a functional block diagram for explaining the functions of the geomagnetism measurement system SYS. Specifically, FIG. 10 illustrates a function realized by the CPU 10 of the terminal device 1 executing the terminal-side magnetic data processing program 70 among the functions of the geomagnetism measurement system SYS, and the CPU 910 of the server device SV as a server. It represents functions realized by executing the side magnetic data processing program 960.
In FIG. 10, for convenience of description, a symbol “1” is assigned to a function realized by the CPU 10 of the terminal device 1 executing the terminal-side magnetic data processing program 70, and the CPU 910 of the server device SV A code “SV” is given to a function realized by executing the server-side magnetic data processing program 960.

In the geomagnetism measurement system SYS, the terminal device 1 includes a storage unit 110 that stores a plurality of magnetic data q _i , a terminal-side transmission / reception unit 120 that communicates with the server device SV, and a magnet that is sequentially output from the three-dimensional magnetic sensor 60. A geomagnetism calculation unit 130 that calculates the orientation of the geomagnetism Bg based on the data q _i , and an approximate center point calculation unit 140 that calculates the coordinates of the approximate center point c _SB based on a plurality of magnetic data stored in the storage unit 110. .
Further, in the geomagnetism measurement system SYS, the server device SV includes a server-side transmission / reception unit 720 that performs communication with the terminal device 1, a data control unit 710 that manages information transmitted / received to / from the terminal device 1, and a terminal It comprises ellipsoid correction unit 200, which calculates the coordinates and optimum ellipsoidal correction matrix T _OP of the optimum center point c _EOP based on a plurality of magnetic data transmitted from the apparatus 1.
Here, the optimum center point c _EOP is the center point of the optimum ellipse surface V _EOP that is an ellipsoid surface determined so as to minimize an error from the coordinates indicated by each of the plurality of magnetic data transmitted from the terminal device 1. It is. The optimal ellipsoid correction matrix T _OP is a 3 × 3 symmetry for converting coordinates on the optimal ellipsoid V _EOP into coordinates on the spherical surface S _EOP centered on the optimal center point c _EOP. It is a matrix.

The storage unit 110 includes a first storage unit BU1 and a second storage unit BU2, and inputs information to the terminal-side transmission / reception unit 120, the geomagnetism calculation unit 130, and the approximate center point calculation unit 140, and outputs them. Information to manage.
Specifically, the storage unit 110 stores the magnetic data q _i sequentially output from the three-dimensional magnetic sensor 60 in the first storage unit BU1. Then, the storage unit 110, are N magnetic data _q 1 to q _N stored in the first storage unit BU1, when the N number of the magnetic data _q 1 to q _N terminal side receiving unit 120 has acquired, The data stored in the first storage unit BU1 is discarded. As described above, N is a natural number equal to or greater than “9” that represents the specified number of measurements of magnetic data necessary to accurately derive the offset.
Here, the first storage unit BU1 is formed by the first storage area Area1 of the RAM 20, and the second storage unit BU2 is formed by the second storage area Area2 of the RAM 20.
In the present embodiment, the storage unit 110, when outputting the N pieces of magnetic data _q 1 to q _N stored in the first storage unit BU1, all of the N pieces of magnetic data _q 1 to q _N Discard, but only a certain percentage of data from the oldest may be discarded.
In the present embodiment, the storage unit 110 stores all the magnetic data q _i sequentially output from the three-dimensional magnetic sensor 60 in the first storage unit BU1, but the present invention is not limited to such an aspect. Absent. For example, the storage unit 110, three-dimensional coordinate indicated by the magnetic data q _i sequentially output from the magnetic sensor 60, the distance is a predetermined value between the coordinate indicated by the magnetic data q _i-1 stored immediately before the storage unit 110 The magnetic data q _i may be stored in the first storage unit BU1 only when it is larger than the first storage unit BU1. In addition, the storage unit 110 includes coordinates indicated by the magnetic data q _i sequentially output from the three-dimensional magnetic sensor 60, and coordinates indicated by each of the magnetic data q _{1 to} q _i−1 already stored in the storage unit 110. The magnetic data q _i may be stored in the first storage unit BU1 only when the distance is greater than a predetermined value.

Further, when the magnetic data q _i sequentially output from the three-dimensional magnetic sensor 60 satisfies the following formula (2.a), the storage unit 110 stores the magnetic data q _i in the second storage unit BU2. In the following, the magnetic data stored in the second storage unit BU2 among the magnetic data q may be expressed as “q _B ”.
Here, the coordinates indicated by the magnetic data q _i are represented by a three-dimensional vector shown in the following equation (2.b). Further, M (second specified number) is a natural number that satisfies 0 <M ≦ N, and “k” is a natural number that satisfies 1 ≦ k <M. In the present embodiment, M is “4”. Further, “q _Bn ” appearing in the following equation (2.a) indicates each of the magnetic data stored in the second storage unit BU2 when the three-dimensional magnetic sensor 60 outputs the magnetic data q _i. It is a coordinate and is represented by a three-dimensional vector shown in the following equation (2.c). Δq is a predetermined value larger than 0. That is, the following equation (2.a) is obtained by the coordinates indicated by the magnetic data q _i output from the three-dimensional magnetic sensor 60 and the k pieces of magnetic data q _{B1 to} q _Bk stored in the second storage unit BU2. Represents the condition that all the distances to the coordinates indicated by each are greater than a predetermined value Δq. This condition is hereinafter referred to as “magnetic data distance condition”. As described above, when the coordinates indicated by the magnetic data q _i satisfy the magnetic data distance condition, the accumulation unit 110 stores the magnetic data q _i in the second storage unit BU2.
The accumulating unit 110 accumulates M pieces of magnetic data q _{B1 to} q _BM in the second storage unit BU2, and the approximate center point calculating unit 140 acquires the M pieces of magnetic data q _{B1 to} q _BM. The data stored in the second storage unit BU2 is discarded.
In the present embodiment, the storage unit 110 stores the magnetic data q _i output from the three-dimensional magnetic sensor 60 in the second storage unit BU2 when the “magnetic data distance condition” is satisfied. You may store in 2nd memory | storage part BU2 without determining whether it is satisfied.

Further, the storage unit 110 stores the response information RES when the response information RES is supplied from the server device SV to the terminal side transmission / reception unit 120. In the present embodiment, response information RES is the coordinates of the response center point _{c SA,} and is information including a response correction matrix _{T A.}
Furthermore, the storage unit 110 stores management information such as various counters and various flags described later.

When the N pieces of magnetic data q _{1 to} q _N are stored in the first storage unit BU 1 of the storage unit 110, the terminal side transmission / reception unit 120 acquires the N pieces of magnetic data q _{1 to} q _N , and the server Transmit to device SV. Further, the terminal side transmission / reception unit 120 receives the response information RES supplied from the server device SV and outputs the response information RES to the storage unit 110.

Approximate center point calculating unit 140, when the M pieces of the magnetic data _q B1 _{to q BM} stored in the second storage unit BU2 accumulation unit 110, indicated by each of the M pieces of the magnetic data _q B1 _{to q BM} coordinates to calculate the coordinates of the center point is approximated center point c _SB spherical (approximate center point calculating spherical) S _B having on the surface a.
The coordinates of the approximate center point c _SB may be calculated by appropriately applying a known method. The coordinates of the approximate center point c _SB are represented by a three-dimensional vector shown in the following equation (3.b). At this time, for example, the coordinates of the approximate center point c _SB can be calculated as a solution of the simultaneous linear equations shown in the following expression (3.a). Note that the variable c _SBw appearing in the equation ( _3.a ) is a variable used for calculation.

The geomagnetism calculation unit 130 performs ellipse correction using the ellipsoid correction matrix _TE and the offset c _{OFF on the} coordinates indicated by the magnetic data q _i output from the three-dimensional magnetic sensor 60, and the sensor coordinate system Σ _S The direction of the geomagnetism ^S Bg at (specifically, the direction of the vector ^S Bs (μ _i )) is calculated.

The geomagnetism calculation unit 130 includes an offset adoption unit 131 and a geomagnetism vector calculation unit 132.
Offset employed 131 either one of the vector representing the coordinates of the vector or the approximate center point c _SB representing the coordinates of the response center point c _SA, adopted as the offset c _OFF. Then, the offset adopted section 131, when employing a vector representing the coordinates of the response center point _{c SA} as an offset _{c OFF,} employing a response correction matrix _{T A} as ellipsoid correction matrix _{T E.} On the other hand, the offset adopted section 131, when employing a vector representing the coordinates of the approximate center point c _SB as an offset c _OFF, employing a unit matrix I of three rows and three columns as an ellipsoid correction matrix T _E.
Geomagnetic vector calculation unit 132, as shown in Equation (1.a), the magnetic data _{q i} output from a 3D magnetic sensor 60, an ellipse correction using the ellipsoid correction matrix _{T E} and the offset _{c OFF} It was carried out, to calculate the direction of the geomagnetic ^S Bg.
As is clear from equation (1.a), if the offset employed 131 employed as an ellipsoid correction matrix _{T E,} the unit matrix I, the orientation of the geomagnetic ^S Bg is simply indicated by the magnetic data _{q i} It is calculated by subtracting the coordinates of the approximate center point c _{SB from} the coordinates. That is, in this case, the geomagnetic vector calculation section 132 is essentially without elliptical correction, to calculate the direction of the geomagnetism ^S Bg by subtraction just vectors.

Server-side transceiver unit 720 receives the N pieces of magnetic data q ₁ to q _N transmitted from the terminal apparatus 1, and stores it in the data control unit 710. Further, when the data control unit 710 generates the response information RES, the server-side transmission / reception unit 720 acquires the response information RES and transmits the response information RES to the terminal device 1. Incidentally, the response information RES is, when it is calculated based on a certain terminal device the N magnetic data q ₁ to q _N received from 1, the server-side transmitting and receiving unit 720, with respect to the certain terminal device 1, the response Information RES is transmitted.

The data control unit 710 manages information input to the server-side transmission / reception unit 720 and the ellipsoidal correction unit 200 and information output from these, and generates response information RES.
Specifically, the data control unit 710 holds a plurality of magnetic data q _{1 to} q _N output from the server-side transmission / reception unit 720.
Further, the data control unit 710, when the ellipsoid correction unit 200 calculates the coordinates and optimum ellipsoidal correction matrix _{T OP} indicated optimum center point _{c EOP,} while adopting an optimum center point _{c EOP} response center point _{c SA} , adopting the optimal ellipsoid correction matrix _{T OP} in response correction matrix _{T a.} Then, the data control unit 710 generates response information RES to the coordinates and response correction matrix _{T A} shows response center point _{c SA} element.

The ellipsoidal correction unit 200 includes an ellipsoidal initial correction value generation unit 300 and an ellipsoidal optimal correction value generation unit 400.
The ellipsoid initial correction value generation unit 300 calculates the coordinates of the initial center point _cE0 and the initial ellipsoid correction matrix T ₀ based on the plurality of magnetic data q _{1 to} q _N stored in the data control unit 710. Here, the initial center point c _E0 is a center point of the initial ellipsoid V _E0 having the coordinates indicated by the plurality of magnetic data q _{1 to} q _{N in} the vicinity. The initial ellipsoid correction matrix T ₀ is a 3-by-3 symmetric matrix for converting coordinates on the initial ellipsoid V _E0 into coordinates on the sphere S _E0 centered on the initial center point c _E0. It is. It will be described later specific method for calculating the initial center point c _E0 and initial ellipsoidal correction matrix T _0.

Ellipsoidal optimum correction value generation unit 400, based on the coordinates and the initial ellipsoidal correction matrix T ₀ of the initial center point c _E0 to ellipsoidal initial correction value generation unit 300 calculates, for a plurality of magnetic data q ₁ to q _N the coordinates of the optimum center point c _EOP an error between the coordinates and ellipsoidal each representing a center point of the ideal ellipsoid V _EOP to minimize, the central point the optimum center point c _EOP from the coordinates of the optimum ellipsoidal V _EOP It calculates the optimum ellipsoidal correction matrix T _OP representing the coordinate transformation to the coordinate on the sphere S _EOP having to.
If the error between the plurality of magnetic data q ₁ to q _N coordinates and ideal ellipsoid V _EOP indicated by is minimized "0", it matches the ellipsoid V _E and the optimum ellipsoidal V _EOP, the optimum center point The c _EOP and the center point c _OG (that is, the coordinates indicated by the internal magnetic field Bi) coincide with each other. It will be described later in detail of a method of calculating the optimum center point c _EOP and optimum ellipsoidal correction matrix T _OP.
[3. Update offset]

FIG. 11 is an explanatory diagram for explaining the offset c _OFF employed by the offset adopting unit 131. Specifically, FIG. 11 shows an offset c _OFF adopted by the offset adoption unit 131, magnetic data q _i output from the three-dimensional magnetic sensor 60, a response center point c _SA supplied from the server device SV, and an approximation. central point calculation unit 140 indicates the relationship between the approximation center point c _SB to calculate.
In this figure, for the sake of simplicity, the “magnetic data distance condition” which is a condition for the storage unit 110 to store a plurality of magnetic data q _{B1 to} q _BM is not considered. That is, in this figure, the storage unit 110, when the three-dimensional magnetic sensor 60 has output the M magnetic data _q 1 to q _M, it is assumed that storing them as magnetic data _q B1 _{to q BM} . In this figure, for the sake of simplicity, the communication time between the terminal device 1 and the server device SV, the calculation time of the response center point c _SA in the server device SV, and the like are not considered. I.e., in this figure, server SV, the three-dimensional magnetic sensor 60 After outputs N magnetic data q ₁ to q _N, calculate the response center point c _SA immediately supplies it to the terminal device 1 Assume that

As shown in FIG. 11, the offset adopting unit 131 executes the approximate center point calculating unit after the CPU 10 executes the terminal side magnetic data processing program 70 and before the server device SV is supplied with the response center point c _SA. The approximate center point c _SB calculated by 140 is adopted as the offset c _OFF (FIG. 11A). Note that when the approximate center point calculation unit 140 newly calculates the approximate center point c _SB when the vector indicating the coordinates of the approximate center point c _SB is employed as the offset c _OFF , the offset adopting unit 131 newly calculates the approximate center point c _SB. The offset c _OFF is updated with a vector indicating the coordinates of the approximate center point c _SB calculated in (1B). After that, when the response center point c _SA is supplied from the server device SV, the offset adoption unit 131 updates the offset c _OFF with a vector indicating the coordinates of the response center point c _SA (FIG. 11C). When a vector indicating the coordinates of the response center point c _SA is adopted as the offset c _OFF , the offset adoption unit 131 does not calculate the approximate center point c _SB even if the approximate center point calculation unit 140 newly calculates the approximate center point c _SB. Although the offset c _OFF is not updated by the point c _SB , when a new response center point c _SA is supplied from the server device SV, a vector indicating the coordinates of the newly supplied response center point c _SA The offset c _OFF is updated (FIG. 11D).

As described above, the internal magnetic field Bi is normally also how to change the attitude of the terminal device 1, as viewed from the terminal apparatus 1 (i.e., in the sensor coordinate system sigma _S) having a constant direction and magnitude . However, when the internal state of the terminal device 1 changes (for example, when the magnitude of the current flowing through the component mounted on the terminal device 1 changes, or the magnetization status of the component mounted on the terminal device 1 changes). If), the direction and magnitude of the internal magnetic field Bi in the sensor coordinate system sigma _S may change. The direction of the geomagnetism Bg is calculated by performing a correction process for subtracting the offset c _OFF representing the vector ^S Bi indicating the internal magnetic field from the coordinates indicated by the magnetic data q _i output from the three-dimensional magnetic sensor 60. Therefore, in order to calculate the correct direction of the geomagnetism Bg, the offset c _OFF needs to accurately represent the vector ^S Bi indicating the internal magnetic field.
Therefore, the terminal device 1 according to the present embodiment determines whether or not the internal magnetic field Bi has changed in the approximate center point calculation unit 140, and if it is determined that the internal magnetic field Bi has changed, the offset adoption unit. In 131, the offset c _OFF is updated to a value representing the changed internal magnetic field Bi.

As described above, the approximate center point c _SB is calculated based on the M pieces of magnetic data q _{B1 to} q _BM . Therefore, the coordinates of the approximate center point c _SB calculated using the magnetic data q _{B1 to} q _BM acquired after the change of the internal magnetic field Bi are the coordinates indicated by the vector ^S Bi representing the changed internal magnetic field. Can be tricked. Further, when the direction and magnitude of the internal magnetic field Bi has changed significantly, and the coordinates indicated by the offset c _OFF which is calculated based on the magnetic data q _i before the change, which is calculated based on the magnetic data q _i after the change The distance from the coordinates indicated by the approximate center point c _SB is large.
Therefore, the approximate center point calculation unit 140 according to the present embodiment includes the coordinates of the approximate center point c _SB calculated by the approximate center point calculation unit 140 and the offset adoption unit 131 as shown in the following equation (4.a). determines but the distance between the adopted by coordinates indicated by the offset c _OFF and is greater than a predetermined threshold .DELTA.c _OFF, as the internal magnetic field Bi is changed. Here, the offset c _OFF appearing in the equation (4.a) is a three-dimensional vector represented by the following equation (4.b).
On the other hand, when the distance between the coordinates of the approximate center point c _{SB and} the coordinates indicated by the offset c _OFF is equal to or less than the predetermined threshold value Δc _OFF , the approximate center point calculation unit 140 according to the present embodiment has the internal magnetic field Bi. Is determined not to have changed.
In the following description, the distance between the coordinates of the approximate center point c _SB calculated by the approximate center point calculation unit 140 and the coordinates indicated by the offset c _OFF adopted by the offset adoption unit 131 is equal to or less than a predetermined threshold Δc _OFF. This condition is referred to as “offset distance condition”. That is, in the present embodiment, whether or not the internal magnetic field Bi is changed is determined by determining whether or not the approximate center point c _SB and the offset c _OFF satisfy the offset distance condition.
Since M is smaller than the N, it is possible as compared with the case of determining the change in internal magnetic field Bi using the response center point c _SA, to grasp the change in internal magnetic field Bi in a short time .

As shown in FIG. 11, when it is determined that the internal magnetic field Bi has changed, the offset adopting unit 131 sets the offset c _OFF using a vector indicating the coordinates of the approximate center point c _SB calculated by the approximate center point calculating unit 140. Update (FIG. 11E). Thereby, even if the internal magnetic field Bi changes, the offset c _OFF can be updated to a value that accurately represents the coordinates indicated by the vector ^S Bi representing the internal magnetic field after the change.
Note that after the internal magnetic field Bi changes and the offset c _OFF is updated with a vector indicating the coordinates of the approximate center point c _SB , the offset adopting unit 131 operates in the same manner as in FIGS. That is, when the approximate center point calculation unit 140 newly calculates the approximate center point c _SB , the offset adopting unit 131 only when a vector indicating the coordinates of the approximate center point c _SB is employed as the offset c _OFF . The offset c _OFF is updated with a vector indicating the newly calculated approximate center point c _SB (FIG. 11F). The offset adoption unit 131
When the response center point c _SA is supplied from the server device SV, the offset c _OFF is updated with a vector indicating the coordinates of the response center point c _SA (FIG. 11 (G)).
As described above, the offset adoption unit 131 can employ the offset c _OFF that accurately and quickly reflects the change in the internal magnetic field Bi.
[4. Flow chart showing operation of geomagnetic measurement system]

  Hereinafter, the operation of the geomagnetism measurement system SYS will be described with reference to FIGS.

  FIG. 12 is a flowchart showing the operation of the terminal device 1. The processing shown in the flowchart is started when the CPU 10 executes the terminal side magnetic data processing program 70.

In step S11, the CPU 10 executes an initialization process. Specifically, the CPU 10 discards the magnetic data q stored in the RAM 20 and initializes various flags and counters. As initialization of the flag and counter, the CPU 10 sets a count value CtA representing the number of magnetic data q _i stored in the first storage area Area1 to “0”, and stores the magnetic data stored in the second storage area Area2. the count value CtB representing the number of q _B is set to "0", the flag FgA indicating whether the response center point c _SA from the server apparatus SV is supplied, the response center point c _SA not supplied is set to a value "0" representing a flag FgB indicating whether approximation center point c _SB is calculated and set to the value "0" indicating that the approximate center point c _SB has not been calculated, the offset The terminal device 1 sets the flag FgO indicating whether or not the distance condition is satisfied to “0” indicating that the condition is satisfied, and sets the flag FgC indicating the type of the offset c _OFF. That employs a vector indicating the coordinates of the approximate center point c _SB as an offset c _OFF (or, that the terminal apparatus 1 is in the state not employing any value as an offset c _OFF) to the value "0" indicating a Set.

Next, in step S13, the CPU 10 executes magnetic data acquisition processing. Specifically, the CPU 10 stores the magnetic data q _i output from the three-dimensional magnetic sensor 60 in the RAM 20.
As described above, the CPU 10 functions as the storage unit 110 by executing the initialization process in step S11 and the magnetic data acquisition process in step S13.
FIG. 13A is a flowchart illustrating details of the magnetic data acquisition process. In step S131, the CPU 10 stores the magnetic data q _i output from the three-dimensional magnetic sensor 60 in the first storage area Area1 provided in the RAM 20. Next, in step S132, the CPU 10 adds “1” to the count value CtA (counts up). In step S133, the CPU 10 determines whether or not the coordinates indicated by the magnetic data q _i satisfy the magnetic data distance condition. If the determination result is affirmative, the process proceeds to step S134. If the determination result is negative, the magnetic data acquisition process is terminated, and the process proceeds to step S15. In step S134, the CPU 10 stores the magnetic data q _i as the magnetic data q _B in the second storage area Area2. In step S135, the CPU 10 adds “1” to the count value CtB, ends the magnetic data acquisition process, and advances the process to step S15.

Next, in step S15, the CPU 10 executes a magnetic data transmission process. Specifically, when the N pieces of magnetic data q _{1 to} q _N are accumulated in the first storage area Area 1 of the RAM 20, the CPU 10 transmits them to the server device SV.
FIG. 13B is a flowchart illustrating details of the magnetic data transmission process. First, in step S151, the CPU 10 determines whether or not the number of magnetic data q _i stored in the first storage area Area1 is N or more. If the determination result is affirmative, the CPU 10 advances the process to step S152. If the determination result is negative, the CPU 10 ends the magnetic data transmission process and then advances the process to step S17. In step S152, CPU 10 has the N pieces of magnetic data _q 1 to q _N stored in the first memory area Area1, and transmits to the server apparatus SV. Thereafter, in step S153, CPU 10 is in helping with discarding the N magnetic data _q 1 to q _N stored in the first memory area Area1, and sets the count value CtA to "0" (initialization), The magnetic data transmission process is terminated, and the process proceeds to step S17.
In this example, the CPU 10 discards all the N pieces of magnetic data q1 to qN stored in the first storage area Area1 in step S153, but discards only a certain percentage of magnetic data from the oldest one. Also good.

