JP5641236B2 - Geomagnetic measurement apparatus, offset determination method, and offset determination program - Google Patents

Description

  The present invention relates to a geomagnetic measurement apparatus, an offset determination method, and an offset determination program.

  In recent years, a three-dimensional magnetic sensor that is mounted on a mobile device such as a mobile phone 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 detecting a scalar quantity by decomposing a vector of a magnetic field into three orthogonal components, and each of the three magnetic sensor modules outputs a scalar quantity. Outputs three-dimensional vector data as three components.

By the way, a device such as a mobile phone on which a three-dimensional magnetic sensor is mounted is often provided with various components that generate magnetic fields, such as various types of magnetized metals and electric circuits. 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 device in addition to a vector representing geomagnetism.
Therefore, in order to accurately know the value of geomagnetism, it is necessary to perform a correction process for removing a vector representing a disturbance component such as an internal magnetic field generated by a component of the device from vector data output from the three-dimensional magnetic sensor.
Thus, in order to obtain an accurate value of the geomagnetism that is the detection target, the value of the disturbance component that is removed from the data output from the three-dimensional magnetic sensor in the correction process is called an offset.

The internal magnetic field is a magnetic field generated by device components. That is, the internal magnetic field is a magnetic field that is directed in a certain direction with respect to the device and has a certain magnitude. Such an internal magnetic field is a vector having a certain direction and a certain magnitude when viewed from a three-dimensional magnetic sensor mounted on the device, regardless of the posture of the device. Represented as:
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 the posture of the device is changed with respect to the ground, the direction of geomagnetism viewed from the device also changes. That is, when viewed from a three-dimensional magnetic sensor mounted on a device, the geomagnetism is expressed as a vector having a certain magnitude whose direction changes with a change in the posture of the device.
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. A method for obtaining an accurate geomagnetism value by calculating a vector having a certain length and performing correction processing for removing the vector representing the internal magnetic field from the output data as an offset is disclosed.

JP 2007-240270 A

  By the way, in the case where an object that generates a magnetic field such as a speaker or a personal computer exists near a device such as a mobile phone on which the three-dimensional magnetic sensor is mounted, the three-dimensional magnetic sensor has the above-described geomagnetism and internal magnetic field, It also detects external magnetic fields emitted by objects outside the device. In general, an external magnetic field is a non-uniform magnetic field whose direction and magnitude vary depending on the relative positional relationship between an object that generates an external magnetic field and a three-dimensional magnetic sensor.

In the conventional method, it is impossible to know the presence / absence of such a non-uniform external magnetic field and the magnitude of the influence of the non-uniform external magnetic field. Therefore, in the conventional method, even when the internal magnetic field vector calculated in the environment where the non-uniform external magnetic field exists has a large error, the correct value calculated in the environment where no external magnetic field exists is used. Since it is determined that it is present and this is adopted as an offset, there is a problem that a large error may be included in the offset.
Similarly, two magnetic sensor modules for detecting a scalar quantity by decomposing a magnetic field vector into two orthogonal components are provided, and the scalar quantity output by each of the two magnetic sensor modules is set as two components. Even in a two-dimensional magnetic sensor that outputs two-dimensional vector data, there is a problem that a large error may be included in the offset.
The present invention has been made in view of the circumstances described above, and more to evaluate the degree of influence of an external magnetic field, and solves problems and determining whether to adopt the offset value.

In order to solve the above-described problems, a geomagnetism measuring apparatus according to the present invention is incorporated in a device having a part that generates a magnetic field, and detects a magnetic component in three directions orthogonal to each other. overlapping means for storing the magnetic data sequentially output from the 3-dimensional magnetic sensor in the case of changing the posture, the coordinates indicated by the plurality of magnetic data stored in the storage means, and a spherical surface and a curved surface Assuming that it is probabilistically distributed in the vicinity of the surface of the aspheric solid obtained by combining , using the objective function representing the error between the coordinates indicated by the plurality of magnetic data and the surface of the solid, the objective function determine when to minimize the value of the error, and calculates a first evaluation value based on component representing the curved surface in the objective function, the first evaluation value to or less than a predetermined magnitude represented by A distortion determination section that, when the a determination result of the distortion determination unit is affirmative, the offset updating means for updating the offset the coordinates of the three-axis representing the magnetic field generated by the components of the part of the magnetic data, It is characterized by providing.