Next, in step S17, the CPU 10 executes approximate center point calculation processing. Specifically, when M pieces of magnetic data q _{B1 to} q _BM are accumulated in the second storage area Area2 of the RAM 20, the CPU 10 calculates the coordinates of the approximate center point c _SB based on these data.
That is, the CPU 10 functions as the approximate center point calculation unit 140 by executing the approximate center point calculation process in step S17.
FIG. 13C is a flowchart illustrating the details of the approximate center point calculation process. First, in step S171, CPU 10, the number of magnetic data _{q B} stored in the second memory area Area2 is, it is determined whether the M or more. If the determination result is affirmative, the CPU 10 advances the process to step S172. If the determination result is negative, the CPU 10 ends the approximate center point calculation process and then advances the process to step S19. In step S172, CPU 10 uses the coordinates indicated by the respective magnetic data _q B1 _{to q BM} stored in the second memory area Area2, the simultaneous linear equation shown in the above Expression (3.a), approximation The coordinates of the center point c _SB are calculated. Next, in step S173, the CPU 10 discards the M pieces of magnetic data q _{B1 to} q _BM stored in the second storage area Area2, and sets (initializes) the count value CtB to “0”. Further, the flag FgB is set to “1”. In step S174, the CPU 10 determines whether or not the coordinates indicated by the approximate center point c _SB calculated in step S172 and the coordinates indicated by the offset c _OFF satisfy the offset distance condition. If the determination result is negative, the CPU 10 advances the process to step S175. If the determination result is positive, the CPU 10 ends the approximate center point calculation process and advances the process to step S19. In step S175, the CPU 10 sets the flag FgO to “1” which is a value indicating that the offset distance condition is not satisfied, ends the approximate center point calculation process, and advances the process to step S19.
In addition, you may implement the process shown to step S173 after the process shown to step S174 and step S175.

Next, in step S19, the CPU 10 executes response center point reception determination processing. Specifically, when the response information RES is supplied from the server device SV, the CPU 10 stores the response information RES in the RAM 20.
Thus, the CPU 10 functions as the terminal-side transmitting / receiving unit 120 by executing the magnetic data transmission process in step S15 and the response center point reception determination process in step S19.
FIG. 13D is a flowchart illustrating details of the response center point reception determination process.
First, in step S191, the CPU 10 determines whether or not the response information RES is supplied from the server device SV. If the determination result is affirmative, the process proceeds to step S192, whereas if the determination result is negative. The response center point reception determination process is terminated, and the process proceeds to step S21. In step S192, the coordinates of the response center point c _SA included in the response information RES and the coordinates indicated by the offset c _OFF are the conditions shown in the following equation (5.a) (hereinafter, “response center point validity condition” It is determined whether or not the above is satisfied. The coordinate of the response center point _{c SA} is represented by the following formula (5.b). If the determination result is affirmative, the CPU 10 advances the process to step S193. If the determination result is negative, the CPU 10 ends the response center point reception determination process and advances the process to step S21.
When the internal magnetic field Bi changes, the coordinates of the response center point c _SA calculated based on the magnetic data q _{1 to} q _N accumulated in the first storage area Area 1 after the internal magnetic field Bi changes (or changes) Is highly likely to be a coordinate separated from the coordinate indicated by the vector ^S Bi representing the internal magnetic field after the change. In addition, when the terminal device 1 transmits the magnetic data q _{1 to} q _N to the server device SV and before the server device SV generates the response center point c _SA , a change occurs in the internal magnetic field Bi. The coordinates indicated by the response center point c _SA are likely to be separated from the coordinates indicated by the vector ^S Bi representing the internal magnetic field after the change. Therefore, in the present embodiment, the response center point c _SA that does not accurately represent the internal magnetic field Bi after the change is used by determining whether or not the response center point c _SA satisfies the response center point validity condition. This prevents the offset c _OFF from being updated.
Next, in step S193, the CPU 10 sets the flag FgA to “1”. Here, the flag FgA being “1” means that the response center point c _SA is supplied from the server device SV and it is appropriate to update the offset c _OFF using the response center point c _SA. Represents. Thereafter, the CPU 10 ends the response center point reception determination process, and advances the process to step S21.
In the present embodiment, in step S192, it is determined whether or not the response center point c _SA satisfies the response center point validity condition. If the determination result in step S191 is affirmative, the process proceeds to step S193. It may be advanced. Even if the offset c _OFF is updated by the response center point c _{SA that} does not accurately represent the changed internal magnetic field Bi, the offset c _OFF subsequently changes the internal magnetic field Bi by the approximate center point c _SB. This is because the value is updated to the represented value.

Next, in step S21, the CPU 10 executes an offset adoption process. Specifically, when the values of the various flags satisfy a predetermined condition, the CPU 10 is a vector indicating the coordinates of the approximate center point c _SB calculated in the approximate center point calculation process in step S17, or the response in step S19. updating the offset value c _OFF by a vector indicating the coordinates of a response center point c _SA included in response information RES supplied from the server apparatus SV at the center point reception determination processing. Then, CPU 10, when employing a vector representing the coordinates of the response center point _{c SA} as an offset _{c OFF,} while employing the response correction matrix _{T A} as ellipsoid correction matrix _{T E,} representing the coordinates of the approximate center point _{c SB} when employing the vector as an offset c _OFF, employing a unit matrix I of three rows and three columns as an ellipsoid correction matrix T _E. Meanwhile, CPU 10, when the value of the flags does not satisfy a predetermined condition does not update the offset _{c OFF} and ellipsoidal correction matrix _{T E.} Although details will be described later, when the values of various flags satisfy a predetermined condition, the value of the flag FgA is “0” and the value of the flag FgB is when the value of the flag FgA is “1”. Is “1” and the value of the flag FgO is “1”, or the value of the flag FgA is “0”, the value of the flag FgB is “1”, and the value of the flag FgC is “0”. ] (Refer to FIG. 14).
As described above, the CPU 10 functions as the offset adoption unit 131 by executing the offset adoption processing in step S21.

FIG. 14 is a flowchart illustrating details of the offset adoption processing.
In step S211, the CPU 10 determines whether or not the flag FgA indicates “1”. If the determination result is affirmative, the process proceeds to step S212, and if the determination result is negative, the process proceeds to step S221. In step S212, CPU 10 has a vector indicating the coordinates of the response center point _{c SA} received in response center point reception determination processing (step S19), and updates the offset _{c OFF.} Further, CPU 10 employs the response correction matrix _{T A} as ellipsoid correction matrix _{T E.} In step S213, the CPU 10 determines whether or not the flag FgB is “1”. If the determination result is affirmative, the process proceeds to step S214, and if the determination result is negative, the process proceeds to step S215. In step S214, the CPU 10 sets the count values CtA and CtB and the flags FgA and FgB to “0”. Also, CPU 10 sets the flag FgC indicating the type of offset _{c OFF,} the value "1" indicating that employs a vector indicating the coordinates of the response center point _{c SA} as an offset _{c OFF.} And CPU10 advances a process to step S23, after complete | finishing an offset adoption process. In step S215, the CPU 10 sets the count value CtA and the flag FgA to “0”, and sets the flag FgC to “1”. And CPU10 advances a process to step S23, after complete | finishing an offset adoption process.
In this way, the CPU 10 is supplied with the response center point c _SA from the server device SV and it is appropriate to update the offset c _OFF using the response center point c _SA (the value of the flag FgA is “ the case 1 "), the vector indicating the coordinates of the response center point _{c SA,} updates the offset _{c OFF.}
On the other hand, in step S221, the CPU 10 determines whether or not the flag FgB indicates “1”. If the determination result is affirmative, the process proceeds to step S222, and if the determination result is negative, the offset adoption process is performed. After the end, the process proceeds to step S23. In step S222, the CPU 10 determines whether or not the flag FgO is “1”. If the determination result is affirmative, the process proceeds to step S223, and if the determination result is negative, the process proceeds to step S225. In step S223, the CPU 10 updates the offset c _OFF with a vector indicating the coordinates of the approximate center point c _SB calculated in the approximate center point calculation process (step S17). Further, CPU 10 employs the identity matrix I as ellipsoid correction matrix _{T E.} In step S224, the CPU 10 sets the flag FgC to a value “0” indicating that the vector indicating the coordinates of the approximate center point c _SB is adopted as the offset c _OFF . Further, the CPU 10 sets the count value CtB, the flags FgB, and FgO to “0”. And CPU10 advances a process to step S23, after complete | finishing an offset adoption process. In step S225, the CPU 10 determines whether or not the flag FgC is “1”. If the determination result is affirmative, the process proceeds to step S226, and if the determination result is negative, the process proceeds to step S227. In step S227, the CPU 10 updates the offset c _OFF with a vector indicating the coordinates of the approximate center point c _SB calculated in the approximate center point calculation process (step S17). Further, CPU 10 employs the identity matrix I as ellipsoid correction matrix _{T E.} In steps S226 and S228, the CPU 10 sets the count value CtB and the flag FgB to “0”, ends the offset adoption processing, and then advances the processing to step S23. In the present embodiment, the CPU 10 determines whether or not the flag FgC is “1” (step S225) after determining whether or not the flag FgO is “1” (step S222). However, the present invention is not limited to such an aspect. When the flag FgO is “1” or the flag FgC is “0”, the offset c _OFF is set based on the approximate center point c _SB. It only needs to be updated.
As described above, when the terminal device 1 adopts the vector indicating the coordinates of the approximate center point c _SB as the offset c _OFF or when the terminal device 1 does not adopt the offset c _OFF (the value of the flag FgC is “0”). ”), Or when the approximate center point c _SB and the offset c _OFF do not satisfy the offset distance condition (the value of the flag FgO is“ 1 ”), the CPU 10 performs the approximation calculated in the approximate center point calculation process of step S17. Based on the center point c _SB , the offset c _OFF is updated.

Next, in step S23, the CPU 10 executes a geomagnetism calculation process. Specifically, CPU 10 performs the elliptic correction using the ellipsoid correction matrix _{T E} and the offset _{c OFF,} to calculate the direction of the geomagnetism ^S Bg. That, CPU 10, from the coordinates indicated by the magnetic data _{q i} output from a 3D magnetic sensor 60, a vector obtained by subtracting the coordinates indicated by the offset _{c OFF,} the ellipsoidal correction matrix _{T E,} of geomagnetism ^S Bg Calculate the orientation.
That is, the CPU 10 functions as the geomagnetism vector calculation unit 132 by executing the geomagnetism calculation process in step S23.

  In step S25, the CPU 10 executes an end condition determination process. Specifically, the CPU 10 determines whether or not a condition (end condition) for ending the terminal-side magnetic data processing program 70 is satisfied. The termination condition may be appropriately determined based on the specifications of the terminal device 1 and the like. For example, the termination condition may be that the terminal device 1 is turned off. When the end condition is satisfied, the CPU 10 ends the process represented by the flowchart shown in FIG. On the other hand, when the end condition is not satisfied, the CPU 10 advances the process to step S13.

FIG. 15 is a flowchart showing the operation of the server apparatus SV. The process shown in the flowchart is started when the CPU 910 receives a plurality of magnetic data q _{1 to} q _N from the terminal device 1 while the server-side magnetic data processing program 960 is being executed.

In step S31, the CPU 910 executes magnetic data storage processing. Specifically, CPU 910 is of N magnetic data _q 1 to q _N by the communication unit 940 has received and stored in the third memory area Area3.

In step S33, the CPU 910 executes initial ellipsoid generation processing. Specifically, the CPU 910 calls the N pieces of magnetic data q _{1 to} q _N (hereinafter referred to as “N pieces of magnetic data q _{1 to} q _N ” in this section) stored in the third storage area Area 3 by the CPU 910 in step S31. ) on the basis, it determines whether it is possible to calculate the coordinates and the initial ellipsoid correction matrix T ₀ of the initial center point c _E0. If the determination result is affirmative, CPU 910 is, after calculating the coordinate and the initial ellipsoid correction matrix _{T 0} of the initial center point _{c E0,} the process proceeds to step S35.
On the other hand, if the determination result is negative, the CPU 910 advances the process to step S41.
That is, the CPU 910 functions as the ellipsoid initial correction value generation unit 300 by executing the initial ellipsoid generation process in step S33.

In step S35, the CPU 910 executes an optimal ellipsoid generation process. Specifically, CPU 910, based on the initial ellipsoid generation processing initial center point c _E0 and the initial ellipsoid correction matrix T ₀ calculated in step S33, coordinates and ideal ellipsoid correction of the optimum center point c _EOP A matrix _TOP is calculated.
That is, the CPU 910 functions as the elliptical surface optimal correction value generation unit 400 by executing the optimal elliptical surface generation processing in step S35.

In step S37, the CPU 910 executes response information generation processing. Specifically, CPU 910 is calculated in the optimum elliptical surface generation processing in step S35, based on the coordinates of the optimum center point _{c EOP} and the optimum ellipsoidal correction matrix _{T OP,} coordinates and response of the response center point _{c SA} It generates response information RES to the correction matrix T _a and element. Incidentally, CPU 910 is in generating response information RES, while adopting an optimum center point _{c EOP} response center point _{c SA,} employing the optimum ellipsoidal correction matrix _{T OP} in response correction matrix _{T A.}

In step S39, the CPU 910 executes response information transmission processing. Specifically, the CPU 910 transmits the response information RES generated in the response information generation process in step S <b> 37 to the terminal device 1.
That is, the CPU 910 functions as the server-side transmission / reception unit 720 by executing the magnetic data storage process in step S31 and the response information transmission process in step S39.

In step S41, the CPU 910 executes a data initialization process. Specifically, CPU 910 discards and N magnetic data _q 1 to q _N, and information generated based on the N magnetic data _q 1 to q _N such response information RES. Then, the CPU 910 ends the process shown in the flowchart.
That is, the CPU 910 functions as the data control unit 710 by executing the response information generation process in step S37 and the data initialization process in step S41.

  As described above, in the terminal device 1 and the server device SV, the CPU 10 of the terminal device 1 executes the process shown in the flowchart of FIG. 12, and the CPU 910 of the server device SV executes the process shown in the flowchart of FIG. It functions as a geomagnetic measurement system SYS.

  Details of the ellipsoid initial correction value generation unit 300 and the ellipsoid optimal correction value generation unit 400 will be described below.

[5. Generation of initial ellipsoid]
FIG. 16 is a functional block diagram illustrating a functional configuration of the ellipsoid initial correction value generation unit 300.
Based on the plurality of magnetic data q _{1 to} q _N , the ellipsoid initial correction value generation unit 300 firstly includes a first ellipse V _xx and a second ellipse having the coordinates indicated by the plurality of magnetic data q _{1 to} q _N nearby. After generating the surface V _yy and the third elliptical surface V _zz , an initial elliptical surface V _E0 is generated based on these three elliptical surfaces. Hereinafter, a method for generating the initial ellipsoid V _E0 in the present embodiment will be specifically described.

The ellipsoid initial correction value generation unit 300 includes a coefficient matrix (D _xx , D _yy , D _zz ) and a center point of each of the first ellipse V _xx , the second ellipse V _yy , and the third ellipse V _zz. c _xx , c _yy , c _zz ) coordinates of the initial ellipsoid generation unit 310, the first ellipsoid V _xx , the second ellipse V _yy , and the third ellipse V _zz coefficient matrix and center point Based on the initial ellipsoid correction matrix T ₀ and the initial center point c _E0 to determine whether it is appropriate to calculate the initial ellipsoid determination unit 320, and the first ellipsoid V _xx , second An initial correction value generation unit 330 that calculates the coordinates of the initial ellipsoid correction matrix T ₀ and the initial center point c _E0 based on the coefficient matrix and the coordinates of the center point of each of the ellipsoid V _yy and the third ellipse V _zz. Is provided.

Initial ellipsoid generating unit 310, based on a plurality of magnetic data _q 1 to q _N stored in the data control unit 710, a first ellipsoidal coefficient matrix _{D xx} representing the shape of the first ellipsoid _{V xx,} the first ellipsoid generating unit 311 calculates the coordinates of the center point _{c xx} of 1 ellipsoidal _{V xx,} based on a plurality of magnetic data _q 1 to q _N, second ellipse representing the shape of the second ellipsoid _{V yy} Based on the second ellipsoid generating unit 312 that calculates the surface coefficient matrix D _yy and the coordinates of the center point c _yy of the second ellipsoid V _Vy , and the third ellipse based on the plurality of magnetic data q _{1 to} q _N and a third ellipsoid coefficient matrix _{D zz} representing a shape of the surface _{V zz,} third ellipsoid generating unit 313 for calculating the coordinates of the center point _{c zz} third ellipsoid _{V zz,} the.
In the following, a first ellipsoidal coefficient matrix _{D xx,} a second elliptical surface coefficient matrix _{D yy,} and a third elliptical surface coefficient matrix _{D zz,} the center point _{c xx} coordinates, the coordinates of the center point _{c yy,} and the center point c _A method for calculating the coordinates of _zz will be described.

When the variable representing the coordinates indicated by the magnetic data q output from the three-dimensional magnetic sensor 60 is expressed by equation (1.c), the equation of the ellipsoid having the magnetic data q on the surface (elliptic surface equation) is (6) Note that since Equation (6) represents an ellipsoidal surface, the coefficients θ _xx , θ _yy , and θ _zz that appear in Equation (6) are all positive values.

The ellipsoidal equation shown in the equation (6) is transformed into the following equation (7).

When all of the coordinates indicated by the plurality of magnetic data q _{1 to} q _N are located on the ellipsoid represented by Expression (6), the following Expression (8) is established.
However, the vector θ _XX is a nine-dimensional vector in which the nine coefficients of Expression (7) are arranged as shown in Expression (9). In addition, as shown in Expression (10), the matrix R _xx is the coordinates indicated by the plurality of magnetic data q _{1 to} q _N shown in Expression (11) with respect to the nine-dimensional vector Q _xx shown in Expression (13). Is a matrix of N rows and 9 columns arranged in each row after transposing N vectors obtained by substituting each of. The vector W _xx is an N-dimensional vector having a value obtained by multiplying the square value of the x component by minus among the coordinates indicated by the plurality of magnetic data q _{1 to} q _N , as shown in the equation (12). Is a vector.

Equation (8) is a simultaneous linear equation with each element of the vector θ _XX as a variable. Therefore, by solving the equation (8) with respect to the vector θ _XX , the coefficient of the equation (7) is determined, and the ellipsoidal equation having the coordinates indicated by the plurality of magnetic data q _{1 to} q _N on the surface can be specified.
However, considering a measurement error of the 3D magnetic sensor 60, all of each of the coordinate indicated by the plurality of magnetic data q ₁ to q _N is present in a position that exactly matches the elliptic plane shown in Equation (7) Never do. Therefore, Equation (8) has no solution, and the vector θ _XX cannot be calculated as the solution of Equation (8). Therefore, in the present embodiment, a plausible vector θ _XX is calculated as a solution of Expression (8) by using a statistical method.
For example, eight terms (xy, xz, y ² , yz, z ² , x, y, and z) appearing on the right side of Equation (7) are regarded as independent variables and appear on the left side of Equation (7). the x ² after having regarded as the dependent variable, by using the least square method to derive the normal equation shown in equation (14), as a solution, obtaining the vector theta _XX. A vector θ _XX expressed as a solution of this normal equation can be expressed by Expression (15) when the matrix (R _xx ^T R _xx ) is regular. An ellipsoid represented by applying the vector θ _XX calculated by the equation (15) to the equation (7) as a coefficient is referred to as a first ellipsoid V _xx .

Here, as shown in FIG. 17A, an eight-dimensional space π _xx having eight axes representing each of xy, xz, y ² , yz, z ² , x, y, and z as variables, and , X ² , and a first evaluation axis ξ ₁ representing the value as a variable, each of a plurality of magnetic data q _{1 to} q _N is plotted on a nine-dimensional space Ω. At this time, the first ellipsoid V _xx minimizes the error in the first evaluation axis ξ ₁ direction between the first ellipse V _xx and the coordinates indicated by the plurality of magnetic data q _{1 to} q _N on the space Ω. It is calculated | required as a solid (8-dimensional plane on space Ω). That is, the first ellipsoidal _{V xx} is a plurality of magnetic data _q 1 to q _N, the elements of a plurality of 8-dimensional vector _q πxx1 ~q πxxN obtained by plotting the spatial [pi _xx formula (7) minimize the error between the value _q xx1 _{to q xxn} obtained by substituting the right hand side, a square value _x ¹ 2 _~x ^{N 2} in the x-axis component of the coordinates indicated by the plurality of magnetic data _q 1 to q _N of It is determined as a three-dimensional solid.

The equation of the first ellipsoidal surface _Vxx shown in Equation (7) is transformed into Equation (16) using the first ellipsoidal coefficient matrix _Dxx shown in Equation (17). At this time, the coordinates of the center point c _xx of the first ellipsoid V _xx are expressed by Expression (18). As described above, the first ellipsoid generating unit 311 calculates the first ellipsoid coefficient matrix D _xx and the center point c _xx of the first ellipsoid V _xx and outputs them. Note that a necessary condition for the expression (16) to represent an ellipsoid is that the first ellipsoid coefficient matrix _Dxx is a positive definite value.

Next, the ellipsoidal equation shown in the equation (6) is transformed into the following equation (19).

The equation shown in Equation (19) is transformed into Equation (20), which is a simultaneous linear equation with each element of the vector θ _YY as a variable. Similar to equation (8), since vector θ _YY cannot be calculated as the solution of equation (20), vector θ _YY is calculated as a plausible value as the solution of equation (20). Specifically, in the normal equation shown in Expression (24), when the matrix (R _yy ^T R _yy ) is regular, the vector θ _YY is calculated by Expression (25). An ellipsoid represented by applying the vector θ _YY specified by the equation (25) to the equation (19) as a coefficient is referred to as a second ellipsoid V _yy . The vector θ _YY is a 9-dimensional vector shown in Expression (21), the matrix R _yy is an N-row 9-column matrix shown in Expression (22), and the vector W _yy is expressed in Expression (23). This is an N-dimensional vector.

Here, as shown in FIG. 17B, an eight-dimensional space π _yy having eight axes representing each of x ² , xy, xz, yz, z ² , x, y, and z as variables, and , Y ^{2 and} a second evaluation axis ξ ₂ representing the values as variables, and plotting each of a plurality of magnetic data q _{1 to} q _N on a nine-dimensional space Ω. At this time, the second ellipsoid V _yy minimizes the error in the second evaluation axis ξ ₂ direction between the second ellipse V _yy and the coordinates indicated by the plurality of magnetic data q _{1 to} q _N on the space Ω. It is calculated | required as a solid (8-dimensional plane on space Ω). That is, the second ellipsoidal _{V yy,} a plurality of magnetic data _q 1 to q _N, the elements of a plurality of 8-dimensional vector _q πyy1 ~q πyyN obtained by plotting the spatial [pi _yy formula (19) The _error between the values q _yy1 to q _yyN obtained by substituting for the right side of y and the square values y ₁ ^{2 to} y _N ² of the y-axis component among the coordinates indicated by the plurality of magnetic data q _{1 to} q _N is minimized. It is determined as a three-dimensional solid.

The equation of the second ellipsoidal surface V _yy shown in Equation (19) is transformed into Equation (26) using the second ellipsoidal coefficient matrix D _yy shown in Equation (27). At this time, the coordinates of the center point c _yy of the second ellipsoidal surface V _yy are expressed by Expression (28). As described above, the second ellipsoid generating unit 312 calculates the second ellipsoid coefficient matrix D _yy and the center point c _yy of the second ellipsoid V _yy and outputs them. Note that a necessary condition for the expression (26) to represent an ellipsoid is that the second ellipsoid coefficient matrix D _yy is a positive definite value.

Next, the ellipsoidal equation shown in the equation (6) is transformed into the following equation (29).

The equation shown in Equation (29) is transformed into Equation (30), which is a simultaneous linear equation with each element of the vector θ _ZZ as a variable. Similar to equation (8), since vector θ _ZZ cannot be calculated as the solution of equation (29), vector θ _ZZ is calculated as a plausible value as the solution of equation (29). Specifically, in the normal equation shown in Expression (34), when the matrix (R _zz ^T R _zz ) is regular, the vector θ _ZZ is calculated by Expression (35). The ellipsoid represented by applying the identified vector theta _ZZ by equation (35) into equation (29) as a factor, it referred to as a third ellipsoid V _zz. The vector θ _ZZ is a 9-dimensional vector shown in Expression (31), the matrix R _zz is an N-row 9-column matrix shown in Expression (32), and the vector W _zz is expressed in Expression (33). This is an N-dimensional vector.

Here, as shown in FIG. 17C, an eight-dimensional space π _zz having eight axes representing each of x ² , xy, xz, y ² , yz, x, y, and z as variables, and , Z ² , and a third evaluation axis ξ ₃ that represents the value as a variable, each of a plurality of magnetic data q _{1 to} q _N is plotted on a nine-dimensional space Ω. At this time, the third ellipsoid V _zz minimizes the error in the third evaluation axis ξ ₃ direction between the third ellipse V _zz and the coordinates indicated by the plurality of magnetic data q _{1 to} q _N on the space Ω. It is calculated | required as a solid (8-dimensional plane on space Ω). That is, the third ellipsoid _{V zz} is a plurality of magnetic data _q 1 to q _N, the elements of a plurality of 8-dimensional vector _q πzz1 ~q πzzN obtained by plotting the spatial [pi _zz formula (29) The _error between the values q _zz1 to q _zzN obtained by substituting for the right side and the square values z ₁ ^{2 to} z _N ² of the z-axis component among the coordinates indicated by the plurality of magnetic data q _{1 to} q _N is minimized. It is determined as a three-dimensional solid.

The equation of the third ellipsoidal surface _Vzz shown in Equation (29) is transformed into Equation (36) using the third ellipsoidal coefficient matrix _Dzz shown in Equation (37). At this time, the coordinates of the center point c _zz of the third ellipsoid V _zz are expressed by Expression (38). Third ellipsoid generating unit 313, as shown above, to calculate a third ellipsoid coefficient matrix _{D zz} and the center point _{c zz} third ellipsoid _{V zz,} and outputs these. Note that a necessary condition for the expression (36) to represent an ellipsoid is that the third ellipsoid coefficient matrix _Dzz is a positive definite value.

Thus, the initial ellipsoid generating unit 310, a first ellipsoidal coefficient matrix _{D xx,} second ellipsoidal coefficient matrix _{D yy,} third ellipsoid coefficient matrix _{D zz,} the coordinates of the center point _{c xx,} center point _{c yy} And the coordinates of the center point _czz are calculated.

As shown in FIG. 16, the initial ellipsoid determining unit 320 includes an initial ellipsoid coefficient matrix determining unit 321 and an initial ellipsoid center point determining unit 322. Here, a condition that all of the first ellipsoidal coefficient matrix _Dxx , the second ellipsoidal coefficient matrix _Dyy , and the third ellipsoidal coefficient matrix _Dzz are positive definite values is referred to as a first condition. Further, as shown in Expression (39), the distance between the coordinates of the center point c _{xx and} the coordinates of the center point c _yy is equal to or less than the first threshold value Δc, and as shown in Expression (40), the distance between the center point c _yy The distance between the coordinates and the coordinates of the center point c _zz is equal to or smaller than the first threshold value Δc, and the distance between the coordinates of the center point c _{zz and} the coordinates of the center point c _xx is the first threshold value as shown in Expression (41). The condition that it is Δc or less is referred to as a second condition.
At this time, the initial ellipsoidal coefficient matrix determination unit 321 determines whether the first ellipsoidal coefficient matrix _Dxx , the second ellipsoidal coefficient matrix _Dyy , and the third ellipsoidal coefficient matrix _Dzz satisfy the first condition. Determine whether. The initial ellipsoidal central point determining unit 322 determines the coordinates of the center point c _xx, coordinates of the center point c _yy, and coordinates of the center point c _zz is whether to satisfy the second condition.

When the determination result in the initial ellipsoid coefficient matrix determination unit 321 is affirmative and the determination result in the initial ellipsoid center point determination unit 322 is affirmative, the initial correction value generation unit 330 of the initial ellipse surface generation unit 310 based on the calculation result, it calculates the coordinates and initial ellipsoidal correction matrix T ₀ of the initial center point c _E0.
Here, the initial ellipsoidal correction matrix T _0, as shown in FIG. 18, the coordinates on the initial ellipsoid V _E0 centered point the initial center point c _E0, the center point of the initial center point c _E0 This is a matrix for conversion to coordinates on the spherical surface S _E0 . The initial ellipsoid V _E0 is an ellipsoid determined based on at least one ellipsoid among the first ellipsoid V _xx , the second ellipse V _yy , and the third ellipse V _zz. It is an ellipsoid having the coordinates indicated by the data q _{1 to} q _{N in} the vicinity.
The initial correction value generation unit 330 determines the initial ellipse when the determination result by the initial ellipsoidal coefficient matrix determination unit 321 is negative or when the determination result by the initial ellipsoid center point determination unit 322 is negative. It is determined that the plane V _E0 cannot be calculated. In this case, the initial correction value generation unit 330 does not calculate the coordinates and the initial ellipsoidal correction matrix T ₀ of the initial center point c _E0.

Hereinafter, in describing the specific method for calculating the initial ellipsoidal correction matrix T _0, first, when the shape of an ellipsoid V _E is assumed to be known, the method for calculating the ellipsoidal correction matrix T _E described (See paragraph 0039 and FIG. 8). Ellipsoid correction matrix T _E is the coordinates on the ellipsoid V _E, a matrix for converting the coordinates on the sphere S _E of radius 1 centered on the center point c _OG of ellipsoidal V _E, ellipsoidal V _E and ellipsoid coefficient matrix D representing the shape of, is calculated based on the center point c _OG of the ellipsoidal V _E.

Ellipsoidal equation representing the ellipsoidal V _E shown in Formula (6), using the ellipsoid coefficient matrix D shown in the following equation (43) can be transformed into the following equation (42). The center point _c coordinates indicated by _OG ellipsoid _{V E} is expressed by the following equation (44).

Here, when P is a natural number of 2 or more, the relationship of Expression (45) is established between the positive definite symmetric matrix G of P rows and P columns and the positive definite symmetric matrix H of P rows and P columns. The matrix G is called a square root matrix of the matrix H. In the following, the square root matrix G of the matrix H is expressed as a half power of the matrix as shown in Expression (46).

At this time, the square root matrix G of the matrix H is obtained by Expression (47). However, the matrix U and the matrix Λ are matrices calculated by diagonalizing the matrix H as shown in the equation (48). Specifically, the matrix Λ is a matrix of P rows and P columns having P positive eigenvalues λ _{H1 to} λ _HP of the matrix H as diagonal components, as shown in Expression (49). , A rotation matrix of P rows and P columns in which eigenvectors corresponding to the eigenvalues λ _{H1 to} λ _HP of the matrix H are normalized and arranged in each column.

And ellipsoid coefficient matrix D, the relationship between the ellipsoid correction matrix T _E, using the square root matrix as defined above, is expressed by the following equation (50). Note that the value r (D) includes a plurality of coordinates obtained by converting the coordinates indicated by the plurality of magnetic data q _{1 to} q _{N using} the square root matrix of the ellipsoidal coefficient matrix D, and the center as shown in the following formula (51): It is a value representing the average value of the distance from the point c _OG .

Each of the eigenvalues lambda _D1, lambda _D2, and lambda _D3 ellipsoid coefficient matrix D, the length of the major axis of the ellipsoidal _{V E r E1, r E2,} and equal to the inverse of the squared value of each of the _{r E3.} Accordingly, each eigenvalue lambda _T1, lambda _T2, and lambda _T3 ellipsoidal correction matrix _{T E,} the length of the major axis of the ellipsoidal _{V E r E1, r E2,} and equal to each of the inverse of _{r E3.} Therefore, the ellipsoidal correction matrix T _E, the coordinates on the ellipsoid V _E, can be converted into coordinates on a spherical surface S _E of radius 1.

Next, a method for calculating the coordinates of the initial ellipsoid correction matrix T ₀ and the initial center point c _E0 will be described.
The initial ellipsoid correction matrix T ₀ is calculated based on at least one of the first ellipsoid coefficient matrix D _xx , the second ellipsoid coefficient matrix D _yy , and the third ellipsoid coefficient matrix D _zz . The coordinates of the initial center point _{c E0} is the center point _{c xx,} center point _{c yy,} and out of the center point _{c zz,} are calculated based on at least one.
When the second condition described above is satisfied, the distance between any two of the center point c _xx , the center point c _yy , and the center point c _zz is closer than the first threshold value Δc. Therefore, when the value of the first threshold Δc is sufficiently small, each of the first ellipsoid V _xx , the second ellipse V _yy , and the third ellipse V _zz is a plurality of magnetic data q _{1 to} q _N. These three ellipsoids are considered to be substantially the same ellipsoid (although strictly having different shapes) because the coordinates shown are in the vicinity and any center point can be regarded as the same coordinates. Can be tricked. In this case, the initial ellipsoid _{V E0,} first ellipsoidal _{V xx,} second ellipsoidal _{V yy,} and all the may be adopted in the third ellipsoid _{V zz.}
In the present embodiment, the first ellipsoid V _xx is employed as the initial ellipsoid V _E0 . At this time, the coordinates of the initial ellipsoid correction matrix T ₀ and the initial center point c _E0 are expressed by the following equations (52) and (53).
As described above, the initial correction value generation unit 330 calculates the initial ellipsoid correction matrix T ₀ and the coordinates of the initial center point c _E0 .

In the present embodiment, the first ellipsoid V _xx is adopted as the initial ellipsoid V _E0 , but the present invention is not limited to such a form. For example, the second ellipsoidal surface V _yy may be adopted as the initial ellipsoidal surface V _E0 . At this time, the initial ellipsoid correction matrix T ₀ is expressed by the equation (54), and the center point c _yy is adopted as the initial center point c _E0 . It is also possible to employ a third ellipsoid _{V zz} as an initial ellipsoidal _{V E0.} In this case, the initial ellipsoid correction matrix T ₀ is expressed by the equation (55), and the center point c _zz is adopted as the initial center point c _E0 .

The initial ellipsoid correction matrix T ₀ may be calculated by the following equation (56). In this case, the coordinates of the initial center point _cE0 may be calculated by the following formula (57) or formula (58).

By the way, as a method for calculating the initial ellipsoid correction matrix T ₀ , there is a method described below (hereinafter referred to as “comparative”) (see “Non-patent Document 2”).
Specifically, first, the ellipsoidal equation shown in the equation (6) is divided by any one of the terms x ² , y ² , or z ² , and The equivalent linear equation shown in the following formula (59) is transformed. Next, the normal equation shown in the following formula (60) is calculated from the formula (59) using the least square method. When the matrix (R ^T R) is regular, the vector θ indicating the shape of the ellipsoid is calculated by the following equation (61) as a solution of the normal equation represented by the equation (60). The initial ellipsoid correction matrix T ₀ and the initial center point c _E0 are calculated using the vector θ calculated by the expression (61) and the expressions (43), (44), and (50).
Note that, for example, when the simultaneous linear equation shown in the equation (59) is calculated by dividing the elliptical equation shown in the equation (6) by the term of z ² , the vector θ is expressed by the following equation (62): The matrix R is obtained by substituting the coordinates indicated by the plurality of magnetic data q _{1 to} q _N shown in the equation (11) into the 9-dimensional vector Q shown in the following equation (63). The obtained vector is transposed and arranged in each row to generate a matrix of N rows and 9 columns shown in the following formula (64), and the vector W is a 9-dimensional vector shown in the following formula (65).

In contrast, the shape of the ellipsoid is determined by a simultaneous linear equation generated by dividing the ellipsoidal equation by one of the terms x ² , y ² , or z ^2. To do. That is, the proportionality is equivalent to calculating one ellipsoid using only one evaluation axis among the first evaluation axis ξ ₁ , the second evaluation axis ξ ₂ , and the third evaluation axis ξ ₃ .
In this case, even if the distribution shape of the coordinates indicated by the plurality of magnetic data q _{1 to} q _N is the same, if the selected evaluation axis is different, the calculated shape of the ellipsoid is different. However, since the contrast is calculated only for one ellipsoid, if two or more ellipsoids are calculated using two or more evaluation axes, the difference between the shapes of a plurality of ellipsoids that can be grasped is calculated. I ca n’t figure out. For example, the determination using the second condition on the assumption that two or more ellipsoidal surfaces are calculated cannot be performed.
Accordingly, as in the example illustrated in FIG. 19, at least two ellipsoids among the first ellipsoid V _xx , the second ellipse V _yy , and the third ellipse V _zz are calculated by the method according to the present embodiment. If so, even if the determination result for the second condition is negative, the initial ellipsoid correction matrix T ₀ is calculated according to the proportionality.
Thus, comparative example, even if it is difficult to identify the shape of the ellipsoid from the shape of the distribution of the coordinate indicated by the plurality of magnetic data q ₁ to q _N, a plurality of magnetic data q ₁ to q An initial ellipsoid correction matrix T ₀ based on an inappropriate initial ellipse V _E0 that does not accurately represent the distribution shape of the coordinates indicated by _N is generated.

On the other hand, the elliptical surface initial correction value generation unit 300 generates the first elliptical surface V _xx , the second elliptical surface V _yy , and the third elliptical surface in generating the initial elliptical surface correction matrix T ₀ and the initial center point c _E0 . Three ellipsoids of ellipsoid _Vzz are generated. The first ellipsoid V _xx is an ellipsoid that minimizes an error from the coordinates indicated by the plurality of magnetic data q _{1 to} q _N with reference to the first evaluation axis ξ ₁ on the space Ω. _yy is an ellipsoid that minimizes an error from the coordinates indicated by the plurality of magnetic data q _{1 to} q _N with respect to the second evaluation axis ξ ₂ on the space Ω, and the third ellipsoid V _zz is a space Ω. This is an ellipsoid that minimizes an error from the coordinates indicated by the plurality of magnetic data q _{1 to} q _N with reference to the third evaluation axis ξ ₃ above. That is, the ellipsoid initial correction value generation unit 300 generates three different ellipsoids using three different evaluation axes on the space Ω.
Furthermore, the ellipsoid initial correction value generation unit 300 determines that the three calculated ellipsoids have shapes close to each other using the first condition and the second condition. That is, the shape of the distribution of coordinates indicated by the plurality of magnetic data q _{1 to} q _N is significantly different from the shape of the ellipsoid, and the first ellipse V _xx , the second ellipse V _yy , and the third ellipse When one or more of _Vzz has a shape different from the ellipsoid, the first condition is not satisfied. Further, as in the example illustrated in FIG. 19, the second condition is not satisfied when the calculated distances between the center points of the three ellipsoidal surfaces are separated.
Thus, the ellipsoid initial correction value generation unit 300 generates three different ellipsoids when generating the initial ellipsoid correction matrix T ₀ , and the first condition and the second condition are satisfied. to determine whether it has, from the shape of the distribution of the coordinate indicated by the plurality of magnetic data q ₁ to q _N, in case where it is difficult to identify the shape of an ellipsoid, a plurality of magnetic data q ₁ to q _N The generation of an inappropriate initial ellipsoid correction matrix T ₀ based on an inaccurate initial ellipsoid V _E0 that is different from the shape of the coordinate distribution indicated by is prevented.

[6. Generation of optimal ellipsoid]
As shown in the equation (66), the initial ellipsoid correction matrix T ₀ is a vector (q _i −c _EO ) starting from the initial center point c _{E0 and} having the coordinates indicated by the magnetic data q _i as the end point. This is a matrix that is converted into a vector (s _0i −c _EO ) with the coordinates indicated by the converted magnetic data s _0i as the starting point, with the initial center point c _E0 as the starting point, by expanding and contracting in the three principal axis directions of V _E0 . When the coordinates indicated by the magnetic data q _i are present on the initial ellipsoid V _E0 , the coordinates indicated by the converted magnetic data s _0i are located on the spherical surface S _E0 centered on the initial center point c _E0 .
As shown in FIG. 18, the initial ellipsoid V _E0 is the ellipsoid defined coordinates indicated by the plurality of magnetic data q ₁ to q _N to have in the vicinity, of a plurality of magnetic data q ₁ to q _N It is not an ellipsoid determined so as to minimize the error from the coordinates shown. Accordingly, when the error between the coordinates indicated by the plurality of magnetic data q _{1 to} q _N and the initial ellipsoid V _E0 is large, the coordinates indicated by the initial center point c _E0 that is the center point of the initial ellipsoid V _E0 ; error between the sphere S _G center point c coordinates indicated by _OG of representing the geomagnetism Bg increases. In this case, the converted magnetic data s _0i elliptically corrected by the magnetic data q _i initial ellipsoidal correction matrix coordinates indicated by T ₀ and the initial center point c _E0, on the basis of the initial center point c _E0, accurate geomagnetism Bg The correct direction cannot be calculated.

Therefore, in the present embodiment, the optimum ellipsoid correction matrix T _OP defined based on the optimum ellipsoid _VEOP that minimizes the error from the coordinates indicated by the plurality of magnetic data q _{1 to} q _N and the optimum ellipsoid _VEOP The coordinates indicated by the magnetic data q _i are elliptically corrected on the basis of the optimum center point c _EOP that is the center point of. Specifically, the geomagnetic measurement system SYS according to the present embodiment, while adopting the optimum ellipsoidal correction matrix T _OP as ellipsoid correction matrix T _E, the vector indicating the coordinates of the optimum center point c _EOP as an offset c _OFF By adopting, equation (1.a) is transformed into the following equation (67) The geomagnetic measurement system SYS, by performing the elliptical correction shown in expression (67), calculates a vector _{(s i -c EOP)} indicating the direction of the geomagnetism ^S Bg. Hereinafter, the vector (q _i −c _EOP ) appearing on the right side of Expression (67) is referred to as a first magnetic vector, and the vector (s _i −c _EOP ) appearing on the left side of Expression (67) is referred to as a second magnetic vector.
Optimal ellipsoid _{V EOP} are the ellipsoid to minimize the error between the coordinates indicated by the plurality of magnetic data _q 1 to q _N, and ellipsoid _{V E,} the optimum ellipsoidal _{V EOP,} the same figure Can be seen. Therefore, the error between the coordinates indicated by the optimum center point c _{EOP and} the coordinates indicated by the center point c _OG (offset c _OFF ) is larger than the error between the coordinates indicated by the initial center point c _{E0 and} the coordinates indicated by the center point c _OG. It can be considered that the optimal center point c _EOP and the center point c _OG are small and indicate the same coordinates. Such, the optimum ellipsoidal correction matrix T _OP, based on the optimum center point c _EOP, by ellipse correcting the coordinates indicated by the magnetic data q _i, it is possible to obtain the orientation of the correct geomagnetism Bg.

The ellipsoidal optimal correction value generation unit 400 minimizes the value of the ellipsoidal optimization function f _EL (T, c) shown in the following equation (68) and the variable vector T and the variable vector c. A non-linear optimization operation that sequentially updates each element is performed, and the variable matrix T and the variable vector c when the value of the ellipsoidal optimization function f _EL (T, c) is minimized are expressed as the optimal ellipsoid correction matrix T. Calculated as _OP and optimum center point c _EOP .
Here, the ellipsoidal optimization function f _EL (T, c) is expressed by each component of the variable matrix T, which is a symmetric matrix of 3 rows and 3 columns shown in the following formula (69), and in the formula (1.e). A function having each element of the variable vector c as a variable and can be expressed as the following equation (70). The initial value of the variable matrix T and variable vector c, the coordinates of the initial ellipsoidal correction matrix T ₀ and the initial center point c _E0 is applied.

As shown in Expression (68), the ellipsoidal optimization function f _EL (T, c) has a plurality of _first values representing coordinates indicated by a plurality of magnetic data q _{1 to} q _N starting from the coordinates indicated by the variable vector c. What is the average value of the lengths of the plurality of second variable vectors T (q _i -c) obtained by converting each of the variable vectors (q _i -c) by the variable matrix T from “1”? It is a function indicating whether or not there is a difference.
That is, the ellipsoidal optimization function f _EL (T, c) has a plurality of second variable vectors T (q _i −c) arranged such that the coordinates indicated by the variable vector c are the starting points. It represents an error between the coordinates indicated by each of the two variable vectors and the spherical surface having a radius of 1 centered on the coordinates indicated by the variable vector c. At this time, data representing a plurality of coordinates indicated by a plurality of second variable vectors T (q _i -c) is referred to as a plurality of post-conversion data s _{X1 to} s _XN . By minimizing the value of the ellipsoidal optimization function f _EL (T, c), a spherical surface having a radius of 1 centered on the coordinates indicated by the plurality of converted data s _{X1 to} s _{XN and} the coordinates indicated by the variable vector c And the error can be minimized. The plurality of converted data s _{X1 to} s _XN that minimize the value of the ellipsoidal optimization function f _EL (T, c) are referred to as a plurality of converted magnetic data s _{1 to} s _N.
In this embodiment, for convenience of explanation, the second variable vector T (q _i −c) is arranged starting from the coordinates indicated by the variable vector c, but the second variable vector T (q _i −c) is used. the origin of the sensor coordinate system sigma _S is may be arranged such that the starting point. That is, equation (68), when the origin of the second variable vector _{T (q} i -c) the sensor coordinate system sigma _S is arranged so that a starting point, indicated by the second variable vector _{T (q} i -c) representing the coordinates, the error between the sphere of radius 1 centered at the origin of the sensor coordinate system sigma _S. In this case, the plurality of post-conversion magnetic data s _{1 to} s _N are distributed in the vicinity of the spherical surface with the radius 1 centered on the origin.