According to the present invention, in the strain determination means, it is assumed that the coordinates indicated by the plurality of magnetic data are probabilistically distributed near the surface of a solid having a distorted shape other than the spherical surface obtained by superimposing the spherical surface and the curved surface. Then, an objective function representing an error between the coordinates indicated by the plurality of magnetic data and the surface of the solid is introduced. This objective function is formed from a component representing a spherical surface and a component representing a curved surface. Then, by the first evaluation value that evaluates the influence of the component representing the curved surface of the objective function, how far the coordinates indicated by the plurality of magnetic data are away from the surface of the spherical surface represented by the component representing the spherical surface of the objective function Can be evaluated. That is, the first evaluation value can be used to evaluate how much the three-dimensional shape has a difference from the spherical shape (that is, how much distortion is present).
By providing such a distortion determination means, when a plurality of magnetic data are distributed near the surface of a solid, if the solid is so approximate that it has substantially the same shape as a spherical surface, It can be considered that the coordinates indicated by the magnetic data are distributed near the spherical surface . When the coordinate represented by a plurality of magnetic data is distributed in a spherical near, since the center point of the spherical surface having the coordinates indicated by the plurality of magnetic data in the vicinity is a coordinate indicated by the vector representing the internal magnetic field, a plurality of magnetic data A spherical center point having the indicated coordinates in the vicinity is adopted as an offset. On the other hand, if the solid has a distorted shape that is significantly different from the spherical surface, the coordinates indicated by the plurality of magnetic data cannot be considered to be distributed near the spherical surface. the center point of the spherical surface having it is possible to prevent the adoption as an offset. That is, the above-described geomagnetic measurement apparatus has an advantage that only an appropriate value can be adopted as an offset. As a result , since a value including a large error is not adopted as an offset, it is possible to prevent erroneous geomagnetism from being detected.

  In the geomagnetism measuring apparatus described above, when the first evaluation value is larger than the predetermined size, the user is prompted to change the posture of the device without changing the position of the device. Preferably means are provided.

According to the present invention, the above-described geomagnetism measuring device shows a plurality of magnetic data output from the three-dimensional magnetic sensor when the strain determination means determines that the first evaluation value is larger than a predetermined size. When the coordinates are distributed in the vicinity of the surface of the solid, when the shape of the solid has a large distortion from the spherical surface, there is provided means for urging the user to change the posture of the device without changing the position of the device.
The three-dimensional magnetic sensor detects, in addition to the geomagnetism as a measurement target, an internal magnetic field generated by a component provided in the device and an external magnetic field generated by an external object. The external magnetic field is a non-uniform magnetic field that changes direction and magnitude depending on the mutual positional relationship between an external object and the three-dimensional magnetic sensor. When the influence of the non-uniform external magnetic field is large, the plurality of magnetic data are distributed in the vicinity of the surface of a solid having a distorted shape that is significantly different from the spherical surface, and are indicated by the plurality of magnetic data. Since it cannot be considered that the coordinates are distributed in the vicinity of the spherical surface, the center point of the spherical surface cannot be adopted as an offset.
However, such a non-uniform external magnetic field is only a magnetic field of a certain magnitude directed in a certain direction when the mutual positional relationship with an external object that generates the external magnetic field does not change. That is, when the posture is changed without changing the position of the three-dimensional magnetic sensor, the external magnetic field is detected by the three-dimensional magnetic sensor as a magnetic field having a certain magnitude and changing only the direction. In this case, the coordinates indicated by the plurality of magnetic data output from the three-dimensional magnetic sensor are distributed in the vicinity of a certain spherical surface. And since the center point of this spherical surface is almost the same as the coordinate indicating the component of the magnetic field (internal magnetic field) generated by the component provided in the device, the spherical surface having the coordinates indicated by a plurality of magnetic data nearby. The center point can be used as an offset.
Therefore, the geomagnetism measuring apparatus described above is provided with means for prompting the user to change the posture of the device without changing the position of the device, so that an appropriate offset can be obtained even in a place where a non-uniform external magnetic field exists. It is possible to prompt the user to perform an operation that can be calculated.