A non-linear optimization calculation for calculating the optimal ellipsoid correction matrix _TOP and the optimal center point _cEOP by minimizing the value indicated by the ellipsoidal optimization function f _EL (T, c) can be performed by appropriately applying known methods. That's fine. For example, the Newton method may be applied as the nonlinear optimization calculation.
In nonlinear optimization operations such as Newton's method and steepest descent method, the values of the variables of the nonlinear function are sequentially updated so as to optimize (minimize or maximize) the value indicated by the nonlinear function. The nonlinear optimization calculation stops updating the variable value when the value of the nonlinear function and the value of the variable satisfy a predetermined stop criterion, and adopts the value of the variable at this time as an optimal solution. .
It should be noted that a known standard may be applied as appropriate as the non-linear optimization calculation stop criterion. For example, you may apply the Armijo's rule.

The nonlinear optimization operation is an operation for calculating an optimum solution of a nonlinear function, that is, a global optimum solution that minimizes (or maximizes) the nonlinear function. However, if the initial value applied to the nonlinear optimization operation is a value that is significantly different from the global optimal solution, the optimal solution calculated by the nonlinear optimization operation is a local optimal solution that is different from the global optimal solution. Sometimes. If an initial value that is significantly different from the global optimal solution is applied, there may be a local optimal solution that is closer to the initial value than the global optimal solution. This is because there is a high possibility that is updated to the local optimal solution before being updated to the global optimal solution. Therefore, in order to prevent the local optimal solution from being calculated by the nonlinear optimization calculation, it is necessary to adopt a value as close as possible to the global optimal solution as the initial value.
In the present embodiment, an initial ellipsoid correction matrix T ₀ and an initial center point c _E0 are calculated based on the initial ellipsoid V _E0 , and these values are applied as initial values for nonlinear optimization calculation. The initial ellipsoid V _EO determined to have the coordinates indicated by the plurality of magnetic data q _{1 to} q _{N in} the vicinity is the ellipsoid V that minimizes the error from the coordinates indicated by the plurality of magnetic data q _{1 to} q _{N. It} has a shape close to _E. Accordingly, the coordinates indicated by the initial ellipsoid correction matrix T ₀ and the initial center point c _E0 are close to the coordinates indicated by the ellipsoid correction matrix T _E and the center point c _OG , which are values to be calculated as a global optimum solution. Yes (see FIGS. 8 and 18). The coordinates indicated by the optimal ellipsoid correction matrix _TOP and the optimal center point _cEOP calculated by performing the nonlinear optimization operation using such initial values are not the local optimal solution but the global optimal solution (strict (Approximate value of global optimum solution). As described above, in the nonlinear optimization calculation of the present embodiment, since an appropriate initial value close to the global optimal solution is set, the global optimal solution is calculated as the optimal solution without falling into the local optimal solution. can do.

By the way, in the present embodiment, as shown in the equation (69), a variable matrix T that is a real symmetric matrix as a variable of the ellipsoidal optimization function f _EL (T, c) to be optimized in the nonlinear optimization calculation. but using, instead of the variable matrix T, there is also a method of performing nonlinear optimization calculation using the variable matrix T _R representing a real matrix generally not limited to symmetric matrix as a variable (see "non-Patent Document 1").
However, the variable matrix T _R is not limited to symmetric matrices, in addition to the coordinate transformation for each stretch any vector three eigenvectors direction variable matrix T _R, it may represent a coordinate transform that rotates the orientation of any vector . Therefore, the vector T _R (q _i -c) obtained by converting the first variable vector (q _i -c) by the variable matrix T _R rotates the second magnetic vector T (q _i -c) by an arbitrary angle. May be calculated as a vector. That is, as shown in FIG. 20, the coordinates indicated by the converted magnetic data ^RO s _i may be calculated by using a variable matrix T _R, the coordinates indicated by the converted magnetic data s _i may be calculated by using a variable matrix T , Calculated as coordinates rotated by an arbitrary angle on the spherical surface S _EOP .
In this case, based on the coordinates indicated by the converted magnetic data ^RO s _i may be calculated by using a variable matrix T _R, it is difficult to calculate the direction of the geomagnetism Bg.

According to Non-Patent Document 1, by direction as viewed from the three-dimensional magnetic sensor 60 using known reference magnetic field, to identify the angle of rotation generated in the coordinate transformation performed by the variable matrix T _R, the rotation in the coordinate transformation The coordinates indicated by the converted magnetic data s _i when not generated are calculated. This method requires the terminal device 1 to have an opportunity to measure the reference magnetic field.

On the other hand, in this embodiment, the variable matrix T is limited to a real symmetric matrix. The real symmetric matrix has three eigenvectors orthogonal to each other and three eigenvalues corresponding to the three eigenvectors. When a vector is converted using a real symmetric matrix, the converted vector is expressed as a sum of three vectors facing the three eigenvector directions of the real symmetric matrix. The sum of three vectors obtained by expanding and contracting by the corresponding eigenvalue multiple without changing the direction is calculated. That is, the real symmetric matrix is a matrix that performs coordinate transformation for expanding and contracting an arbitrary vector in each eigenvector direction of the real symmetric matrix.
Therefore, nonlinear optimization calculation using a variable matrix T is a real symmetric matrix, the optimum ellipsoidal correction matrix T _OP, represents a coordinate conversion for each stretch any vector to each eigenvector direction of the optimum ellipsoidal correction matrix T _OP Since the calculation is performed as a matrix, the optimal ellipsoid correction matrix _TOP does not perform coordinate conversion with rotation. Such optimum ellipsoidal correction matrix T _OP, the coordinates indicated by the magnetic data q _i, by converting into a coordinate indicated by the converted magnetic data s _i, it is possible to obtain an accurate orientation of the geomagnetic Bg.
Further, the variable matrix T _R has nine independent components by a matrix of three rows and three columns, the variable ellipsoid optimization function f _{EL (T} R, _c) whereas the 12, the Since the variable matrix T according to the embodiment is a symmetric matrix, it has six independent components, and the ellipsoidal optimization function f _EL (T, c) has nine variables. Therefore, the nonlinear optimization operation in accordance with this embodiment, fewer variables than the nonlinear optimization calculation using a variable matrix T _R, the computation load is reduced.

The ellipsoidal optimal correction value generation unit 400 stores the optimal ellipsoidal correction matrix _TOP and the optimal center point _cEOP in the data control unit 710.
The elliptical surface optimal correction value generation unit 400 determines that the calculated optimal elliptical surface correction matrix _TOP is a positive definite matrix, and only when the determination result is affirmative, the optimal elliptical surface correction matrix _TOP and the optimal elliptical surface correction matrix _TOP The center point c _EOP is stored in the data control unit 710, and when the determination result is negative, these calculation results may be discarded. Optimum ellipsoidal correction matrix T _OP, the coordinates on the ellipsoid, by expanding and contracting in the main axis direction of the ellipsoid, since a matrix for transforming into coordinates on a sphere, with the optimum ellipsoidal correction matrix T _OP This is because all three eigenvalues must be positive values.

Incidentally, the coordinates and the optimum ellipsoidal correction matrix T _OP of the optimum center point c _EOP calculated by the ellipsoidal optimum correction value generation unit 400 is transmitted as response information RES to the terminal apparatus 1, offset these offsets employed 131 when employed as c _OFF and ellipsoidal correction matrix _{T E,} the geomagnetic vector calculating unit 132, to the coordinates indicated by the magnetic data _{q i} of the three-dimensional magnetic sensor 60 is successively outputted, elliptical correction based on equation (67) Is performed to calculate the direction of the geomagnetism Bg (see FIG. 8). Specifically, the geomagnetic vector calculation unit 132 uses the coordinates of the optimum center point c _EOP as the starting point and the first magnetic vector (q _i −c _EOP ) whose origin is the coordinate indicated by the magnetic data q _i as the optimum ellipsoidal correction. converted by the matrix _{T OP,} calculated second magnetic vector _{(s i -c EOP).} At this time, the second magnetic vector (s _i −c _EOP ) faces the same direction as the geomagnetism Bg unless the shift angle ψ is taken into consideration. The geomagnetic vector calculation unit 132 calculates the direction of the geomagnetism Bg from the second magnetic vector (s _i −c _EOP ) in consideration of the shift angle ψ if necessary (see FIG. 8 and paragraph 0041).
In the present embodiment, for convenience of explanation, the second magnetic vector (s _i −c _EOP ) is arranged starting from the coordinates indicated by the optimum center point c _EOP (see FIG. 8). the _(s i _{-c EOP),} may be disposed as a starting point the origin of the sensor coordinate system sigma _S. In this case, the spherical surface S _EOP represents a spherical surface with a radius 1 centered on the origin of the sensor coordinate system Σ _S , and the converted magnetic data s _i is distributed in the vicinity of the spherical surface with a radius 1 centered on the origin.

[7. Conclusion of First Embodiment]
As described above, the geomagnetism measurement system SYS according to the first embodiment assumes that the coordinates indicated by the plurality of magnetic data q _{1 to} q _N are distributed in the vicinity of the ellipsoid, and the plurality of magnetic data q _{1 to} q. the coordinates indicated by the _N identifies the ellipsoid having in the vicinity, and the coordinates indicated by the plurality of magnetic data q ₁ to q _N performed elliptical correction for coordinate transformation into a spherical neighborhood having the same center point and the ellipsoid.
As a result, when the device on which the three-dimensional magnetic sensor 60 is mounted includes a soft magnetic material and the soft iron effect is generated, the accurate direction of the geomagnetism Bg is calculated based on the plurality of magnetic data q _{1 to} q _N. can do.

In addition, the geomagnetism measurement system SYS according to the first embodiment calculates information (the coordinates of the optimum center point c _EOP and the optimum ellipsoid correction matrix T _OP ) necessary for performing the ellipse correction by the server SV.
As described above, it is larger than the approximate center point calculation process for calculating the approximate center point c _SB by solving the quaternary linear simultaneous equations using the coordinates indicated by the M pieces of magnetic data q _{B1 to} q _BM. Based on the N pieces of magnetic data q _{1 to} q _N , an initial ellipsoid generation process for calculating the initial center point c _E0 and the initial ellipsoid correction matrix T ₀ , the optimum center point c _EOP and the optimum ellipsoid correction matrix T _OP The optimal ellipsoid generation process for calculating is a process with a large load.
The geomagnetism measurement system SYS according to the first embodiment performs all processing with a large processing load in the server device SV among the processing for calculating the orientation of the geomagnetism Bg such as ellipse correction. It can be kept small. That is, the geomagnetism measurement system SYS according to the present embodiment is accurate and accurate even when the processing capability of the CPU provided in the terminal device 1 is limited or when the memory capacity of the terminal device 1 is limited. The direction of geomagnetism Bg can be calculated at high speed. In addition, the geomagnetism measurement system SYS according to the present embodiment uses a mobile device such as a mobile phone, a PDA terminal, or the like that is powered by a battery to reduce the processing load in the terminal device 1 and the power consumption. When applied as 1, the direction of the geomagnetism Bg can be calculated without reducing the battery usage time of the terminal device 1.

Note that even if the device on which the three-dimensional magnetic sensor 60 is mounted does not include a soft magnetic material and the soft iron effect does not occur, the coordinates indicated by the plurality of magnetic data q _{1 to} q _N are in the vicinity of the ellipsoid. May be distributed. For example, it provided the three-dimensional magnetic sensor 60, if the sensitivity of the three sensors X-axis geomagnetic sensor 61, Y-axis geomagnetic sensor 62 and the Z-axis geomagnetic sensor 63, there is a variation, the original spherical near the sensor coordinate system sigma _S coordinates indicated by the plurality of magnetic data q ₁ to q _N supposed distributed is distributed the spherical surface ellipsoidal neighborhood obtained by stretching in the direction of each axis in the sensor coordinate system sigma _S in accordance with the sensitivity of the three sensors. That is, if there is a variation in sensor sensitivity, coordinates indicated by the plurality of magnetic data q ₁ to q _N, distributed in the vicinity ellipsoid with three principal axes oriented in the same direction as the direction of the three axes of the sensor coordinate system sigma _S To do.
In the first embodiment, ellipse correction is performed assuming that the coordinates indicated by the plurality of magnetic data q _{1 to} q _N are distributed in the vicinity of the ellipsoid. Three major axis of the ellipsoidal used in the elliptical correction, it is possible to face any direction while maintaining the orthogonal relation, elliptical correction according to the first embodiment, the third main shaft and the sensor coordinate system sigma _S ellipsoidal The present invention can also be applied when the directions of the axes coincide.
Therefore, the ellipse correction according to the first embodiment is performed when the coordinates indicated by the plurality of magnetic data q _{1 to} q _N are distributed in the vicinity of the ellipsoid due to variations in sensor sensitivity, that is, the ellipse principal axis and the sensor coordinate system Σ. _Even when the directions of the three axes of _S coincide with each other, it is possible to calculate the correct direction of the geomagnetism Bg.

In the first embodiment, three different evaluation axes, the first evaluation axis ξ ₁ , the second evaluation axis ξ ₂ , and the third evaluation axis ξ ₃ on the space Ω, are used in calculating the initial ellipsoid V _E0. Te, after generating three different ellipsoid, determining whether all the mutual distance of these three different ellipsoidal each of the center point of equal to or less than the first threshold value Δc in the sensor coordinate system sigma _S did. Only when the determination result is affirmative, the coordinates of the initial ellipsoid correction matrix T ₀ and the initial center point c _E0 were calculated.
Thus, the shape of the distribution of the coordinate indicated by the plurality of magnetic data q ₁ to q _N, when it is difficult to identify the shape of the ellipsoid, the distribution of coordinate indicated by the plurality of magnetic data q ₁ to q _N It is possible to prevent generation of inappropriate initial ellipsoid correction matrix T ₀ and initial center point c _E0 coordinates based on an inaccurate initial ellipsoid V _E0 different from the shape. It became possible to prevent the value from being adopted as an offset.

In the first embodiment, the respective components and the coordinate of the initial center point c _E0 of the initial ellipsoidal correction matrix T ₀ that is determined based on the initial ellipsoid V _E0 having a shape similar to ellipsoid V _E and the initial value The coordinates of the optimum ellipsoid correction matrix _TOP and the optimum center point _cEOP were calculated by nonlinear optimization calculation.
Nonlinear optimization uses a value close to the global optimal solution as the initial value to reduce the possibility that the local optimal solution is calculated as the optimal solution, and the global optimal solution is calculated as the optimal solution. Increase possibilities. Therefore, the nonlinear optimization operation according to this embodiment, incorrect geomagnetism due to a local optimum solution to reduce the likelihood calculated as an optimal solution, elliptical correction using inappropriate optimum ellipsoidal correction matrix T _OP The possibility of calculating the direction of Bg was reduced.

In the first embodiment, the optimum ellipsoid correction matrix T _OP and the optimum center point are minimized by minimizing the ellipsoid optimization function f _EL (T, c) having the variable matrix T which is a real symmetric matrix as a variable. c _EOP was calculated. Thus, the optimum ellipsoidal correction matrix T _OP is an arbitrary vector, to be calculated as an optimal ellipsoid correction matrix T 3 single matrix to perform the coordinate transformation to be stretchable in the eigenvector direction of the _OP, coordinate conversion involving rotation performed Absent.
That is, the coordinates indicated by the converted magnetic data s _i calculated by elliptically correcting the coordinates indicated by the magnetic data q _i located in the vicinity of the optimum ellipsoidal plane V _EOP are the geomagnetism Bg as seen from the optimum center point c _EOP. since it obtained as coordinates the same direction, based on the converted magnetic data s _i, can calculate the direction of the correct geomagnetism Bg.

<B. Second Embodiment>
Hereinafter, a second embodiment will be described.

[8. Outline of Geomagnetic Measurement Device According to Second Embodiment]
In the first embodiment, the magnetic field to be measured by the three-dimensional magnetic sensor 60 is limited to the geomagnetism Bg, the internal magnetic field Bi, and the magnetizing magnetic field Bm, and the coordinates indicated by the plurality of magnetic data q _{1 to} q _N are elliptical surfaces. A case of distribution in the vicinity was assumed.
However, if the object to produce a magnetic field to the outside of the terminal device 1 exists, due to the influence of an external magnetic field Bx generated by the object, the coordinates indicated by the plurality of magnetic data q ₁ to q _N, distributed in different shapes and ellipsoidal Sometimes. In this case, the coordinates indicated by the center point of the ellipsoid calculated on the assumption that the coordinates indicated by the plurality of magnetic data q _{1 to} q _N are distributed in the vicinity of the ellipsoid are coordinates indicating the offset of the three-dimensional magnetic sensor 60. And the correct geomagnetism Bg direction cannot be obtained even if correction is performed using the coordinates indicated by the center point of the ellipsoid as an offset.
Further, since the soft iron effect does not occur when the terminal device 1 does not include the soft magnetic material 21, the coordinates indicated by the plurality of magnetic data q _{1 to} q _N are distributed near the spherical surface as shown in FIG. It is not distributed near the ellipsoid. In this case, an accurate geomagnetic Bg direction can be obtained without performing ellipse correction.
In the second embodiment, the geomagnetic measurement corresponding to the case where the external magnetic field Bx emitted by the object outside the terminal device 1 exists and the case where the terminal device 1 does not include the soft magnetic material 21 and the magnetizing magnetic field Bm does not exist. The purpose is to realize the system.

  FIG. 21 is a block diagram showing a configuration of a geomagnetism measurement system SYSa according to the second embodiment. As shown in FIG. 21, the geomagnetism measurement system SYSa according to the second embodiment includes a plurality of terminal devices 1, a plurality of terminal devices 1a, and a server device SVa. Each of the plurality of terminal devices 1 is connected to the server device SVa via the network NW. Similarly, each of the plurality of terminal devices 1a is connected to the server device SVa via the network NW. The terminal device 1a has the same configuration as the terminal device 1 except that the component 2a not including the soft magnetic material 21 is provided instead of the component 2 (see FIG. 23). That is, unlike the terminal device 1, the terminal device 1a does not generate the magnetizing magnetic field Bm. Similarly to the terminal device 1, the terminal device 1 a includes a CPU 10 and a ROM 30 in which the terminal-side magnetic data processing program 70 is stored (see FIG. 9A). That is, the terminal device 1a functions as part of the geomagnetism measurement system SYSa when the CPU 10 included in the terminal device 1a executes the terminal-side magnetic data processing program 70. The server apparatus SVa is shown in FIG. 9B except that the second server-side magnetic data processing program according to the second embodiment is stored in the hard disk 950 instead of the server-side magnetic data processing program 960. The configuration is the same as that of the server device SV.

FIG. 22 is a functional block diagram illustrating functions realized by the CPU 910 of the server apparatus SVa executing the second server-side magnetic data processing program. In FIG. 22, for convenience of description, reference numeral “SVa” is given to a function realized by the CPU 910 of the server apparatus SVa executing the second server-side magnetic data processing program.
As illustrated in FIG. 22, the server device SVa according to the second embodiment includes a distribution determination unit 620, a center point calculation unit 640, an ellipsoid spherical surface conversion unit 520, and a distortion determination unit 540, and a data control unit 710. The server apparatus SV is configured in the same manner as the server apparatus SV (see FIG. 10) according to the first embodiment except that a data control unit 710a is provided instead of the server apparatus SV.

Distribution determining unit 620 determines the sensor coordinate system sigma _S, the distribution of coordinate indicated by the plurality of magnetic data q ₁ to q _N is whether it has a three-dimensional spread.
Central point calculation unit 640, the sensor coordinate system sigma _S, calculates the coordinates indicated by the center point c _S of the spherical S having coordinates indicated by the plurality of magnetic data q ₁ to q _N in the vicinity. As described in FIG. 4, a magnetic field three-dimensional magnetic sensor 60 is measured, when a geomagnetism Bg and internal magnetic field Bi, coordinates indicated by the plurality of magnetic data q ₁ to q _N, distributed in the vicinity of the spherical S _G to end, the sphere S and the sphere S _G can be regarded to match, the vector indicating the coordinates of the center point c _S of the spherical S, can be adopted as the offset c _OFF. The server device SVa according to the second embodiment includes the center point calculation unit 640 so that the magnetization magnetic field Bm does not exist and the coordinates indicated by the plurality of magnetic data q _{1 to} q _N are distributed in the vicinity of the spherical surface. It becomes possible to calculate coordinates that are candidates for the offset c _OFF of the three-dimensional magnetic sensor 60 by a simple method.

Ellipsoid spherical conversion unit 520, the optimum ellipsoidal correction matrix _{T OP,} the optimum center point _{c EOP,} and, a plurality of the magnetic data _q 1 to q _N, generates a plurality of converted magnetic data _s 1 ~s _N. Specifically, as shown in Expression (67), the ellipsoid spherical surface conversion unit 520 starts with the coordinates of the optimum center point c _EOP as the starting point and the first magnetic vector (q _i with the coordinates indicated by the magnetic data q _i as the ending point. the -c _EOP), was transformed by the optimum ellipsoidal correction matrix _{T OP,} a second magnetic vector with the end point coordinates indicating the converted magnetic data _{s i} the optimum center point _{c EOP} starting _{(s i -c EOP)} By calculating, the coordinates indicated by the converted magnetic data s _i are calculated.
Distortion determination section 540 in the sensor coordinate system sigma _S, there are a plurality of input coordinate (coordinate indicated by the plurality of magnetic data _q 1 to q _N or coordinates indicated by the plurality of the converted magnetic data _s 1 ~s _N,) Assuming that the three-dimensional shape is distributed in the vicinity of the solid, the degree of difference between the shape of the solid and the shape of the spherical surface is evaluated to determine whether or not the shape of the solid can be regarded as a spherical surface.
When the external magnetic field Bx exists and the coordinates indicated by the plurality of magnetic data q _{1 to} q _N are distributed in the vicinity of a distorted solid different from the spherical surface or the ellipsoidal surface, the offset c _OFF candidate of the three-dimensional magnetic sensor 60 is It is difficult to calculate such a value.
The server apparatus SVa according to the second embodiment includes the distortion determination unit 540, so that the influence of the external magnetic field Bx is large, and it is difficult to calculate the coordinates that are candidates for the offset c _OFF. c It can be prevented from being adopted as _OFF . Thereby, it becomes possible to prevent the terminal device 1 and the terminal device 1a from calculating the incorrect direction of the geomagnetism Bg by the correction processing using the incorrect offset.