Further, the above-described geomagnetism measurement apparatus indicates that the coordinates indicated by the plurality of magnetic data stored in the storage means are probabilistically distributed in the vicinity of the center point calculation spherical surface, and is indicated by the plurality of magnetic data. Center point calculating means for calculating a center point of the center point calculating sphere so as to minimize an error between the three-axis coordinates and the center point calculating sphere, wherein the curved surface in the objective function is The component to be expressed is a vector composed of each element corresponding to each of the plurality of magnetic data, and each element corresponds to a function expressed by a quadratic form of three variables having a first evaluation matrix as a coefficient matrix. is a value obtained by substituting the values of three axes that represent the magnetic data in a coordinate system with its origin the center point, the first evaluation value, Ri norm der of the first evaluation matrix, wherein The offset is Heart point der Rukoto is preferable.

According to the present invention, the component representing the curved surface in the objective function used in the strain determination means is obtained by substituting values corresponding to each of the coordinates indicated by the plurality of magnetic data into the function represented in the quadratic form. It is expressed by a vector whose element is the value.
That is, the component representing the curved surface has an error under the restriction that each of the errors between the coordinates indicated by the plurality of magnetic data and the spherical surface exists on the curved surface indicated by the same function expressed in quadratic form. Is a vector that expresses With the component representing the curved surface, an error between the coordinates represented by the plurality of magnetic data and the spherical surface can be absorbed by the curved surface represented by the function represented by the quadratic form.
If the error between the coordinates and the spherical surface indicated by a plurality of magnetic data is represented by a vector having a variable without any restrictions as an element, each element of the vector, that is, each of the errors corresponding to the plurality of magnetic data, Expressed as independent of each other. When the error between the coordinates indicated by the plurality of magnetic data and the spherical surface is minimized, the plurality of errors represented by this vector are white noise having symmetry as a whole and having no direction dependency. .
On the other hand, the objective function used in the distortion determination means can express an error caused by a component representing a curved surface separately from such white noise by introducing a component representing a curved surface. It is now possible to separate errors caused by components representing curved surfaces that are not white noise from errors that were uniformly regarded as white noise.
Therefore, the geomagnetism measuring apparatus described above can evaluate the influence of the component representing the curved surface by separating the error caused by the component representing the curved surface from the error between the coordinates and the spherical surface indicated by the plurality of magnetic data. It is possible to determine whether the error included in the magnetic data detected by the geomagnetism measuring device is just white noise, or whether it contains some disturbance component other than white noise, and at the same time, This has the advantage that the magnitude of the influence of the disturbance component can be evaluated.

  In the above-described geomagnetism measuring apparatus, the center point calculating unit calculates a second evaluation value for evaluating that the coordinates indicated by the plurality of magnetic data are distributed with a three-dimensional spread. It is preferable to calculate the center point when the second evaluation value is equal to or larger than a predetermined size.

According to the present invention, a plurality of magnetic points in which an accurate center point cannot be derived by evaluating the size of the three-dimensional spread of coordinates indicated by the plurality of magnetic data using the second evaluation value. It is possible to prevent the center point calculation process based on the data.
This has the advantage of avoiding the use of an inappropriate center point as an offset and preventing the detection of a geomagnetic value with a large error, and is also inappropriate based on inappropriate magnetic data. By preventing the center point calculation process for deriving the center point, it is possible to reduce the time until the correct offset is adopted.

In the geomagnetism measuring apparatus described above, it is preferable that the center point calculating means calculates x that minimizes the value of the second objective function f ₁ (x) below as the center point.

  According to the present invention, it is possible to derive a center point as an offset candidate by simple calculation. Therefore, the geomagnetism measuring apparatus described above has the advantage of improving the processing speed.

In the geomagnetism measuring apparatus described above, the objective function is represented by f ₂ (E, x), where E is a variable, where E is the first evaluation matrix and x ₀ is the center point. The first evaluation value is preferably a norm of E that minimizes f ₂ (E, x).