The data control unit 710a includes information input to the server-side transmission / reception unit 720, the distribution determination unit 620, the center point calculation unit 640, the ellipsoid correction unit 200, the ellipsoid spherical surface conversion unit 520, and the distortion determination unit 540, and these And the response information RES is generated under a predetermined condition.
Specifically, the data control unit 710a holds a plurality of magnetic data q _{1 to} q _N output from the server-side transmission / reception unit 720. The data control unit 710a also includes a plurality of converted magnetic data s _{1 to} s _N calculated by the ellipsoid spherical surface conversion unit 520, the coordinates of the center point c _S of the spherical surface S calculated by the center point calculation unit 640, and the ellipse. and coordinates and the optimum ellipsoidal correction matrix T _OP of the optimum center point c _EOP for calculating surface correction unit 200, information indicating the judgment result in the distribution determination unit 620, and information indicating a determination result in the distortion determination section 540, the holding To do.
The details will be described later, the data control unit 710a, under predetermined conditions, adopting one of the best center point _{c EOP} or center point _{c S} as a response center point _{c SA.} Then, the data control unit 710a, when employing the optimum center point _{c EOP} response center point _{c SA,} by employing the optimum ellipsoidal correction matrix _{T OP} in response correction matrix _{T A,} and generates the response information RES. On the other hand, the data control unit 710a, when employing the center point _{c S} as a response center point _{c SA,} by employing the unit matrix I in three rows and three columns as a response correction matrix _{T A,} and generates the response information RES.
When the data control unit 710a employs the center point c _S as the response center point c _SA and the offset adoption unit 131 employs a vector indicating the coordinates of the response center point c _SA as the offset c _OFF , the expression (1 .), The geomagnetic vector calculation unit 132 subtracts the coordinates of the center point c _S from the coordinates indicated by the magnetic data q _i sequentially output by the three-dimensional magnetic sensor 60, thereby calculating the geomagnetism ^S Bg. Calculate the orientation. That is, in this case, the geomagnetic vector calculation unit 132 does not perform the elliptical correction, will calculate the direction of the geomagnetism ^S Bg as a subtraction process just vectors.

  Below, the property of the external magnetic field Bx will be described as a premise for explaining the geomagnetism measurement system SYSa according to the second embodiment.

Figure 23 is a detection target of the 3-dimensional magnetic sensor 60, a geomagnetic Bg, internal magnetic field Bi, magnetizing field Bm, and an external magnetic field Bx is a conceptual diagram illustrating the ground coordinate system sigma _G. Here, the position P _S shown in FIG. 23, representing the position of the origin of the sensor coordinate system sigma _S in ground coordinate system sigma _G (i.e., in the ground coordinate system sigma _G, the three-dimensional magnetic sensor 60 position).

As shown in FIG. 23, the external magnetic field Bx is a magnetic field generated by the object 3 existing outside the terminal device 1 or the terminal device 1a, and is nonuniform in which the direction and magnitude change depending on the relative positional relationship with the object 3. Magnetic field. When changing the position Ps of the 3D magnetic sensor 60 in the ground coordinate system sigma _G, three-dimensional magnetic sensor 60 is the direction and magnitude of the external magnetic field Bx changes to be measured. Accordingly, the external magnetic field Bx is the ground coordinate system sigma _G, is represented as a vector ^G Bx (Ps) varying both the direction and magnitude depending on the position Ps. Also, when changing the posture of the 3D magnetic sensor 60 in the ground coordinate system sigma _G mu, three-dimensional magnetic sensor 60 is the direction of the external magnetic field Bx changes to be measured.

Figure 24 is the position Ps of the three-dimensional magnetic sensor 60 with varying the _P S1 _{to P SN,} when measuring the magnetic field by changing the posture _μ μ 1 ~μ _N, and outputs the three-dimensional magnetic sensor 60 a plurality of magnetic data _q 1 to q _N, is a plot in the sensor coordinate system sigma _S.
In FIG. 24, for the sake of simplicity, it is assumed that the magnetizing magnetic field Bm does not exist and only the internal magnetic field Bi, the geomagnetic Bg, and the external magnetic field Bx exist.

External magnetic field Bx, in the sensor coordinate system sigma _S, depending on the position Ps of the 3D magnetic sensor 60 is changed both the direction and magnitude, to change the direction depending on the orientation of the three-dimensional magnetic sensor 60 mu It is expressed as a vector ^S Bx (μ, Ps).
When the three-dimensional magnetic sensor 60 measures the internal magnetic field Bi, the geomagnetism Bg, and the external magnetic field Bx, the coordinates represented by each of the plurality of magnetic data q _{1 to} q _N represent the vector ^S Bi representing the internal magnetic field and the geomagnetism. A vector ^S Bg (μ) and a vector representing the sum of vectors ^S Bx (μ, Ps) representing an external magnetic field are indicated. Therefore, the coordinates indicated by the plurality of magnetic data _q 1 to q _N is the origin and spherical _{S G} representing the end point of the vector ^S Bg (mu) representing the geomagnetism originating the center point _{c OG,} the center point _{c OG} The curved surface SX representing the end point of the vector ^S Bx (μ, Ps) representing the external magnetic field is distributed in the vicinity of the surface of the solid SD superimposed with the center point c _OG as the starting point.

When the curved surface SX representing the external magnetic field Bx has a distorted shape different from the spherical surface, the solid SD also has a distorted shape different from the spherical surface. When the solid SD has a distorted shape different from that of the spherical surface, the coordinates of the center point c _OG of the spherical surface S _G representing the geomagnetism Bg are calculated based on the coordinates indicated by the plurality of magnetic data q _{1 to} q _N. Have difficulty. Even if the spherical surface S having the coordinates indicated by the plurality of magnetic data q _{1 to} q _N is determined in the vicinity and the center point c _S of the spherical surface S is calculated, the center point c _S of the spherical surface S and the spherical surface S _G This is because there is a high possibility that the coordinates are different from the center point _cOG . (See FIG. 31). Thus, they have different distorted shapes and three-dimensional SD spherical, when the calculation of the coordinates indicating the center point c _OG of the spherical S _G is difficult, based on a plurality of magnetic data q ₁ to q _N Therefore, it is necessary to prevent the offset c _{OFF from} being calculated.

However, small influence of non-uniform external magnetic fields Bx, when the shape of the three-dimensional SD is that substantially spherical and regarded, on the basis of the coordinate indicated by the plurality of magnetic data q ₁ to q _N, the center point of the spherical surface S _G c The coordinates indicated by the _OG can be calculated. For example, as shown in FIG. 25 (A), when the external magnetic field Bx is weak, the spherical _{S G} representing the geomagnetism Bg, a is stereoscopic SD is superposition of the curved surface SX representing the external magnetic field Bx, spherical _{S G} And almost the same figure. Therefore, the coordinates indicated by the plurality of magnetic data _q 1 to q _N, because it can be considered that the distribution in the vicinity of the spherical surface _{S G,} a plurality of the magnetic data _q 1 to q _N, sphere _S center point of _G c The coordinates indicated by _OG can be calculated.
Further, as shown in FIG. 25B, even when the non-uniform external magnetic field Bx is large, the shape of the solid SD may be regarded as a substantially spherical surface. For example, even when there is a non-uniform external magnetic field Bx, when the N pieces of magnetic data q _{1 to} q _N are acquired, the user of the terminal device 1 or the terminal device 1 a can use the terminal device 1 or the terminal device. 1a rather than the position P _S of the three-dimensional magnetic sensor 60 swings to vary holding by hand, in case of changing fixed and only the posture μ position P _S of the three-dimensional magnetic sensor 60, the external magnetic field Bx is the sensor coordinate system sigma _S, is represented as a direction only certain varying the magnitude of the vector ^S Bx (mu) based on the attitude mu. In this case, the shape of the curved surface SX representing the external magnetic field Bx is, since the spherical surface centered at the center point c _OG, the spherical S _G centered on the center point c _OG, the spherical surface centered at the center point c _OG a curved SX shape, the shape of the three-dimensional SD superimposed around a central point c _OG is a spherical surface centered at the center point c _OG. Therefore, based on the coordinates indicated by the plurality of magnetic data q ₁ to q _N, by calculating the coordinates of the center point of the sphere representing three-dimensional SD, it is possible to calculate the center point c coordinates indicated by _OG spherical S _G it can.

The server apparatus SVa according to the present embodiment is based on the coordinates indicated by the plurality of magnetic data q _{1 to} q _N , the magnitude of the influence of the external magnetic field Bx, that is, the degree of difference between the shape of the solid SD and the shape of the spherical surface To evaluate. Accordingly, the server apparatus SVa determines whether or not the coordinates that are candidates for the offset c _OFF can be calculated based on the coordinates indicated by the plurality of magnetic data q _{1 to} q _N , and the terminal apparatus 1 or the terminal apparatus 1a. , The inaccurate offset c _OFF affected by the external magnetic field Bx is prevented from being adopted.

Although details will be described later, the server apparatus SVa according to the present embodiment uses the ellipsoid correction unit 200, the ellipsoid spherical surface conversion unit 520, and the distortion determination unit 540 to indicate the coordinates indicated by the plurality of magnetic data q _{1 to} q _N. The degree of difference between the shape of the distribution and the shape of the ellipsoid can also be evaluated. The coordinates indicated by the plurality of magnetic data q ₁ to q _N, when converted into coordinates representing a plurality of the converted magnetic data s ₁ ~s _N by the elliptical correction, coordinate indicated by the plurality of the converted magnetic data s ₁ ~s _N if you can regarded as spherical shape of the three-dimensional SD _E having in the vicinity of, the shape of the three-dimensional SD with coordinates indicated by the plurality of magnetic data q ₁ to q _N in the vicinity can be regarded as ellipsoidal Because.
That is, as shown in FIG. 22, the ellipsoid correction unit 200, the ellipsoid spherical surface conversion unit 520, and the distortion determination unit 540 consider that the shape of the distribution of coordinates indicated by the plurality of magnetic data q _{1 to} q _N is a spherical surface. Judging whether it falls into a shape that can be considered as an elliptical surface, or a distorted shape that cannot be considered as a spherical surface or an elliptical surface, It functions as the strain shape determination unit 500.
Then, the shape of the coordinate distribution indicated by the plurality of magnetic data q _{1 to} q _N is a shape that can be regarded as a spherical surface, or a shape that can be regarded as an elliptical surface. When it is determined that there is a response, the server apparatus SVa generates a response center point c _SA indicating coordinates that are candidates for the offset c _OFF , but when it is determined that the shape is a distorted shape different from both the spherical surface and the ellipsoid surface, the response center point c _Does not generate _SA .
As described above, the geomagnetism measurement system SYSa according to the present embodiment includes the distortion shape determination unit 500, thereby preventing an inaccurate offset due to the influence of the external magnetic field Bx from being calculated. When the influence of the external magnetic field Bx is small enough to be ignored, it is possible to accurately calculate the offset c _OFF regardless of the presence or absence of the soft iron effect.

  Hereinafter, the operation of the server apparatus SVa in the present embodiment will be specifically described.

[9. Flowchart showing operation of geomagnetism measuring apparatus according to second embodiment]
FIG. 26 is a flowchart showing the operation of the server apparatus SVa according to the second embodiment. The processing shown in the flowchart is started when the CPU 910 receives a plurality of magnetic data q _{1 to} q _N from the terminal device 1 or the terminal device 1a in a state where the second server-side magnetic data processing program is being executed. The

In step S51, the CPU 910 executes magnetic data storage processing. Specifically, CPU 910 is of N magnetic data _q 1 to q _N by the communication unit 940 has received and stored in the third memory area Area3.

In step S53, the CPU 910 executes magnetic data distribution determination processing. Specifically, CPU 910, the third memory area Area3 stored in the N pieces of magnetic data _q 1 to q _N (hereinafter the magnetic data storage processing in step S51, in this section, "the N magnetic data _q 1 ~ q _N ”) is a sensor coordinate system Σ _S (hereinafter referred to as“ sensor coordinate system Σ _S ”in this section) in the terminal device 1 or the terminal device 1a that has transmitted the N pieces of magnetic data q _{1 to} q _N. It is determined whether or not the distribution of coordinates shown in FIG. If the determination result is affirmative, the CPU 910 advances the process to step S55. On the other hand, when the determination result is negative, that is, when the distribution of coordinates indicated by the plurality of magnetic data q _{1 to} q _N is two-dimensional or one-dimensional, the CPU 910 advances the process to step S 71.
That is, the CPU 910 functions as the distribution determination unit 620 by executing the magnetic data distribution determination process in step S53.

In step S55, the CPU 910 executes center point calculation processing. Specifically, CPU 910 is, N pieces of the magnetic data _q 1 to q _N calculates the coordinates of the center point _{c S} of the spherical S having coordinates indicating the sensor coordinate system sigma _S in the vicinity.
That is, the CPU 910 functions as the center point calculation unit 640 by executing the center point calculation process in step S55.

In step S57, the CPU 910 executes a distortion determination process. Specifically, CPU 910, first, each of the N magnetic data _q 1 to q _N is the coordinate that shows the sensor coordinate system sigma _S, is employed as the input coordinates. Next, assuming that a plurality of input coordinates are distributed in the vicinity of the solid SD, the CPU 910 evaluates the degree of difference between the shape of the solid SD and the shape of the spherical surface, so that the shape of the solid SD is regarded as a spherical surface. Determine whether you can hesitate. If the determination result is affirmative, the CPU 910 advances the process to step S67. On the other hand, when the determination result is negative (ie, when the solid SD has a distorted shape different from the spherical surface), the CPU 910 advances the process to step S59.

In step S59, the CPU 910 executes an initial ellipsoid generation process. Specifically, CPU 910 determines on the basis of the N pieces of magnetic data _q 1 to q _N, whether it is possible to calculate the coordinates and the initial ellipsoid correction matrix _{T 0} of the initial center point _{c E0} . If the determination result is affirmative, CPU 910 is, after calculating the coordinate and the initial ellipsoid correction matrix _{T 0} of the initial center point _{c E0,} the process proceeds to step S61. On the other hand, if the determination result is negative, the CPU 910 advances the process to step S71.
That is, the CPU 910 functions as the ellipsoid initial correction value generation unit 300 by executing the initial ellipsoid generation process in step S59.

In step S61, the CPU 910 executes optimal ellipsoid generation processing. Specifically, CPU 910, based on the initial ellipsoid generation processing initial center point c _E0 and the initial ellipsoid correction matrix T ₀ calculated in the step S59, the coordinates and the optimum ellipsoidal optimal correction of the center point c _EOP A matrix _TOP is calculated.
That is, the CPU 910 functions as the elliptical surface optimal correction value generation unit 400 by executing the optimal elliptical surface generation processing in step S61.

In step S63, the CPU 910 executes an ellipsoidal sphere conversion process. Specifically, CPU 910, based on the optimum ellipsoidal correction matrix _{T OP} and the optimum center point _{c EOP,} the coordinates indicated by the N magnetic data _q 1 to q _N existing near optimum ellipsoidal _{V EOP,} N Conversion into coordinates in the vicinity of the spherical surface S _EOP represented by the pieces of converted magnetic data s _{1 to} s _N is performed. Thereafter, the CPU 910 stores N pieces of post-conversion magnetic data s _{1 to} s _N in the third storage area Area 3.
That is, the CPU 910 functions as the ellipsoid spherical surface conversion unit 520 by executing the ellipsoid spherical surface conversion process in step S63.

In step S65, the CPU 910 executes a distortion determination process. Specifically, CPU 910, first, the coordinates indicated in each sensor coordinate system sigma _S of N transformed magnetic data s ₁ ~s _N calculated in ellipsoidal spherical conversion processing in step S63, as the input coordinate adopt. Next, CPU 910, assuming that the distribution in the vicinity of the three-dimensional SD _E which have multiple input coordinates, to assess the degree of difference between the shape and the spherical shape of the three-dimensional SD _E, the shape of the three-dimensional SD _E It is determined whether or not it can be regarded as a spherical surface. If the determination result is affirmative, the CPU 910 advances the process to step S67. On the other hand, if the determination result is negative (i.e., if the three-dimensional SD _E has a shape with a different strain spherical), CPU 910 is the processing procedure goes to step S71.
That is, the CPU 910 functions as the distortion determination unit 540 by executing the distortion determination process in step S57 or the distortion determination process in step S65.
In the following description, when the distortion determination process performed by the CPU 910 in step S57 is distinguished from the distortion determination process performed by the CPU 910 in step S65, the former is referred to as a first distortion determination process and the latter is referred to as a second distortion determination process. Called. Further, in order to distinguish from the solid SD whose shape is evaluated in the first distortion determination process, the solid whose shape is evaluated in the second distortion determination process is referred to as a solid SD _E. The first distortion determination process and the second distortion determination process are the same process except that the values of a plurality of input coordinates are different.

In this embodiment, when the determination result in step S65 is negative, the CPU 910 advances the process to step S71. At that time, the terminal device 1 (or the terminal device 1a) outputs some message to the display unit 50. As such, the terminal device 1 (or the terminal device 1a) may be instructed.
When acquiring the N pieces of magnetic data q _{1 to} q _N , the user does not hold the terminal device 1 (or the terminal device 1 a) with his hand and rotate it, but the position of the terminal device 1 (or the terminal device 1 a). If only the posture is changed while the position is fixed, the influence of the external magnetic field Bx can be kept low (see FIG. 25B). Therefore, when the determination result in step S65 is negative, the user may be instructed to rotate the terminal device 1 (or terminal device 1a) while fixing the position thereof. The user may be instructed by displaying an image, a moving image, or the like on the display unit 50 of the terminal device 1 (or the terminal device 1a) or using a voice or the like.

In step S67, the CPU 910 executes response information generation processing. Specifically, when the determination result in the distortion determination process in step S57 is affirmative, the CPU 910 adopts the center point c _S calculated by the CPU 910 in the center point calculation process in step S55 as the response center point c _SA. It employs an identity matrix I rows and three columns as a response correction matrix T _a, and generates the response information RES to coordinate the response correction matrix T _a and the elements of the response center point c _SA.
On the other hand, when the determination result in the distortion determination process in step S57 is negative, the CPU 910 adopts the optimum center point c _EOP calculated by the CPU 910 in the optimum ellipsoidal surface generation process in step S61 as the response center point c _SA , and step S61. optimal in ellipsoidal generation process CPU910 adopts the optimum ellipsoidal correction matrix T _OP calculated in response correction matrix T _a, the response information RES to the coordinates of the response center point c _SA and response correction matrix T _a and element Generate.

In step S69, the CPU 910 executes response information transmission processing. Specifically, the CPU 910 transmits the response information RES generated in the response information generation process in step S67 to the terminal device 1 (or the terminal device 1a).
That is, the CPU 910 functions as the server-side transmitting / receiving unit 720 by executing the magnetic data storage process in step S51 and the response information transmission process in step S69.

In step S71, the CPU 910 performs a data initialization process. Specifically, CPU 910 discards and N magnetic data _q 1 to q _N, and information generated based on the N magnetic data _q 1 to q _N such response information RES. Then, the CPU 910 ends the process shown in the flowchart.
That is, the CPU 910 functions as the data control unit 710a by executing the response information generation process in step S67 and the data initialization process in step S71.

As described above, in step S57, the server apparatus SVa according to the present embodiment has a distorted shape in which the coordinates indicated by the N pieces of magnetic data q _{1 to} q _N are distributed in the vicinity of the spherical surface S or different from the spherical surface. It is determined whether it is distributed in the vicinity of the solid SD. If it is determined that the coordinates indicated by the N pieces of magnetic data q _{1 to} q _N are distributed in the vicinity of the distorted solid SD different from the spherical surface, N pieces of magnetic data q _{1 to} q _N are obtained by executing steps S59 to S65. It is determined whether or not the coordinates indicated by the magnetic data q _{1 to} q _N exist in the vicinity of the optimum ellipsoid _VEOP .
That is, in the geomagnetism measuring apparatus according to this embodiment, the distribution shape of the coordinates indicated by the N pieces of magnetic data q _{1 to} q _N is any of a spherical shape, an elliptical surface, and a solid with a distorted shape different from the spherical surface and the elliptical surface. It is possible to discriminate whether it is appropriate to consider the shape of the object.
As a result, the geomagnetic measurement system SYSa according to the present embodiment employs these center points as offsets when the coordinates indicated by the N pieces of magnetic data q _{1 to} q _N are distributed in the vicinity of a spherical surface or an ellipsoid. By doing so, an accurate geomagnetic direction can be calculated. On the other hand, when the coordinates indicated by the N pieces of magnetic data q _{1 to} q _N are distributed in the vicinity of a distorted solid different from the spherical surface and the elliptical surface, the geomagnetic measurement system SYSa according to the present embodiment calculates the offset. In order to prevent this, it is possible to prevent inaccurate calculation of the geomagnetic direction.

  Details of the magnetic data distribution determination process, the center point calculation process, and the distortion determination process will be described below. In order to facilitate understanding, the magnetic data distribution determination process will be described after the description of the center point calculation process.

[10. Center point calculation process]
With reference to FIG. 27, the center point calculation process executed by the server apparatus SVa (CPU 910) in step S55 will be described. Central point calculation process, the coordinates indicated by the N magnetic data q ₁ to q _N supplied from the terminal device 1 (or the terminal device 1a) is, on the assumption that the distribution in the vicinity of the sphere S of radius r _S, spherical This is a process of calculating the coordinates of the center point c _S of _S. The spherical surface S is used to obtain the coordinates of the center point of the spherical surface determined so as to have the coordinates indicated by the plurality of magnetic data q _{1 to} q _{N in} the vicinity in the sensor coordinate system Σ _S of the terminal device 1 (or the terminal device 1a). to, for convenience introduced is spherical calculations are different spherical spherical S _G representing the geomagnetism Bg. Note that the vectors and coordinates described below are expressed in the sensor coordinate system Σ _S of the terminal device 1 (or the terminal device 1a) unless otherwise specified.

The calculation of the coordinates of the center point c _S of the spherical surface S having the coordinates indicated by the plurality of magnetic data q _{1 to} q _{N in} the vicinity may be applied as appropriate. For example, it may be calculated by the following method.

When the coordinates indicated by the magnetic data q _i are expressed by the equation (11) and the coordinates of the center point c _S are expressed by the following equation (72), the coordinates indicated by the plurality of magnetic data q _{1 to} q _N have the radius r _S. The presence on the spherical surface S is expressed by the following formula (71).