According to the present invention, the objective function and the first evaluation value can be obtained by simple calculation.
Therefore, the above-mentioned geomagnetism measuring apparatus can adopt an appropriate offset in a short time, and an accurate geomagnetism value can be obtained without overloading the CPU of the device in which the geomagnetism measuring apparatus is incorporated. This has the advantage that accurate geomagnetism can be measured at all times.

In the geomagnetism measuring apparatus described above, it is preferable that the second evaluation value is a minimum eigenvalue of the following matrix A.

  According to the present invention, the above-described geomagnetism measuring apparatus can calculate the second evaluation value for evaluating the size of the three-dimensional extent of the coordinates indicated by the plurality of magnetic data by simple calculation. Therefore, the geomagnetism measuring apparatus described above has the advantage of improving the processing speed.

Next, the geomagnetism measuring apparatus according to the present invention is:
A two-dimensional magnetic sensor that is incorporated in a device including a component that generates a magnetic field and detects magnetic components in two directions orthogonal to each other;
Storage means for storing magnetic data sequentially output from the two-dimensional magnetic sensor when the posture of the device is changed;
Assuming that the coordinates indicated by the plurality of magnetic data stored in the storage means are probabilistically distributed in the vicinity of the circumference centered on the coordinates indicating the magnetic field component generated by the component, Center point calculating means for calculating a center point of the circumference so as to minimize an error between the coordinates of the two axes indicated by the magnetic data and the circumference;
Assuming that the coordinates indicated by the plurality of magnetic data are probabilistically distributed in the vicinity of the second curve having a shape other than the circumference obtained by superimposing the circumference and the first curve, the plurality of magnetic data The first curve in the third objective function when the error value represented by the third objective function is minimized by using the third objective function representing the error between the coordinates indicated by the data and the second curve. And a distortion determination unit that calculates a third evaluation value based on a component representing the value and adopts the center point as an offset of the two-dimensional magnetic sensor when the third evaluation value is equal to or smaller than a predetermined magnitude. It is characterized by that.

According to the present invention, when the plurality of magnetic data output from the two-dimensional magnetic sensor are distributed in the vicinity of the second curve having a shape different from the circumference, how close the shape of the second curve is to the circumference. Depending on what, it is determined whether or not to adopt the center point of the circumference as an offset, so when a large error is included in the value of the calculated center point of the circumference, it is prevented to adopt this as an offset, It is possible to prevent detection of erroneous geomagnetism.

Next, the offset determination method used in the geomagnetism measuring apparatus according to the present invention is:
A three-dimensional magnetic sensor that is incorporated in a device having a part that generates a magnetic field and detects magnetic components in three directions orthogonal to each other, and is sequentially output from the three-dimensional magnetic sensor when the posture of the device is changed. An offset determining method used in a geomagnetism measuring device comprising: a storage means for storing magnetic data;
Assuming that the coordinates indicated by the plurality of magnetic data stored in the storage means are probabilistically distributed in the vicinity of the center point calculation spherical surface with the coordinates indicating the magnetic field component generated by the component as the center point , Calculating a center point of the center point calculating sphere so as to minimize an error between the three-axis coordinates indicated by the plurality of magnetic data and the center point calculating sphere;
Assuming that the coordinates indicated by the plurality of magnetic data are probabilistically distributed near the surface of an aspheric solid obtained by superimposing a spherical surface and a curved surface, the coordinates indicated by the plurality of magnetic data and the A first evaluation value based on a component representing the curved surface in the objective function when the error value represented by the objective function is minimized is calculated using an objective function representing an error with the surface of the solid, When one evaluation value is equal to or smaller than a predetermined size, the center point is employed as an offset of the three-dimensional magnetic sensor.

According to the present invention, when a plurality of magnetic data are distributed near the surface of a solid, whether or not the center point of the center point calculation spherical surface is adopted as an offset depends on how close the shape of the solid is to the spherical surface. Therefore, when a large error is included in the value of the center point of the center point calculation spherical surface , it is possible to prevent this from being adopted as an offset and to prevent erroneous geomagnetism.

Next, the offset determination program used in the geomagnetism measuring apparatus according to the present invention is:
A three-dimensional magnetic sensor that is incorporated in a device having a part that generates a magnetic field and detects magnetic components in three directions orthogonal to each other, and is sequentially output from the three-dimensional magnetic sensor when the posture of the device is changed. An offset determining program for use in a geomagnetism measuring device comprising a storage means for storing magnetic data.
Assuming that the coordinates indicated by the plurality of magnetic data stored in the storage means are probabilistically distributed in the vicinity of the center point calculation spherical surface with the coordinates indicating the magnetic field component generated by the component as the center point , so as to minimize the error between the coordinates and the center point calculation spherical three axes indicated by the plurality of magnetic data, the processing for calculating the center point of the center point calculation spherical,
Assuming that the coordinates indicated by the plurality of magnetic data are probabilistically distributed near the surface of an aspheric solid obtained by superimposing a spherical surface and a curved surface, the coordinates indicated by the plurality of magnetic data and the A first evaluation value based on a component representing the curved surface in the objective function when the error value represented by the objective function is minimized is calculated using an objective function representing an error with the surface of the solid, When one evaluation value is equal to or smaller than a predetermined size, the computer is caused to execute a process of adopting the center point as an offset of the three-dimensional magnetic sensor.

According to the present invention, when a plurality of magnetic data are distributed near the surface of a solid, whether or not the center point of the center point calculation spherical surface is adopted as an offset depends on how close the shape of the solid is to the spherical surface. Therefore, when a large error is included in the value of the center point of the center point calculation spherical surface , it is possible to prevent this from being adopted as an offset and to prevent erroneous geomagnetism.

It is a conceptual diagram explaining the outline | summary of the magnetic field which the three-dimensional magnetic sensor which concerns on embodiment of this invention detects. It is a conceptual diagram explaining the geomagnetism and internal magnetic field which the three-dimensional magnetic sensor which concerns on embodiment of this invention detects. It is a conceptual diagram explaining the geomagnetism, the internal magnetic field, and the external magnetic field which the three-dimensional magnetic sensor which concerns on embodiment of this invention detects. It is a conceptual diagram explaining the geomagnetism, the internal magnetic field, and the external magnetic field which the three-dimensional magnetic sensor which concerns on embodiment of this invention detects. It is a block diagram which shows the structure of the apparatus by which the three-dimensional magnetic sensor which concerns on embodiment of this invention is mounted. It is the flowchart which showed the flow of the process which concerns on embodiment of this invention. It is a conceptual diagram explaining the process of the center point calculation process which concerns on embodiment of this invention. It is a conceptual diagram explaining the necessity of the magnetic data distribution determination process which concerns on embodiment of this invention. It is a conceptual diagram explaining the magnetic data distribution determination process which concerns on embodiment of this invention. It is a conceptual diagram explaining the distortion determination process which concerns on embodiment of this invention. It is a conceptual diagram explaining the distortion determination process which concerns on embodiment of this invention. It is a figure explaining the data used by the simulation of this invention. It is a simulation result table | surface of this invention.

  Embodiments of the present invention will be described below.

[1. Outline of magnetic field detected by 3D magnetic sensor]
In this embodiment, as a magnetic field detected by the three-dimensional magnetic sensor, in addition to the geomagnetism that is the detection target, an internal magnetic field that is a magnetic field generated by a component of the device on which the three-dimensional magnetic sensor is mounted, and an object outside the device The existence of an external magnetic field is assumed.
These three types of magnetic fields have different properties in the direction, magnitude, and uniformity of the magnetic field. That is, when these magnetic fields are detected by a three-dimensional magnetic sensor, if the position and orientation of the three-dimensional magnetic sensor change, the direction and magnitude of vector data indicating the magnetic field output from the three-dimensional magnetic sensor also change. The method of changing the output data has a difference in each of the three types of magnetic fields.
Hereinafter, an outline of these three types of magnetic fields assumed in the present embodiment and vector data output when the three-dimensional magnetic sensor detects these magnetic fields will be described with reference to FIGS.

FIG. 1 is a diagram for explaining the types and properties of magnetic fields existing around the three-dimensional magnetic sensor 60 mounted on the device 1.
The magnetic field existing around the three-dimensional magnetic sensor 60 includes, in addition to the geomagnetism Bg to be measured, the internal magnetic field Bi generated by the components of the device 1 on which the three-dimensional magnetic sensor 60 is mounted, and the surroundings of the device 1. There is an external magnetic field Bx emitted by the object 2 that performs.