As shown in FIG. 27, when the coordinates indicated by the magnetic data q _i are expressed by a vector (q _i −q _C ) starting from the coordinates indicated by the center of gravity q _C of the plurality of magnetic data q _{1 to} q _N The following formula (73) can be obtained based on the formula obtained by substituting each of the coordinates indicated by the plurality of magnetic data q _{1 to} q _N with respect to (71) and the formula (71). Hereinafter, the equation shown in Equation (73) is referred to as a spherical equation. Here, the center of gravity q _C is a three-dimensional vector defined by the following equations (74) and (75). The matrix X is an N × 3 matrix shown in Expression (76), the vector j is an N-dimensional vector shown in Expression (77), and the value R _AVE is a value shown in Expression (78). It is.

The spherical equation shown in the equation (73) has a solution when all of the coordinates indicated by the plurality of magnetic data q _{1 to} q _N completely coincide on the spherical surface S centered on the center point c _S. However, considering the measurement error of the three-dimensional magnetic sensor 60 and the like, since all of the plurality of magnetic data q _{1 to} q _N do not completely coincide with the spherical surface S, the spherical equation has no solution. Therefore, the statistical method, in order to obtain a plausible solution of spherical equations, introducing a first spherical error vector [delta] _S is a vector that absorbs errors expressed by equation (79). Here, the variable vector c appearing in the equation (79) is the three-dimensional vector shown in the equation (1.e), but in this section, it is used as a variable for representing the coordinates of the center point c _S.

Vector c to the norm of the first spherical error vector [delta] _S to a minimum, in other words, coordinates, spherical S of the center point c _S represented by the vector c which minimizes the ^{_{(δ S) T (δ S}} ) It can be said that the coordinates are reasonable. Here, if the center point calculation function f _S (c) represented by the following expression (80) is defined, the coordinates represented by the vector c that minimizes the center point calculation function f _S (c) are the center point of the spherical surface S. c A reasonable value for the coordinates of _S. The coordinates of the center point c _S are calculated by the equation (81) when the 3 × 3 covariance matrix A shown in the equation (82) is regular.

As described above, three-dimensional magnetic sensor 60, when detecting only the internal magnetic field Bi and geomagnetism Bg has a sphere S, the sphere S _G representing the geomagnetism Bg, becomes almost the same spherical surface, the center point of the spherical surface S and c _S, with the center point _{c OG} of the spherical _{S G,} becomes almost the same coordinates. Therefore, when the three-dimensional magnetic sensor 60 detects only the internal magnetic field Bi and the geomagnetism Bg, the vector indicating the coordinates of the center point c _S shown in the equation (81) can be adopted as the offset c _OFF of the magnetic sensor. .

[11. Magnetic data distribution judgment process]
Below, the magnetic data distribution determination process which server apparatus SVa (CPU910) performs in step S53 is demonstrated.

In the above-described center point calculation process, in order to calculate the center point c _S of the spherical surface S, the coordinates indicated by the plurality of magnetic data q _{1 to} q _N have a three-dimensional spread in the sensor coordinate system Σ _S. Must be distributed. However, since the orientation μ of the three-dimensional magnetic sensor 60 changes when the user of the terminal device 1 (or terminal device 1a) moves the terminal device 1 (or terminal device 1a) by hand, the terminal device 1 (or terminal) If the method of moving the device 1a) is insufficient, the terminal device 1 (or the terminal device 1a) may change its posture in two dimensions instead of three. In this case, the coordinates indicated by the plurality of magnetic data q ₁ to q _N in the sensor coordinate system sigma _S is two-dimensionally distributed without a three-dimensional spread.
For example, as shown in FIG. 28, when the coordinates indicated by the plurality of magnetic data q _{1 to} q _N are two-dimensionally distributed in the vicinity of a circle π _C on the plane π of the sensor coordinate system Σ _S , the spherical surface S is Only a spherical surface having a circle π _C in the cut surface can be specified. A spherical surface having a circle π _C as a cut surface may be a spherical surface S _π1 centered on a central point c _π1 on a straight line π _L passing through the central point π _CO of the circle π _C and orthogonal to the plane π, You may be a spherical S _.pi.2 around the center point c _.pi.2 on the line [pi _L. In other words, the center point c _S of the sphere S is up to be located on the straight line [pi _L but can be identified, it is specifically not specific about what exists in which position on the line [pi _L. As described above, when the coordinates indicated by the plurality of magnetic data q _{1 to} q _N are two-dimensionally distributed, the accurate coordinates (offset c _OFF candidate coordinates are determined based on the plurality of magnetic data q _{1 to} q _N. The central point c _S can not be calculated.

To calculate the center point _{c S} of the sphere S is based on a plurality of magnetic data _q 1 to q _N, as shown in FIG. 29, indicated by a plurality of magnetic data _q 1 to q _N in the sensor coordinate system sigma _S It is necessary that the coordinates are distributed in a three-dimensional manner. In the magnetic data distribution determination process, the server device SVa (CPU 910) determines whether or not the coordinates indicated by the plurality of magnetic data q _{1 to} q _N are three-dimensionally distributed. For determining whether or not the coordinates indicated by the plurality of magnetic data q _{1 to} q _N are distributed three-dimensionally, a known method may be applied as appropriate. You may determine using A. Hereinafter, the properties of the covariance matrix A will be described.

The eigenvalues of the covariance matrix A are set to the largest eigenvalue λ ₁ , the intermediate eigenvalue λ ₂ , and the minimum eigenvalue λ ₃ in descending order, and the eigenvectors normalized to the magnitude 1 corresponding to each eigenvalue are represented by u ₁ , u ₂ , u ₃ . In addition, a vector representing the magnetic data q _i in the centroid coordinate system Σ _C having the centroid q _C as an origin is represented as ^C q _i . At this time, the eigenvalue λ _j (j = 1, 2, 3) is equal to the variance σ ² _j in the eigenvector u _j direction.
As shown in FIG. 29, placing each eigenvector _u 1 ~u ₃ as the starting point the origin _{q C} of the center of gravity coordinates sigma _C. At this time, for example, consider the case of j = 1. The eigenvalue λ ₁ is the average of the square (L _i1 ) ² of the length L _{i1 obtained} by projecting the vector ^C q _i onto the eigenvector u ₁ with respect to the N pieces of magnetic data ^C q _i (i = 1, 2,... N). Is equal to That is, the eigenvalue λ _j is determined by how far the N pieces of magnetic data ^C q _i are away from the center of gravity q _{C in the} eigenvector u _j direction, that is, the distribution of coordinates indicated by the plurality of magnetic data q _{1 to} q _N is the eigenvector. u represents the extent of spread in the _j direction.

Direction of the eigenvector u ₃ corresponding to the minimum eigenvalue lambda ₃ is the smallest direction spread of the distribution of the coordinate indicated by the plurality of magnetic data q ₁ to q _N, the minimum eigenvalue lambda _3, a plurality of magnetic data q ₁ ~ spread of the distribution of the coordinate indicated by q _N is an index indicating the degree of spread in the smallest direction. Therefore, in order for the coordinates indicated by the plurality of magnetic data q _{1 to} q _N to be three-dimensionally distributed, the value of the minimum eigenvalue λ ₃ must be equal to or greater than a certain threshold value (dispersion allowable value) λ _0. That's fine.

In the magnetic data distribution determination process, if the minimum eigenvalue λ ₃ of the covariance matrix A is greater than or equal to the threshold λ ₀ , the server device SVa (CPU 910) has a sufficient distribution of coordinates indicated by the plurality of magnetic data q _{1 to} q _N. If it is determined to be three-dimensional, the process proceeds to the center point calculation process in step S55 described above. On the other hand, when the minimum eigenvalue λ ₃ is less than the threshold λ ₀ , the server device SVa (CPU 910) determines that the coordinates indicated by the plurality of magnetic data q _{1 to} q _N do not have a three-dimensional spread. Then, the process proceeds to the data initialization process in step S71.

[12. Distortion judgment processing]
The server device SVa (CPU 910) executes the first distortion determination process in step S57, and executes the second distortion determination process in step S65. The second distortion determination process is performed except that the coordinates indicated by the plurality of converted magnetic data s _{1 to} s _N are used as the plurality of input coordinates instead of the coordinates indicated by the plurality of magnetic data q _{1 to} q _N. This is the same process as the first distortion determination process.
In the following, Section 12.1 describes the first distortion determination process, and Section 12.2 describes the second distortion determination process.

[12.1. First distortion determination process]
In the distortion determination process, it is assumed that a plurality of input coordinates, that is, the coordinates indicated by the plurality of magnetic data q _{1 to} q _N are distributed in the vicinity of the surface of the distorted solid SD different from the spherical surface. As shown in FIG. 30, the solid SD is a figure obtained by adding the spherical surface (second spherical surface) S ₂ and the distortion error vector k (E), and is represented by the following equation (83). The Hereinafter, the equation shown in Equation (83) is referred to as a solid equation.
Here, the spherical surface S ₂ is a spherical surface centered on the central point (the central point of the second spherical surface) c _S2 , and the component “X (c−q _C ) other than the distortion error vector k (E) in the solid equation. ) -J ".
The distortion error vector k (E) is an N-dimensional vector represented by the following equation (84). However, the distortion evaluation matrix E is a 3 × 3 symmetric matrix expressed by the following equation (85), and the reference point w _KE is a three-dimensional vector expressed by the following equation (86). Further, 0 _N appearing on the right side of the equation (83) is an N-dimensional zero vector. Variable vector c appearing in the left-hand side of equation (83) is a three-dimensional vector represented by the formula (1.e), in this section, it is used as a variable for representing the center point c _S2 spherical S _2.
Distortion determination process, among the three-dimensional equations, by assessing the magnitude of the component k (E) representing the distortion, the three-dimensional SD shape, and a spherical S ₂ shapes are evaluated for how well different . Specifically, the magnitude of the influence of the distortion error vector k (E) in the three-dimensional equation is evaluated based on the distortion evaluation value g _D (E) represented by the expressions (93) and (94) described later.

Of the N elements constituting the N-dimensional distortion error vector k (E), the element ke (q _i −w _KE ) in the i-th row is a function ke (v expressed by the following equation (87). ) _Is substituted by a vector (q _i −w _KE ) representing the coordinates indicated by the magnetic data q _i starting from the coordinates indicated by the reference point w _KE . The function ke (v) is a function expressed in a quadratic form in which the distortion evaluation matrix E shown in Expression (85) is a coefficient matrix and the three elements of the vector v shown in Expression (88) are variables. That is, the function ke (v) represents the inner product of the vector v and the vector Ev obtained by converting the vector v by the distortion evaluation matrix E.
In the first distortion determination process, the center point c _S of the spherical surface _S is adopted as the reference point w _KE as shown in the following equation (89).

Considering the measurement error of the three-dimensional magnetic sensor 60, all the coordinates indicated by the plurality of magnetic data q _{1 to} q _N do not exist at positions that completely coincide with the solid SD. The solid equation shown has no solution. Therefore, in order to obtain a plausible value as a solution of the solid equation by a statistical method, a solid error vector δ _SD that is a vector that absorbs the error represented by the equation (90) is introduced. The stereo error vector δ _SD is obtained by adding a second spherical error vector δ _S2 expressed by the following equation (91) and a distortion error vector k (E). The second spherical error vector δ _S2 is a component corresponding to the component “X (c−q _C ) −j” representing the spherical surface S ₂ in the solid equation.
The three-dimensional error vector δ _SD is an N-dimensional vector that represents an error between the coordinates indicated by the plurality of magnetic data q _{1 to} q _N and the surface of the three-dimensional SD. The variable vector c and the distortion evaluation matrix E that minimize the norm of the stereo error vector δ _SD , in other words, the variable vector c that minimizes the distortion evaluation function f _SD (E, c) represented by the following equation (92) A three-dimensional SD having the coordinates indicated by the plurality of magnetic data q _{1 to} q _{N in} the vicinity of the surface is represented by the strain evaluation matrix E.

Hereinafter, the property of the stereo error vector δ _SD shown in the equation (90) will be described in comparison with the property of the first spherical error vector δ _S shown in the equation (79).
First, the first spherical error vector δ _S is a vector for absorbing the error between the coordinates indicated by the plurality of magnetic data q _{1 to} q _N and the spherical surface S. Each element of the first row ~N row constituting the first spherical error vector [delta] _S is an independent variable. Thus, the first spherical error vector [delta] _S, in the case of absorbing the error between the coordinates and the sphere S is represented by a plurality of magnetic data q ₁ to q _N, coordinates and spherical showing multiple magnetic data q ₁ to q _N Each of the N errors from S is a value that is independent of each other and that N is determined independently of each other. That, the N error expressed by a first spherical error vector [delta] _S is for each determined probabilistically independent, as a whole the N error has symmetry, and the direction-dependent There is no white noise.
That is, the center point calculation process, the coordinates indicated by the plurality of magnetic data q ₁ to q _N, the error between the sphere S represented by the first spherical error vector [delta] _S is a white noise, the first spherical error vector [delta] _S Is a process for obtaining the center point c _S of the spherical surface S that minimizes.

On the other hand, the solid error vector δ _SD is a vector represented by the sum of the second spherical error vector δ _S2 and the distortion error vector k (E), and the coordinates indicated by the magnetic data q _{1 to} q _N and the solid SD It is a vector that absorbs errors.
The second spherical error vector [delta] _S2, similarly to the first spherical error vector [delta] _S, the coordinates indicated by the magnetic data q ₁ to q _N, the error between the sphere S _2, a vector representing a white noise.
On the other hand, the distortion error vector k (E) is a vector having each function of the function ke (v) in the three-variable quadratic form shown in the equation (87). The quadratic form of three variables is a function in which the variable is composed of quadratic terms, and various curved surfaces in a three-dimensional space, for example, straight lines, planes, cylindrical surfaces, spherical surfaces, ellipsoidal surfaces, conical surfaces, and one leaf A hyperboloid, a two-leaf hyperboloid, and various parabolas can be drawn. Therefore, the distortion error vector k (E) is not independent of each of the N errors between the coordinates indicated by the magnetic data q _{1 to} q _N and the spherical surface S _2. It is expressed as a value having a constraint that it exists on a curved surface in a three-dimensional space represented by the same function ke (v).
Thus, the three-dimensional error vector [delta] _SD, N number of error between the coordinates and spherical _{S 2} indicated by each magnetic data _q 1 to q _N, a second spherical error vector [delta] _S2 is a white noise, the spherical _{S 2} And a distortion error vector k (E) representing the distortion from the above.

When the influence of the distortion error vector k (E) in the solid equation is small enough to be ignored, the solid SD and the spherical surface S ₂ can be regarded as equal figures, and the distortion evaluation function f defined in the equation (92) _SD (E, c) and the center point calculation function f _S (c) defined in Equation (80) can be regarded as equal functions. At this time, the solid SD obtained by minimizing the distortion evaluation function f _SD (E, c) and the spherical surface S obtained by minimizing the center point calculation function f _S (c) are regarded as equal. Therefore, it can be considered that the coordinates indicated by the plurality of magnetic data q _{1 to} q _N distributed near the surface of the solid SD are also distributed near the spherical surface S. As described above, if you regarded as three-dimensional SD shape spherical, the coordinates indicated by the center point of the sphere represented by the three-dimensional SD, and the center point c _OG of the spherical S _G, it can be considered matching. Thus, a coordinate indicated by the center point c _S of the spherical S, the coordinate indicated by the central point c _OG of the spherical S _G can be regarded as equal.
Thus, when the influence of the distortion error vector k in the three-dimensional equation (E) is small, the coordinates indicated by the center point c _S of the spherical S calculated at the center point calculating unit, coordinates indicated by the central point c _OG of the spherical S _G to be considered equal if the coordinates indicated by the center point c _S can be adopted as the offset c _OFF.

Conversely, when the influence of the strain error vector k (E) in the solid equation is large, as shown in FIG. 30, the error between the coordinates indicated by the plurality of magnetic data q _{1 to} q _N and the spherical surface S ₂ is white noise. there second spherical error vector [delta] _S2, is absorbed by the distortion error vector representative of the distortion from the spherical S ₂ k (E). In this case, the shape of the solid SD has a shape different from the spherical surface.
Further, when the influence of the strain error vector k (E) in the solid equation is large, the strain evaluation function f _SD (E, c) and the center point calculation function f _S (c) are different functions. In this case, as shown in FIG. 31, the solid SD obtained by minimizing the distortion evaluation function f _SD (E, c) and the spherical surface S obtained by minimizing the center point calculation function f _S (c) are: The coordinates indicated by the plurality of magnetic data q _{1 to} q _{N that} are different figures and distributed in the vicinity of the surface of the solid SD cannot be regarded as being distributed in the vicinity of the spherical surface S.
The center point calculation process can be regarded as being equal to the center point c _OG of the spherical surface S _{G on} the assumption that the coordinates indicated by the plurality of magnetic data q _{1 to} q _N exist in the vicinity of the spherical surface S. it is a process of calculating the coordinates indicated by the center point c _S. Therefore, when the coordinates indicated by the plurality of magnetic data q _{1 to} q _N do not exist in the vicinity of the spherical surface S, the center point c _S and the center point c _OG do not match. In this case, a vector indicating the coordinates of the center point c _S cannot be adopted as the offset c _OFF .

Thus, by evaluating the magnitude of the influence of the distortion error vector k (E) in the solid equation, it is possible to determine whether or not the center point c _S of the spherical surface S can be adopted as the offset c _OFF. is there. Hereinafter, a method for evaluating the magnitude of the influence of the distortion error vector k (E) in the solid equation will be described.

Here, distortion evaluation values g _D (E) shown in the following equations (93) and (94) are defined as evaluation values for evaluating the magnitude of the influence of the distortion error vector k (E) in the solid equation. The distortion evaluation value g _D (E) is an absolute value of the maximum eigenvalue λ _E1 having the maximum absolute value among the three eigenvalues of the distortion evaluation matrix E (that is, the norm of the distortion evaluation matrix E).
If the strain evaluation value g _D (E) is a small value equal to or less than the strain allowable value δ ₀ , the solid SD and the spherical surface S ₂ can be regarded as the same figure, and distributed near the surface of the solid SD. It can be considered that the coordinates indicated by the plurality of magnetic data q _{1 to} q _N are distributed in the vicinity of the spherical surface S. In this case, a vector representing the coordinates of the center point c _S of the spherical surface S obtained by the center point calculation process can be adopted as the offset c _OFF of the magnetic sensor.

As described above, each element of the distortion error vector k (E) includes a vector (q _i −w _KE ) representing the coordinates indicated by the magnetic data q _i from the coordinates of the reference point w _KE , and the vector (q _i − w _KE ) is an inner product with the vector E (q _i −w _KE ) converted by the distortion evaluation matrix E.
That is, the absolute value of a plurality of elements constituting the distortion error vector k (E) represented the coordinates indicated by the magnetic data q _i corresponding to the element from the coordinates indicated by the reference point w _KE vector (q _i -w _KE ) And the eigenvector u _E1 corresponding to the maximum eigenvalue λ _E1 having the maximum absolute value among the three eigenvalues of the distortion evaluation matrix E are parallel to each other.
Accordingly, an eigenvector corresponding to the direction represented from the coordinates indicated by the reference point w _KE and the maximum eigenvalue λ _E1 of the distortion evaluation matrix E in a region where there are many magnetic data q _i indicating coordinates having a large error from the spherical surface S _2. When each component of the strain evaluation matrix E is determined so that the direction of u _E1 is equal, the strain error vector k (E) is an error between the coordinates indicated by the plurality of magnetic data q _{1 to} q _N and the spherical surface S _2. Express the size of.
The strain evaluation matrix E that minimizes the strain evaluation function f _SD (E, c) is determined so as to accurately represent the error between the coordinates indicated by the plurality of magnetic data q _{1 to} q _N and the spherical surface S ₂ . Thus, each component of the distortion evaluation matrix E, the table from the maximum eigenvalue λ and orientation of the eigenvector u _E1 corresponding to _E1, the coordinates indicated by the reference point w _KE regions error is large magnetic data exist many from spherical S ₂ The direction of the vector is determined so as to approach. The maximum eigenvalue λ _E1 of the distortion evaluation matrix E is a value representing the magnitude of the error for the magnetic data q _i having a large error from the spherical surface S ₂ .
In the present embodiment, the distortion evaluation value g _D (E) indicating the degree of difference in shape between the solid SD and the spherical surface is determined based on the maximum eigenvalue λ _E1 of the distortion evaluation matrix E. Therefore, the distortion evaluation value g _{D (E),} and magnetic data q _i of the distance from the sphere S ₂ exhibits a large coordinate, an error in the size of the spherical S _2, i.e., the difference in shape of the three-dimensional SD and the spherical It is possible to evaluate the degree of.

Hereinafter, a method for obtaining the strain evaluation value g _D (E) will be described.
First, the function ke (v) shown in the equation (87) can be transformed into the following equation (95). Further, the element ke (q _i −w _KE ) of the i-th row of the distortion error vector k (E) is expressed by the 6-dimensional vector ke ₂ (i) expressed by the equation (97) and the equation (98). By using a 6-dimensional vector e _{E in} which the components of the distortion evaluation matrix E represented are arranged, the following equation (96) can be obtained.

We introduce the matrix _{X 2} represented by the formula (99). The matrix X ₂ is generated by arranging a vector of 1 row and 6 columns obtained by transposing the vector ke ₂ (i) and a vector of 1 row and 3 columns obtained by transposing the vector (q _i −q _C ) in each row. It is a matrix with 9 rows.

The distortion evaluation function f _SD (E, c) shown in the equation (92) is transformed into a function g _SD (e) expressed in the following equation (100) by using the matrix X ₂ . Note that the vector e is a nine-dimensional vector in which the vector e _E and the three-dimensional vector e _X shown in the following equation (102) are arranged as shown in the following equation (101).

The solution e = e ₀ that minimizes the function g _SD (e) shown in the equation (100) applies the Gaussian elimination method, the Cholesky decomposition method, or the like to the simultaneous equations shown in the following equation (103). Is required. Equation (103) is a normal equation calculated by applying the least square method to equation (100).

Based on the solution e ₀ obtained in this way, the distortion evaluation matrix E of Expression (85) is restored. Then, the value of the strain evaluation value g _D (E) shown in the equation (93), that is, the norm of the strain evaluation matrix E is obtained, and the value of the strain evaluation value g _D (E) is equal to or less than the strain allowable value δ _0. It is determined whether or not. Note that the norm of the distortion evaluation matrix E is equal to the absolute value of the eigenvalue λ _E1 having the maximum absolute value among the three eigenvalues of the distortion evaluation matrix E, and thus can be obtained by the Jacobian method or the power method.