The geomagnetism Bg is a vector having a direction toward the magnetic pole north, and is a magnetic field having a uniform direction and magnitude. 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 generated by components of the device 1, and the direction of the internal magnetic field Bi has a certain direction when viewed from the device 1. That is, when viewed from the three-dimensional magnetic sensor 60 mounted on the device 1, the internal magnetic field Bi is detected as a magnetic field having a certain direction and magnitude even if the posture of the device 1 is changed. For example, when the user holds the device 1 with his hand and turns his wrist, the posture of the device 1 changes. At this time, since the geomagnetism Bg faces the north of the magnetic pole, the components of each of the three axes of the geomagnetism Bg detected by the three-dimensional magnetic sensor 60 change. On the other hand, in the three-dimensional magnetic sensor 60, the relative positional relationship between the three-dimensional magnetic sensor 60 and the component that generates the internal magnetic field is fixed. The components of are constant.
The external magnetic field Bx is a magnetic field generated by the external object 2 and is a non-uniform magnetic field in which the direction and magnitude of the magnetic field change depending on the distance and direction from the object 2. That is, when viewed from the three-dimensional magnetic sensor 60 mounted on the device 1, the external magnetic field Bx is a magnetic field that changes its direction and magnitude depending on the mutual positional relationship between the object 2 and the three-dimensional magnetic sensor 60. Detected as

For convenience of explanation, a ground coordinate system Σ _G and a sensor coordinate system Σ _S as shown in FIG. 1 are introduced. Subscript G attached to the upper left of each vector described in Figure 1 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. Here, the position and orientation of the three-dimensional magnetic sensor 60 as viewed from the ground coordinate system sigma _G, respectively, to be expressed with the position Ps, and orientation [theta] s.
Sensor coordinate system sigma _S is a coordinate system fixed to the 3D magnetic sensor 60, the output values of each of the three sensor modules having the three-dimensional magnetic sensor 60, respectively, x-axis, y-axis, the z-axis Is a coordinate system provided for plotting. 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, when viewed from the ground coordinate system sigma _G, the origin of the sensor coordinate system sigma _S is the position Ps, the attitude is attitude [theta] s.

FIG. 2 is a diagram showing what values the geomagnetism Bg and the internal magnetic field Bi are detected by the three-dimensional magnetic sensor 60. That is, FIG. 2, the three-dimensional magnetic sensor 60 when the posture θs as viewed from the ground coordinate system sigma _G was measured magnetic field while changing the theta ₁ through? _N, N pieces of output from the three-dimensional magnetic sensor 60 magnetic data _q 1 to q _N, is a plot in the sensor coordinate system sigma _S (N is 5 or more natural number). In FIG. 2, it is assumed that only the geomagnetism Bg and the internal magnetic field Bi exist, and the external magnetic field Bx does not exist. Also, subscript S attached to the upper left of each vector described in Figure 2, it means that the vector is a vector expressed in the sensor coordinate system sigma _S.
Internal magnetic field Bi is in the sensor coordinate system sigma _S, 3-dimensional position-independent Ps and orientation θs of magnetic sensors 60, vector ^S Bi (center point x from the origin of the sensor coordinate system sigma _S having a certain direction and magnitude ₍ Vector toward _0G ).
On the other hand, geomagnetism Bg resides in a sensor coordinate system sigma _S, is a size of a predetermined orientation varies with the posture θs of the three-dimensional magnetic sensor 60. That is, the geomagnetic Bg resides in a sensor coordinate system sigma _S, having an orientation that depends on the orientation [theta] s of the 3D magnetic sensor 60 is represented as a constant magnitude of the vector ^S Bg ([theta] s), in the case of changing the [theta] s Is located on a spherical surface centered at the center point _x0G .
Accordingly, the magnetic data _q 1 to q _N output from the 3D magnetic sensor 60 in the sensor coordinate system sigma _S, the center point of the center point _{x 0G,} the magnitude of the geomagnetism Bg radius, on a spherical surface _{S G} Will be distributed. If, when the size of the internal magnetic field Bi is 0, the center point x _0G, will coincide with the origin of the sensor coordinate system sigma _S.
The three-dimensional magnetic sensor 60, since it has a measurement error, the magnetic data _q 1 to q _N is strictly to stochastically distributed in the vicinity of the sphere _{S G.}

By calculating the coordinates of the center point _x0G of the spherical surface S _G from such magnetic data q _{1 to} q _N , the vector ^S Bi representing the internal magnetic field can be obtained, and the output value of the three-dimensional magnetic sensor 60 can be obtained. By subtracting the internal magnetic field ^S Bi from certain magnetic data q _{1 to} q _N , it is possible to calculate the geomagnetism ^S Bg. That is, if the magnetic detected by 3-dimensional magnetic sensor 60 is a geomagnetic Bg and internal magnetic field Bi, the center point _{x 0G} spherical _{S G} corresponds to the offset c of the three-dimensional magnetic sensor 60.

3, when the external magnetic field Bx is present, the position Ps of the 3D magnetic sensor 60 with varying the P ₁ to P _N, the posture θs by changing the theta ₁ through? _N when measuring a magnetic field a diagram of the magnetic data _q 1 to q _N, plotted in the sensor coordinate system sigma _S output by the three-dimensional magnetic sensor 60.
External magnetic field Bx is a heterogeneous magnetic field, according to the position in the ground coordinate system sigma _G, direction and magnitude changes. Therefore, when the position Ps of the three-dimensional magnetic sensor 60 is changed, the direction and magnitude of the external magnetic field Bx detected by the three-dimensional magnetic sensor 60 also changes. Such external magnetic fields Bx, in the sensor coordinate system sigma _S, is represented as a three-dimensional magnetic sensor 60 and orientation [theta] s and direction depending on the position Ps and size vector ^S Bx varying both the ([theta] s, Ps) The
The magnetic data q _{1 to} q _N measured while changing the posture θs and the position Ps of the three-dimensional magnetic sensor 60 are the internal magnetic field ^S Bi, the geomagnetism ^S Bg (θs), and the external magnetic field ^S Bx (θs, Ps). Is output as the sum of the vectors. Accordingly, the magnetic data _q 1 to q _N, in the sensor coordinate system sigma _S, a spherical _{S G} centered on the center point _{x 0G,} stereoscopic SD superimposed with a curved surface SX having different distorted shape than spherical It will be distributed near the surface. Here, the curved surface SX is a curved surface representing the external magnetic field ^S Bx (θs, Ps) in the sensor space Σ _S , and the internal magnetic field ^S Bi among the magnetic data q _{1 to} q _N output from the three-dimensional magnetic sensor 60. Represents the sum of the external magnetic field ^S Bx (θs, Ps).

Since the solid SD has a shape different from the spherical surface, a vector of the center point _x0G indicating the value of the internal magnetic field ^S Bi is obtained from the magnetic data q _{1 to} q _N distributed near the surface of the solid SD. It is difficult.
However, when the external magnetic field Bx is weak, the solid SD has a shape close to a spherical surface.
FIG. 4 (A), when the external magnetic field Bx is weak, a diagram of the magnetic data q ₁ to q _N, plotted in the sensor coordinate system sigma _S output by the three-dimensional magnetic sensor 60. When the external magnetic field Bx is weak, the magnetic data q _{1 to} q _N output from the three-dimensional magnetic sensor 60 includes a spherical surface S _G centered at a center point x _0G drawn by a vector ^S Bg (θs) representing geomagnetism, It is distributed in the vicinity of the surface of the solid SD having a shape close to a spherical surface, which is a superposition with the curved surface SX drawn by the vector ^S Bx (θs, Ps) representing the external magnetic field. In this case, a vector that substantially matches the center point x _0G can be obtained from the magnetic data q _{1 to} q _N.