When the strain evaluation value g _D (E) is equal to or less than the strain allowable value δ ₀ , the vector representing the coordinates of the center point c _S of the spherical surface S can be set as the offset c _OFF . In this case, the server device SVa (CPU 910) advances the process to the response information generation process in step S67, and adopts the center point c _S of the spherical surface _S as the response center point c _SA .
On the other hand, when the strain evaluation value g _D (E) is larger than the strain allowable value δ ₀ , a vector representing the coordinates of the center point c _S of the spherical surface S cannot be adopted as the offset c _OFF . In this case, the server device SVa (CPU 910) advances the process to the initial ellipsoid generation process in step S59.

As described above, the server device SVa (CPU 910) determines the degree of difference in shape between the solid SD and the spherical surface having the coordinates indicated by the plurality of magnetic data q _{1 to} q _{N in} the _first distortion determination process in step S57. To evaluate. If the difference in shape between the solid SD and the spherical surface is small enough to be ignored, the solid SD can be regarded as a spherical surface. Therefore, a vector representing the coordinates of the center point c _S of the spherical surface S is set as an offset c _OFF. Can be adopted. In this case, since it can be considered that the soft iron effect does not occur, the geomagnetism measurement system SYSa can calculate the geomagnetism Bg without performing ellipse correction. That is, in this case, the server device SVa performs the processes shown in steps S59 to S65 (the initial ellipsoid generation process, the optimal ellipsoid generation process, the ellipsoidal sphere conversion process, and the second distortion determination process), Response information RES can be generated.
That is, the geomagnetism measurement system SYSa according to the present embodiment determines the presence or absence of the soft iron effect by performing the first distortion determination process, and if it is determined that the soft iron effect does not occur, the ellipse correction The direction of the geomagnetism Bg is calculated without performing. Thereby, the geomagnetism measurement system SYSa according to the present embodiment can greatly reduce the calculation load related to the calculation of the direction of the geomagnetism Bg.

When the strain evaluation value g _D (E) is equal to or less than the strain allowable value δ ₀ , the server device SVa (CPU 910) uses the center point c _S of the spherical surface _S as the response center point in the response information generation process in step S67. Although adopted as c _SA , the center point c _S2 of the spherical surface S ₂ may be adopted as the response center point c _SA . When the value of the strain evaluation value g _D (E) is equal to or less than the threshold value δ ₀ , the coordinates indicated by the center point c _S of the spherical surface S and the coordinates indicated by the center point c _S2 of the spherical surface S ₂ are substantially equal. This is because any of them can be adopted as the offset c _OFF .
Note that the coordinates of the center point c _S2 of the spherical surface S ₂ are the three-dimensional vectors corresponding to e _X in the equation (101) among the solutions e ₀ that minimize the function g _SD (e) in the equation (102). When substituted, it is calculated as a variable vector c.

[12.2. Second distortion determination process]
With reference to FIG. 32, the second distortion determination process performed by the server apparatus SVa (CPU 910) in step S65 will be described.
In the second distortion determination process, when the determination result in step S57 (first distortion determination process) is negative, that is, as shown in FIG. 32A, a plurality of pieces of magnetic data q _{1 to} q _N are indicated. If the shape of the three-dimensional SD having coordinates in the vicinity is determined to be a different distorted shape from spherical, as shown in FIG. 32 (B), the coordinates indicated by the plurality of the converted magnetic data s ₁ ~s _N This is a process for evaluating the distribution shape. That is, the second distortion determination process uses coordinates indicated by a plurality of converted magnetic data s _{1 to} s _N as a plurality of input coordinates.

In the first distortion determination process, when it is evaluated that the shape of the solid SD having the coordinates indicated by the plurality of magnetic data q _{1 to} q _N is a distorted shape different from the spherical surface, the cause of the distortion of the solid SD However, there may be a soft iron effect instead of the non-uniform external magnetic field Bx. Inhomogeneous external magnetic field Bx is absent, and, if the soft iron effect occurs, stereo SD is having coordinates indicated by the plurality of magnetic data q ₁ to q _N in the vicinity, the same shape as the ellipsoid V _E Can be considered as having In this case, the coordinates indicated by the plurality of magnetic data _q 1 to q _N, coordinates indicated by the optimum ellipsoidal correction matrix _T after multiple conversion obtained by converting the _OP magnetic data _s 1 ~s _N, spherical _{S EOP} vicinity to distribution, the shape of the three-dimensional SD _E with coordinates indicated by the plurality of the converted magnetic data s ₁ ~s _N in the vicinity can be regarded as spherical.
Conversely, when there is a non-uniform external magnetic field Bx, as shown in FIG. 32A, the solid SD having the coordinates indicated by the plurality of magnetic data q _{1 to} q _N is distorted differently from the spherical surface. It has a shape and a shape different from the elliptical surface. In this case, the coordinates indicated by the plurality of magnetic data _q 1 to q _N, coordinates indicated by the optimum ellipsoidal correction matrix _T after multiple conversion obtained by converting the _OP magnetic data _s 1 ~s _N, FIG. 32 (B distributed in the vicinity of the three-dimensional SD _E of different distorted shape from the spherical S _EOP as shown in).

Thus, the server SVa (CPU 910) is, in the second distortion determination process in step S65, the three-dimensional SD _E with coordinates indicated by the plurality of the converted magnetic data _s 1 ~s _N adjacent shape and spherical (e.g. By evaluating the degree of difference from the shape of the spherical surface S _EOP ), the shape of the solid SD having the coordinates indicated by the plurality of magnetic data q _{1 to} q _N and the elliptical surface (for example, the elliptical surface V _E ) Evaluate the degree of difference from the shape.

Incidentally, the shape of the three-dimensional SD _E, if it can be regarded as equal to the spherical shape, but soft iron effect occurs, the influence of non-uniform external magnetic field Bx can be regarded as there is no . In this case, the geomagnetic measurement system SYSa, by performing the elliptical correction using the optimum center point c _EOP, it is possible to calculate the direction of the geomagnetism Bg. That is, in this case, the server device SVa (CPU 910) employs the optimum center point c _EOP as the response center point c _SA in the response information generation process of step S67.
On the other hand, as shown in FIG. 32 (B), the shape of the three-dimensional SD _E, if the spherical shape is evaluated as a shape having a different strain, a plurality of magnetic data q ₁ to q _N is uneven It can be considered that it is influenced by the external magnetic field Bx. In this case, the geomagnetism measurement system SYSa cannot calculate the direction of the geomagnetism Bg. That is, in this case, the server apparatus SVa (CPU 910) ends the process shown in the flowchart of FIG. 26 without generating the response information RES.

Hereinafter, specific processing contents of the second distortion determination processing will be described.
As described above, the second distortion determination process uses a plurality of converted magnetic data s _{1 to} s instead of using the coordinates indicated by the plurality of magnetic data q _{1 to} q _N as the plurality of input coordinates used for the distortion determination process. _The process is the same as the first distortion determination process except that the coordinates indicated by _N are used.
That is, the second distortion determination process is performed with respect to the coordinates indicated by the plurality of magnetic data q _{1 to} q _N used in the first distortion determination process, by a plurality of expressions shown in the following expressions (104) and (105). This is a process of executing the first distortion determination process described in section 12.1 after substituting the coordinate values indicated by the converted magnetic data s _{1 to} s _N. In this case, among values such as various matrices and vectors used in the first distortion determination process, values calculated based on the plurality of magnetic data q _{1 to} q _N are a plurality of values in the second distortion determination process. It is calculated based on the converted magnetic data s _{1 to} s _N. Specifically, among the values used in the distortion determination process, the values calculated in the center point calculation process described in section 10, for example, the matrix X that appears in the solid equation shown in the equation (83), are a plurality of magnetic data. Instead of the coordinates indicated by q _{1 to} q _N , the calculation is performed using the coordinates indicated by the plurality of post-conversion magnetic data s _{1 to} s _N. In addition, the second distortion determination processing is performed by using a plurality of expressions shown in the following equation (106) instead of the center of gravity q _C (see equation (74)) calculated based on the plurality of magnetic data q _{1 to} q _N. The center of gravity s _C calculated based on the coordinates indicated by the converted magnetic data s _{1 to} s _N is used. Further, in the second distortion determination process, instead of adopting the center point c _S calculated based on the plurality of magnetic data q _{1 to} q _N as the reference point w _KE (see the formula (89)), the following As shown in Expression (107), the optimum center point c _EOP calculated based on the plurality of converted magnetic data s _{1 to} s _N is employed.
In the second strain determination process, the strain obtained by minimizing the value of the strain evaluation function f _SD (E, c) determined based on the coordinates indicated by the plurality of converted magnetic data s _{1 to} s _N in this way. by the evaluation matrix E calculates a distortion evaluation value g _{D (E),} to assess the degree of difference in the shape of a three-dimensional SD _E and spherical.

When the strain evaluation value g _D (E) calculated based on the coordinates indicated by the plurality of converted magnetic data s _{1 to} s _N is equal to or less than the strain allowable value δ ₀ , the soft iron effect is generated, but is not uniform. It can be considered that there is no influence of the external magnetic field Bx. In this case, the server apparatus SVa (CPU 910) employs the optimum center point c _EOP as the response center point c _SA in the response information generation process of step S67. In this case, the server device SVa (CPU 910) is calculated in the second distortion determination process may be employed center point _{c S2} of the spherical _{S 2} in response center point _{c SA.}
On the other hand, when the strain evaluation value g _D (E) calculated based on the coordinates indicated by the plurality of converted magnetic data s _{1 to} s _N is larger than the strain allowable value δ ₀ , the non-uniform external magnetic field Bx It can be considered that there is an influence. In this case, a vector representing the coordinates of the optimum center point c _EOP of the spherical surface S _EOP cannot be adopted as the offset c _OFF . Therefore, in this case, the server apparatus SVa (CPU 910) ends the process shown in the flowchart of FIG. 26 without generating the response information RES.
In the present embodiment, a distortion allowable value [delta] ₀ in the first distortion determining process, but is set to a value equal to the distortion tolerance [delta] ₀ in the second distortion determination process, it is set to different values Good.

[13. Conclusion of Second Embodiment]
As described above, the geomagnetism measurement system SYSa according to the second embodiment includes the distortion determination unit 540, so that the solid SD and the spherical surface having the coordinates indicated by the plurality of magnetic data q _{1 to} q _{N in} the vicinity. Evaluate the degree of shape difference.
When the shape of the solid SD can be regarded as a spherical surface, the geomagnetism measurement system SYSa can calculate the direction of the geomagnetism Bg by simple calculation. Specifically, in the geomagnetism measurement system SYSa, when the strain determination unit 540 determines that the coordinates indicated by the plurality of magnetic data q _{1 to} q _N are distributed in the vicinity of the spherical surface, the center point calculated by the center point calculation unit 640 the vector representing the coordinates of c _S, can be adopted as the offset _{c OFF.} The geomagnetic measurement system SYSa includes a coordinate indicated by the center point c _S, based on the coordinates indicated by the magnetic data q _i, calculate the direction of the geomagnetism Bg by a simple calculation.
As described above, the geomagnetism measurement system SYSa according to the second embodiment performs ellipse correction when the three-dimensional magnetic sensor 60 is mounted on the terminal device 1a that does not include a soft magnetic material and the soft iron effect does not occur. Without calculating the direction of the geomagnetism Bg, the calculation load can be reduced.

Further, in the geomagnetism measurement system SYSa according to the second embodiment, the solid SD having the coordinates indicated by the plurality of magnetic data q _{1 to} q _N is a spherical shape, an elliptical surface, and a distorted shape different from both the spherical surface and the elliptical surface. A distortion shape determination unit 500 (the ellipsoidal surface correction unit 200, the ellipsoidal spherical surface conversion unit 520, and the distortion determination unit 540). The geomagnetism measurement system SYSa, when the distortion determination unit 540 determines that the shape of the solid SD having the coordinates indicated by the plurality of magnetic data q _{1 to} q _N is a distorted shape different from the spherical surface, to assess the degree of difference in the shape of a three-dimensional SD _E spherical having a coordinate indicated by the plurality of the converted magnetic data s ₁ ~s _N calculated in ellipsoidal spherical conversion unit 520 in the vicinity of the three-dimensional SD strain It is discriminated whether this is due to the soft iron effect or due to the non-uniform external magnetic field Bx.
When the shape of the solid SD _E is a distorted shape different from the spherical surface, that is, when the cause of the distortion of the solid SD is the non-uniform external magnetic field Bx, the geomagnetic measurement system SYSa The offset c _OFF is prevented from being calculated based on the coordinates indicated by the plurality of magnetic data q _{1 to} q _N measured under the influence of the magnetic field Bx.
On the other hand, when the shape of the three-dimensional SD _E is that regarded as a spherical, i.e., has occurred soft iron effect, and, if there is no influence of non-uniform external magnetic field Bx, the geomagnetic measurement system SYSa, the optimum center point c The orientation of the geomagnetism Bg can be calculated based on the coordinates indicated by _EOP , the optimum ellipsoidal correction matrix T _OP , and the coordinates indicated by the magnetic data q _i output from the three-dimensional magnetic sensor 60.
Thus, the geomagnetic measurement system SYSa is provided with the distortion shape determination unit 500 (ellipsoid correction unit 200, ellipsoidal spherical conversion unit 520 and the distortion determination section 540,), a plurality of magnetic data _q 1 to q _N It is determined whether the solid SD having the coordinates shown in the vicinity is a spherical surface, an ellipsoid, or a solid with a distorted shape different from both the spherical surface and the ellipsoid, and the inaccurate geomagnetism Bg due to an inaccurate offset c _OFF is determined. Calculation can be prevented.

Further, organic geomagnetic measurement system SYSa according to the second embodiment is provided with the distribution determining unit 620, a coordinate indicated by the plurality of magnetic data q ₁ to q _N is a three-dimensional expanse in the sensor coordinate system sigma _S It can be determined whether or not distributed.
Thereby, in the geomagnetism measurement system SYSa, when the coordinates indicated by the plurality of magnetic data q _{1 to} q _N are two-dimensionally or one-dimensionally distributed, the center point calculation unit 640 determines the coordinates of the center point c _S. It is possible to prevent calculation.
That is, the geomagnetism measurement system SYSa according to the present embodiment can prevent the inaccurate center point c _{S from} being adopted as the offset c _OFF , and can prevent the unnecessary process from being executed in advance. The load can be reduced.
In addition, when the coordinates indicated by the plurality of magnetic data q _{1 to} q _N are distributed two-dimensionally or one-dimensionally, an elliptical surface is obtained from the shape of the distribution of coordinates indicated by the plurality of magnetic data q _{1 to} q _N. It is often difficult to specify the shape of the. In such a case, the geomagnetism measurement system SYSa according to the present embodiment prevents the ellipsoid correction unit 200 from performing ellipse correction, thereby preventing unnecessary processing from being performed and processing load. Can be reduced.

In addition, the geomagnetism measurement system SYSa according to the second embodiment includes a magnetic data distribution determination process, a center point calculation process, a distortion determination process (a first distortion determination process, a second distortion determination process), an initial ellipsoid generation process, And the optimal ellipsoid generation process is executed in the server device SVa. These processes are processes with a larger load than the approximate center point calculation process for calculating the approximate center point _cSB by solving the quaternary linear simultaneous equations.
Since the geomagnetism measurement system SYSa according to the second embodiment performs all computations with a large processing load in the server device SVa, the processing load in the terminal device 1 (or the terminal device 1a) can be kept small. That is, the geomagnetism measurement system SYSa according to the present embodiment has a limitation in the processing capability of the CPU provided in the terminal device 1 (or the terminal device 1a), or a case in which the memory capacity is limited. The direction of the geomagnetism Bg can be calculated accurately and at high speed.

<C. Modification>
The present invention is not limited to the above-described embodiments, and for example, the following modifications are possible. Also, two or more of the modifications shown below can be appropriately combined within a consistent range.

(1) Modification 1
In the second embodiment described above, the reference point w _KE used for the distortion error vector k (E) is the center point c _S shown in Expression (89) or the optimum center point c _EOP shown in Expression (107). However, the present invention is not limited to such a form, and the center of gravity q _C shown in Expression (74) or the center of gravity s _C shown in Expression (106) is used as the reference point w _KE. It may be adopted.
Each component of the distortion evaluation matrix E, when viewed from the coordinates indicated by the reference point w _KE, the direction of the eigenvector u _E1 corresponding to the largest eigenvalue lambda _E1 distortion evaluation matrix E, an error is large magnetic data q from spherical S ₂ A direction indicating a region where _i (or converted magnetic data s _i ) is present is determined so as to approach. In addition, the maximum eigenvalue λ _E1 of the distortion evaluation matrix E is the coordinates of the magnetic data q _i (or converted magnetic data s _i ) present in the direction of the eigenvector u _E1 and the spherical surface S _{2 when} viewed from the reference point w _KE. Is a value representing the magnitude of the error.
Thus, setting the reference point _{w KE} to any value, the coordinates indicated by the plurality of magnetic data _q 1 to q _N (or more converted magnetic data _s 1 ~s _N), from the reference point _{w KE} In the case of wide distribution as seen, it is possible to evaluate the degree of difference in shape between the solid SD (or solid SD _E ) and the spherical surface S ₂ by the distortion evaluation matrix E.

(2) Modification 2
In the second embodiment and the modification described above, the first distortion determination process and the second distortion determination process are both calculated based on the distortion error vector k (E) using one reference point w _KE. Although the degree of difference in shape between the solid SD (or the solid SD _E ) and the spherical surface is evaluated based on the strain evaluation value g _D (E), the present invention is not limited to such a form. Two distortion evaluation values g _D (E) are calculated from two different distortion error vectors k (E) calculated using the reference point w _KE , and the shapes of the solid SD (or the solid SD _E ) and the spherical surface are calculated. The degree of difference may be evaluated.
For example, the second distortion determination process, first, the difference in shape of the three-dimensional SD _E and the spherical based on the optimum center point c distortion evaluation value was calculated employing the reference point w _KE the _EOP g _{D (E)} After that, the degree of difference in shape between the solid SD _E and the spherical surface is evaluated based on the distortion evaluation value g _D (E) calculated by adopting the center of gravity s _C as the reference point w _KE. Also good. In this case, in both of twice evaluation, if the shape of the three-dimensional SD _E can be regarded as a spherical shape, it may be positive results of the distortion determination process.
In this way, using two reference points w _KE , the magnitude of the error between the coordinates indicated by the plurality of magnetic data q _{1 to} q _N (or the plurality of converted magnetic data s _{1 to} s _N ) and the spherical surface S _2. By evaluating the _height , the degree of difference in shape between the solid SD (or the solid SD _E ) and the spherical surface can be accurately evaluated as compared with the case where only one reference point w _KE is used.

(3) Modification 3
In the second embodiment and the modification described above, the geomagnetic measurement system performs both the first distortion determination process and the second distortion determination process, but the present invention is not limited to such a form. Only one of the first distortion determination process and the second distortion determination process may be performed.
For example, when the geomagnetism measurement system performs only the first distortion determination process, whether or not the shape of the solid SD having the coordinates indicated by the plurality of magnetic data q _{1 to} q _{N in} the vicinity can be regarded as a spherical surface. Therefore, it is possible to determine whether or not the soft iron effect has occurred. When the soft iron effect does not occur, the geomagnetism measurement system changes the direction of the geomagnetism Bg without performing the initial ellipsoid generation process, the optimum ellipsoid generation process, the ellipsoid spherical surface conversion process, and the second distortion determination process. Since it can be calculated, the calculation load can be reduced.

Further, for example, a geomagnetic measurement system, when performing only the second distortion determination process, the shape of the three-dimensional SD _E with coordinates indicated by the plurality of the converted magnetic data s ₁ ~s _N near spherical and regarded Can be determined.
When the determination result in the second distortion determination process is affirmative, the shape of the solid SD having the coordinates indicated by the plurality of magnetic data q _{1 to} q _{N in} the vicinity can be regarded as an ellipsoid, The geomagnetism measurement system performs the ellipse correction using the optimum ellipsoid correction matrix T _OP and the optimum center point c _EOP on the coordinates indicated by the magnetic data q _i output from the three-dimensional magnetic sensor 60, thereby _obtaining the geomagnetism. The direction of Bg can be calculated. Incidentally, since the ellipsoidal include spherical (for example, if three eigenvalues having the ellipsoidal correction matrix T _E are all 1, etc.), the geomagnetic measurement system, regardless of the occurrence of soft iron effect, The direction of the geomagnetism Bg can be calculated.
On the other hand, when the determination result in the second distortion determination process is negative, the plurality of magnetic data q _{1 to} q _N are affected by the non-uniform external magnetic field Bx, and thus the geomagnetism measurement system has a plurality of magnetic data. The offset c _OFF is prevented from being calculated based on q _{1 to} q _N.

(4) Modification 4
In the embodiments and modifications described above, the geomagnetic measurement system comprises a ellipsoidal optimum correction value generation unit 400, based on the optimum ellipsoidal correction matrix T _OP and the optimum center point c _EOP, the coordinates indicated by the magnetic data q _i The ellipse correction to be converted into the coordinates indicated by the converted magnetic data s _i is performed, but the present invention is not limited to such a form, and the geomagnetism measurement system includes an ellipsoidal optimal correction value generation unit 400. It may be configured without. In this case, the geomagnetism measurement system may employ the initial ellipsoid correction matrix T ₀ and the initial center point c _E0 calculated by the ellipsoid initial correction value generation unit 300 as the response correction matrix T _A and the response center point c _SA. Good. In this case, since the geomagnetism measurement system does not perform the optimal ellipsoidal surface generation process, it is possible to reduce the calculation load related to the calculation of the geomagnetism Bg.
Note that the ellipsoid initial correction value generation unit 300 uses three different evaluation axes, ie, a first evaluation axis ξ ₁ , a second evaluation axis ξ ₂ , and a third evaluation axis ξ ₃ on the space Ω. After generating different ellipsoids, it is determined whether or not the distance between the center points of these three ellipsoids is equal to or smaller than the first threshold value Δc, and only when the determination result is affirmative, the initial ellipsoid A correction matrix T ₀ and an initial center point c _E0 are generated. Therefore, the initial ellipsoid V _EO represented by the initial ellipsoid correction matrix T ₀ and the initial center point c _E0 is not an ellipsoid that minimizes an error from the coordinates indicated by the plurality of magnetic data q _{1 to} q _N. The distribution shape of coordinates indicated by the plurality of magnetic data q _{1 to} q _N is accurately represented. That is, the geomagnetism measurement system according to the modified example 4 is capable of accurate geomagnetism Bg by the ellipse correction using the initial ellipsoid correction matrix T ₀ and the initial center point c _E0 even when the soft iron effect occurs. The direction can be calculated.

(5) Modification 5
In the embodiment and the modification described above, the geomagnetism measurement system generates the first ellipsoid V _xx , the second ellipse V _yy , and the third ellipse V _zz in the ellipsoid initial correction value generation unit 300, Based on these three ellipsoids, the initial ellipsoid correction matrix T ₀ and the initial center point c _E0 are calculated. However, the present invention is not limited to such a form, and a known method is appropriately applied. The initial ellipsoid correction matrix T ₀ and the initial center point c _E0 may be calculated.
For example, the initial ellipsoid correction matrix T ₀ and the initial center point c _E0 may be calculated based on the method disclosed in Non-Patent Document 2 (that is, the comparison shown in Section 5). Alternatively, a 3-by-3 unit matrix may be employed as the initial ellipsoid correction matrix T ₀ , and the origin ^S O = (0, 0, 0) ^T of the sensor coordinate system Σ _S may be employed as the initial center point c _E0. Good. In this case, it is possible to reduce the computational load of the calculation of the initial ellipsoidal correction matrix T ₀ and the initial center point c _E0.

(6) Modification 6
In the second embodiment and the modification described above, the geomagnetism measurement system applies the coordinates indicated by the plurality of converted magnetic data s _{1 to} s _N as the plurality of input coordinates used for the second distortion determination process. The present invention is not limited to such a form, and a plurality of vectors representing the coordinates indicated by the plurality of converted magnetic data s _{1 to} s _N starting from the optimum center point c _EOP , that is, the vector (s ₁ -C _EOP ) to vector (s _N -c _EOP ) may be applied to a plurality of input coordinates. In this case, it is possible to reduce the size of data used for the distortion determination process, which has the advantage of saving the memory size necessary for the process and improving the processing speed.

(7) Modification 7
In the embodiment and the modification described above, in the geomagnetism measurement system, the initial ellipsoid determining unit 320 calculates values calculated by the initial ellipsoid generating unit 310 (first ellipsoidal coefficient matrix _Dxx , second ellipsoidal coefficient matrix _Dyy). , Third ellipsoidal coefficient matrix D _zz , center point c _xx , center point c _yy , and center point c _zz ) determine whether or not both the first condition and the second condition are satisfied. However, the present invention is not limited to such a form, and it is determined only whether the center point c _xx , the center point c _yy , and the center point c _zz satisfy the second condition. May be. In this case, the initial ellipsoid determination unit 320 may perform only the determination on the second condition without performing the determination on the first condition. For example, the initial ellipsoid determining unit 320 may be configured by only the initial ellipsoid center point determining unit 322 without including the initial ellipsoid coefficient matrix determining unit 321.
In addition, the initial correction value generation unit 330, when the value calculated by the initial ellipsoid generation unit 310 satisfies the second condition (that is, when the determination result in the initial ellipsoid center point determination unit 322 is affirmative) it is one that calculates the coordinates and initial ellipsoidal correction matrix T ₀ of the initial center point c _E0 may.

(8) Modification 8
In the embodiment and the modification described above, the geomagnetism measurement system has three initial ellipsoidal planes (first ellipsoid _Vxx , second ellipsoid _Vyy , and third ellipsoid _Vzz ) in the initial ellipsoid generator 310. The coordinates of each coefficient matrix and the center point have been calculated, but the present invention is not limited to such a form, and the first ellipsoid V _xx , the second ellipse V _yy , and the third ellipse Of the ellipsoidal surface _Vzz , the coefficient matrix and the coordinates of the center point of each of the two ellipsoidal surfaces may be calculated. In this case, the initial elliptical surface generation unit 310 may include at least two of the first elliptical surface generation unit 311, the second elliptical surface generation unit 312, and the third elliptical surface generation unit 313.
As described in FIG. 19, the degree of difference in shape between two ellipsoidal surfaces among the first ellipsoidal surface _Vxx , the second ellipsoidal surface _Vyy , and the third ellipsoidal surface _Vzz (specifically, two ellipsoidal surfaces By evaluating the distance between two center points of the surface, it is possible to grasp whether or not it is difficult to specify the shape of the ellipsoid from the coordinates indicated by the plurality of magnetic data q _{1 to} q _N Is possible. Therefore, in the initial ellipsoid generation unit 310, the geomagnetism measurement system performs the coefficient matrix and the center of each of at least two ellipsoids among the first ellipse _Vxx , the second ellipse _Vyy , and the third ellipse _Vzz. If the coordinates of the points are calculated, an inappropriate initial ellipsoid correction matrix T ₀ can be prevented from being generated. When the geomagnetic measurement system calculates the coefficient matrix and center point coordinates of each of the two ellipsoids in the initial ellipsoid generation unit 310, the coefficient matrix and center point coordinates of each of the three ellipsoids are calculated. Compared with, the calculation load can be reduced.
When the geomagnetism measurement system calculates the coefficient matrix and the coordinates of the center point of each of the two ellipsoids in the initial ellipsoid generator 310, the geomagnetism measurement system uses the initial correction value generator 330 in the two The initial ellipsoid correction matrix T ₀ may be calculated based on the coefficient matrix of at least one of the ellipsoids. Similarly, in the geomagnetism measurement system, the initial correction value generation unit 330 may calculate the coordinates of the initial center point _cE0 based on the center point of at least one of the two ellipsoidal surfaces.

(9) Modification 9
In the embodiment and the modification described above, the geomagnetism measurement system uses the initial ellipsoid center point determination unit 322 to calculate the distance between the three center points of the center point c _xx , the center point c _yy , and the center point c _zz . All are to determine whether or not the first threshold Δc or less (whether or not the second condition is satisfied), but the present invention is not limited to such a determination method, The initial ellipsoid center point determination unit 322 determines whether or not the distance between two center points of the center point c _xx , the center point c _yy , and the center point c _zz is equal to or less than a first threshold value Δc. It may be.
For example, as in Modification 8, the initial ellipsoid generation unit 310 has two ellipsoids (for example, the first ellipsoid V _xx , the second ellipse V _yy , and the third ellipse V _zz ). When calculating the coordinates of the center points (for example, the center point c _xx and the center point c _yy ) of each of the 1 ellipse surface V _xx and the second ellipsoid surface V _yy ), the initial ellipsoid surface center point determination unit 322 includes the 2 It may be determined whether the distance between the two center points c _xx and c _yy is equal to or less than the first threshold value Δc.
Even with such a determination, it is possible to determine whether or not it is difficult to specify the shape of the ellipsoid from the shape of the distribution of coordinates indicated by the plurality of magnetic data q _{1 to} q _N. Inappropriate initial ellipsoid correction matrix T ₀ can be prevented from being generated.

(10) Modification 10
In the embodiment and the modification described above, the terminal device accumulates all the magnetic data q _i sequentially output by the three-dimensional magnetic sensor 60 in the first storage unit BU1, and N pieces of magnetic data in the first storage unit BU1. when q ₁ to q _N are accumulated, periodically, (see FIG. 11) Although these N magnetic data q ₁ to q _N was to send to the server apparatus, the present invention is as this The first storage unit stores magnetic data q _i sequentially output by the three-dimensional magnetic sensor 60 only when the terminal device requires response information RES for accurate geomagnetism Bg calculation. accumulated in BU1, the stored N pieces of magnetic data q ₁ to q _N may be configured to transmit to the server device.
The geomagnetism measurement system according to the modified example 10 can reduce the communication amount between the terminal device and the server device as compared with the geomagnetism measurement system SYS (or the geomagnetism measurement system SYSa) according to the embodiment, and the terminal device. In addition, it is possible to reduce the processing load on the server device, and to calculate the correct orientation of the geomagnetism Bg without reducing the convenience of the terminal device.

FIG. 33 is an explanatory diagram for explaining the use of the offset c _OFF in the geomagnetism measurement system according to Modification Example 10. In FIG. 33, as in FIG. 11, the “magnetic data distance condition” and various communication times are not considered.
As illustrated in FIG. 33, the terminal device of the geomagnetism measurement system according to the modification 10 is configured to store the first storage unit BU1 when the CPU 10 included in the terminal device executes the terminal-side magnetic data processing program according to the modification 10. Accumulation of magnetic data q _i is started (FIG. 33A). Then, the terminal apparatus, when the N pieces of magnetic data _q 1 to q _N stored in the first storage unit BU1, and sends them to the server device, to the N-number of the magnetic data _q 1 to q _N Based on the response center point c _SA calculated by the server device based on this, the offset c _OFF is adopted (FIG. 33B).
In addition, when the internal magnetic field Bi changes, the terminal device according to the modified example 10 again starts accumulating the magnetic data q _i in the first storage unit BU1 of the accumulating unit 110 (FIG. 33C). Then, the terminal apparatus, when the N pieces of magnetic data _q 1 to q _N stored in the first storage unit BU1, and sends them to the server device, to the N-number of the magnetic data _q 1 to q _N Based on the response center point c _SA calculated by the server device based on this, the offset c _OFF is adopted (FIG. 33D).
Thus, the terminal device according to the modification 10, when it is necessary to update the offset c _OFF on the basis of the response center point c _SA only accumulates the N magnetic data q ₁ to q _N, which server Since the data is transmitted to the device, the amount of communication between the terminal device and the server device can be reduced.

In this case, the terminal device may include a flag FgQ indicating whether or not the first storage unit BU1 is in a state where the magnetic data q _i should be accumulated. Thus, the terminal device, when it is necessary to update the offset _{c OFF} on the basis of the response center point _{c SA} alone, it is possible to accumulate the N magnetic data _q 1 to q _N.
In addition, the terminal device receives the response information RES from the server device after the terminal device transmits N pieces of magnetic data q _{1 to} q _N to the server device while waiting for reception of the response information RES from the server device. It may have a flag FgS indicating whether or not. The response center point calculated by the server device when the internal magnetic field Bi changes after the terminal device transmits N pieces of magnetic data q _{1 to} q _N to the server device and before the server device supplies the response information RES. c The coordinates of _SA do not accurately represent the internal magnetic field Bi after the change. On the other hand, when the terminal device has the flag FgS, when the response center point c _SA that does not accurately represent the internal magnetic field Bi is transmitted from the server device, it can be discarded.

In the embodiments and modifications described above, the server apparatus, when a response center point c _SA and response correction matrix T _A is calculated only, but generates response information RES, the present invention is in such forms is not limited, if the response center point c _SA and response correction matrix T _a is not calculated also generates response information RES, which may be one to be transmitted to the terminal device. In this case, the response information RES, in addition to the response center point c _SA and response correction matrix T _A, may include code Code indicating whether the calculation of the response center point c _SA and response correction matrix T _A is successful .
For example, the server apparatus SVa according to the second embodiment, when the determination result in the magnetic data distribution determination process, the initial ellipsoid generation process, or the distortion determination process is negative, the response center point c _SA and the response correction matrix. T _A is not generated, but in such a case, the server apparatus according to the modified example 10 sets a value “0” indicating that calculation of the response center point c _SA and the response correction matrix T _A has failed in the code Code. After setting, response information RES including the code Code may be generated and transmitted to the terminal device.

  When the CPU 10 executes the terminal-side magnetic data processing program according to the modification 10, the terminal device according to the modification 10 executes each process illustrated in the flowchart of FIG. Is different from the above-described embodiments and modifications. Hereinafter, the operation of the terminal device according to the modified example 10 will be described with reference to FIGS. 12, 34, and 35.

First, in step S11, the CPU 10 executes an initialization process. Specifically, the CPU 10 is in a state where the first storage unit BU1 accumulates the magnetic data q _i in the flag FgQ in addition to initializing the count values CtA and CtB and the flags FgA, FgB, FgC and FgO. A value “1” indicating that this is set, and a value “0” indicating that it is not a period of waiting for transmission of the response information RES from the server device is set in the flag FgS.

Next, CPU10 performs a magnetic data acquisition process in step S13. FIG. 34A is a flowchart illustrating details of the magnetic data acquisition process performed by the terminal device according to Modification 10. As shown in FIG. 34A, the CPU 10 determines whether or not the flag FgQ is “1” in step Sa130. If the determination result is affirmative, the process proceeds to step S131. If the result is negative, the process proceeds to step S133. That is, the terminal device according to the modified example 10 includes the first storage unit only when the flag FgQ is set to a value “1” indicating that the first storage unit BU1 is in a state of accumulating the magnetic data q _i. The magnetic data q _i is stored in BU1. Note that the processes shown in steps S131 to S135 in FIG. 34A are the same as the processes shown in steps S131 to S135 in FIG.

Next, the CPU 10 executes magnetic data transmission processing in step S15. FIG. 34B is a flowchart illustrating the details of the magnetic data transmission process performed by the terminal device according to Modification 10. As shown in FIG. 34 (B), when the CPU 10 transmits N pieces of magnetic data q _{1 to} q _N to the server device SV in step S152, the CPU 10 sends the magnetic data q _i to the flag FgQ in step Sa154. The value is set to “0” indicating that the first storage unit BU1 is not accumulating, and the flag FgS is set to a value “1” indicating that the response information RES is waiting to be transmitted from the server device. To do. Note that the processes shown in steps S151 to S153 in FIG. 34B are the same as the processes shown in steps S151 to S153 in FIG.

Next, in step S17, the CPU 10 executes an approximate center point calculation process. FIG. 35A is a flowchart illustrating details of the approximate center point calculation process performed by the terminal device according to Modification Example 10. As shown in FIG. 35A, when the determination result in step S174 is negative (ie, the coordinates indicated by the approximate center point c _SB calculated in step S172 and the coordinates indicated by the offset c _OFF are shown in FIG. 35A). In the case where the offset distance condition is not satisfied), in step Sa175, the magnetic data stored in the first storage unit BU1 is discarded, the flag FgO is set to “1”, and the count value CtA is set to “0”. The flag FgQ is set to “1”, and the flag FgS is set to “0”. Note that the processes shown in steps S171 to S174 in FIG. 35A are the same as the processes shown in steps S171 to S174 in FIG.
That is, when the internal magnetic field Bi changes, the terminal device according to the modified example 10 discards the magnetic data stored in the first storage unit BU1, initializes the count value CtA to “0”, and sets the flag FgQ Is set to “1” and accumulation of the magnetic data q _{i in} the first storage unit BU1 is started again. Thus, in the N magnetic data q ₁ to q _N transmitted from the terminal device 1 to the server apparatus SV, a magnetic data q _i output from the three-dimensional magnetic sensor 60 before the internal magnetic field Bi is varied Mixing can be prevented.

Next, in step S19, the CPU 10 executes a response center point reception determination process. FIG. 35B is a flowchart illustrating details of the response center point reception determination process performed by the terminal device according to Modification 10. As shown in FIG. 35B, the CPU 10 determines whether or not the flag FgS is “1” in step Sa190. If the determination result is affirmative, the process proceeds to step S191, while the determination result Is negative, the response center point reception determination process is terminated.
When the internal magnetic field Bi changes during the period from when the terminal device transmits N pieces of magnetic data q _{1 to} q _N to the server device until the response information RES is received from the server device, in step Sa175 described above, The flag FgS is set to “0”. Therefore, when it is determined in step Sa190 that the flag FgS is “0”, the response center point c _SA that does not accurately represent the internal magnetic field Bi after the change is obtained by terminating the response center point reception determination process. when transmitted from the server apparatus, it can be prevented from employing the coordinates of the response center point c _SA as an offset c _OFF.
Further, when it is determined in step S191 that the response information RES is supplied from the server device, the CPU 10 determines in step Sa192 whether the value of the code code is “1”. If the determination result in step Sa192 is affirmative, the CPU 10 advances the process to step Sa193, sets the flag FgA to “1”, and initializes the flag FgS to “0”. On the other hand, if the determination result in step Sa192 is negative, the CPU 10 advances the process to step Sa194, sets “1” to the flag FgQ, and initializes the flag FgS to “0”.
If the code Code "0" is set, that is, if it fails to calculate the response center point c _SA and response correction matrix T _A server apparatus, a terminal apparatus newly N number of magnetic data q ₁ to q Preferably, _N is stored, and based on this, the server device generates response information RES including the response center point c _SA and the response correction matrix T _A. When the terminal device according to the modification 10 determines in step Sa192 that the value of the code code is “0”, the terminal FgQ is set to “1”, and the magnetic data q _i to the first storage unit BU1 is set. Is started again, it is possible to receive response information RES including the response center point c _SA and the response correction matrix T _A from the server device.
In step Sa192, the CPU 10 determines whether or not the coordinates of the response center point c _{SA and} the coordinates indicated by the offset c _OFF satisfy the “response center point validity condition” shown in Expression (5.a). It may be determined together. However, when the internal magnetic field Bi changes, the flag FgS is set to “0” in step Sa175, and therefore the determination regarding the “response center point validity condition” is not necessarily required.

(11) Modification 11
In the geomagnetism measurement system according to the embodiment and the modification described above, the terminal device includes the approximate center point calculation unit 140 that calculates the approximate center point c _SB, and provides the offset c _OFF as the response center point c _SA supplied by the server device. or, but was to update based on any of the approximate center point c _SB, the present embodiment is not limited to such embodiments, the offset c _OFF, the response center supplies the server device It may be updated based only on the point c _SA . In this case, the terminal device may not include the approximate center point calculation unit 140 and may not calculate the coordinates of the approximate center point _cSB . Since the terminal device according to the modification 11 can reduce the processing load related to the calculation of the direction of the geomagnetism Bg, even a simple device can be applied to the geomagnetism measurement system.

(12) Modification 12
In the geomagnetism measurement system according to the embodiment and the modification described above, the server device generates the response information RES in consideration of the occurrence of the soft iron effect in the terminal device, but the present invention is limited to such an aspect. The response information RES may be generated without considering the soft iron effect.
For example, the server device includes a center point calculation unit 640 in addition to the data control unit 710 (or data control unit 710a) and the server-side transmission / reception unit 720, and the center point c _{S of} the spherical surface S calculated by the center point calculation unit 640. and it employs the response center point c _SA, a unit matrix I of three rows and three columns, by adopting the response correction matrix T _a, may be configured to generate response information RES. In this case, the terminal device may consider the vector indicating the coordinates of the center point c _S as the offset c _OFF and calculate the direction of the geomagnetism Bg without performing ellipse correction. In this case, the server apparatus further includes a distortion determination unit 540 and a distribution determination unit 620, the distribution shape of coordinates indicated by the magnetic data q _{1 to} q _N is three-dimensional, and the magnetic data q _{1 to} q _The response information RES may be generated when _N is not affected by the external magnetic field Bx.

SYS ... Geomagnetic measurement system, SV ... Server device, 1 ... Terminal device, 60 ... 3D magnetic sensor, 21 ... Soft magnetic material, 2 ... Part, 130 ... Geomagnetic calculation unit, 140 ... Approximate center point calculation unit, 200 ... Ellipse Surface correction unit, 300... Elliptic surface initial correction value generation unit, 400... Ellipse surface optimum correction value generation unit, 540... Strain determination unit, 620. ... server-side transceiver, Bg ... geomagnetism, Bi ... internal magnetic field, Bx ... external magnetic field, Bm ... magnetizing magnetic field, q _i ... magnetic data, s _i ... converted magnetic data, T _E ... ellipsoidal correction matrix, c _OFF ... offset, T _OP ... optimal ellipsoid correction matrix, c _EOP ... optimum center point, c _S ... center point, c _SA ... response center point, c _SB ... approximate center point, T _A ... response correction matrix, RES ... response information .

Claims (4)

A terminal device that communicates with a server device,
A three-dimensional magnetic sensor that detects magnetic components in three directions and sequentially outputs detected values as magnetic data that is vector data expressed in a three-axis coordinate system;
An accumulator that accumulates the magnetic data sequentially output from the three-dimensional magnetic sensor;
When the first prescribed number of magnetic data is stored in the storage unit, the first prescribed number of the magnetic data is transmitted to the server device, and the server device is based on the first prescribed number of the magnetic data. A terminal-side transceiver that receives the offset, which is a vector for calibrating the magnetic data, calculated by
When the magnetic data is stored in the storage unit by a second specified number smaller than the first specified number, a spherical surface defined by coordinates indicated by each of the second specified number of the magnetic data in the coordinate system is stored. An approximate center point calculator that calculates the coordinates of the approximate center point that is the center point;
With
When the distance between the coordinates indicated by the offset and the coordinates of the approximate center point is greater than a predetermined threshold, the offset is updated with a vector indicating the coordinates of the approximate center point.
A terminal device characterized by that. A terminal device that communicates with a server device,
A three-dimensional magnetic sensor that detects magnetic components in three directions and sequentially outputs detected values as magnetic data that is vector data expressed in a three-axis coordinate system;
An accumulator that accumulates the magnetic data sequentially output from the three-dimensional magnetic sensor;
When the first prescribed number of magnetic data is stored in the storage unit, the first prescribed number of the magnetic data is transmitted to the server device, and the server device is based on the first prescribed number of the magnetic data. A terminal-side transceiver that receives the offset, which is a vector for calibrating the magnetic data, calculated by
When the magnetic data is stored in the storage unit by a second specified number smaller than the first specified number, a spherical surface defined by coordinates indicated by each of the second specified number of the magnetic data in the coordinate system is stored. An approximate center point calculator that calculates the coordinates of the approximate center point that is the center point;
With
The storage unit
When the distance between the coordinates indicated by the offset and the coordinates of the approximate center point is larger than a predetermined threshold, accumulation of the first prescribed number of the magnetic data is started.
A terminal device characterized by that. The server device
When the first prescribed number of the magnetic data is supplied from the terminal device,
In the coordinate system, the coordinates of the center point of the optimum ellipsoid determined so as to have the coordinates indicated by each of the first prescribed number of magnetic data in the vicinity, and the coordinates on the optimum ellipsoid are the coordinates of the optimum ellipsoid. An ellipsoidal correction unit that calculates an optimal ellipsoidal correction matrix for coordinate conversion into coordinates on a sphere centered on the center point;
A data control unit that employs the center point of the optimum ellipsoid as a response center point, employs the optimum ellipsoid correction matrix as a response correction matrix, and generates response information including the response center point and the response correction matrix When,
A server-side transmitting / receiving unit that transmits the response information to the terminal device;
With
The terminal side transceiver is
Receiving the response information transmitted by the server-side transceiver unit;
The terminal device according to claim 1, wherein: The server device
A center point calculation unit for calculating coordinates of the center point of the spherical surface determined so as to have the coordinates indicated by each of the first prescribed number of the magnetic data in the coordinate system;
Calculating a distortion evaluation value indicating the degree of difference between the three-dimensional shape defined so as to have the magnetic data of the first prescribed number near the surface and shape of the spherical surface, the distortion evaluation value is less than the distortion tolerance A distortion determination unit that determines whether or not
Further comprising
The data control unit
When the determination result in the distortion determination unit is affirmative,
The center point calculated by the center point calculation unit is adopted as a response center point, and a unit matrix is adopted as a response correction matrix.
When the determination result in the distortion determination unit is negative,
The terminal device according to claim 3 , wherein a center point of the optimum ellipsoid is adopted as a response center point, and the optimum ellipsoid correction matrix is adopted as a response correction matrix.

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