The non-uniform external magnetic field Bx may be detected as a uniform magnetic field by the three-dimensional magnetic sensor 60. For example, even when there is a non-uniform external magnetic field Bx, when acquiring N pieces of magnetic data q _{1 to} q _N , the user does not hold the device 1 with his hand and rotate it. 1 position (strictly speaking, the position of the three-dimensional magnetic sensor 60) in case of changing only the posture while fixing the can, the external magnetic field Bx is the sensor space sigma _S, in the three-dimensional magnetic sensor 60 position θs Based on this, it is expressed as a vector ^S Bx (θs) having a constant magnitude that changes only its direction. In this case, N pieces of the magnetic data q ₁ to q _N output from a 3D magnetic sensor 60, as shown in FIG. 4 (B), in the sensor space sigma _S, the surface of the three-dimensional SD having a substantially spherical shape Distributed in the vicinity. Then, if the shape of the three-dimensional SD is substantially spherical, the center point, the center point x _0G spherical S _{G (i.e.,} coordinates representing the internal magnetic field ^S Bi) substantially equal to the. In this case, a vector that substantially matches the center point x _0G can be obtained from the magnetic data q _{1 to} q _N.

Therefore, in the present embodiment, based on the magnetic data q _{1 to} q _N , the magnitude of the influence of the external magnetic field Bx, that is, how close the solid SD has a spherical shape is evaluated. Based on the result, it is determined whether or not the center point of the spherical surface is adopted as the offset c. Hereinafter, a specific method will be described.

[2. Device configuration and software configuration]
FIG. 5 is a block diagram showing a configuration of the device 1 according to the embodiment of the present invention.
The device 1 includes a CPU 10 that is connected to various components via a bus and controls the entire apparatus, a RAM 20 that functions as a work area of the CPU 10, a ROM 30 that stores various programs and data, a communication unit 40 that performs communication, an image And a three-dimensional magnetic sensor 60 for detecting geomagnetism and outputting geomagnetic data.
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. The magnetic data is output from the X-axis geomagnetic sensor 61, Y-axis geomagnetic sensor 62 and the Z-axis geomagnetic sensor 63, as vector data in the sensor coordinate system sigma _S, of the sensor coordinate system sigma _S, x-axis, y-axis And indicated by the three components of the z-axis.
The CPU 10 executes the magnetic data processing program 70 stored in the ROM 30 to derive an offset from the output of the three-dimensional magnetic sensor 60 and to output an accurate geomagnetism direction and magnitude.
The display unit 50 displays azimuth information indicating the direction of geomagnetism output by the magnetic data processing program 70 by using an arrow or the like. Note that the magnetic data processing program 70 may display an arrow or the like, which is azimuth information indicating the direction of geomagnetism, on a map, assuming cooperation with a map application or the like.
The CPU 10, RAM 20, three-dimensional magnetic sensor 60, and magnetic data processing program 70 calculate a geomagnetic data indicating an accurate geomagnetic direction and magnitude based on the magnetic data detected by the three-dimensional magnetic sensor 60. Function as. The geomagnetic data, a vector having a direction toward the magnetic pole N in ground coordinate system sigma _G, as vector data as viewed from the sensor coordinate system sigma _S, x-axis, indicated by the three components of the y-axis and z-axis.

The magnetic data processing program 70 is composed of a module group such as a buffer management module 71, an offset derivation module 72, and an orientation derivation module 73.
The buffer management module 71 stores magnetic data sequentially output from the three-dimensional magnetic sensor 60 in a buffer. The RAM 20 is used as a means for storing the plurality of magnetic data.
The offset deriving module 72 derives an offset using a plurality of magnetic data stored in the buffer management module 71, and holds the derived offset. The RAM 20 is used as the offset holding means.
The azimuth derivation module 73 corrects the magnetic data sequentially output from the three-dimensional magnetic sensor with the offset held by the offset derivation module 72 to generate accurate azimuth information. The azimuth derivation module 73 calls the buffer management module 71 and the offset derivation module 72 at an appropriate period, and gives an offset update instruction.

[3. Process flow]
FIG. 6 is a flowchart showing the flow of the offset derivation process. This flowchart is executed when the direction deriving module 73 calls the buffer management module 71 and the offset deriving module 72 and gives an instruction to update the offset.
The direction deriving module 73 periodically instructs offset updating. This is because the external magnetic field and the internal magnetic field may change. The internal magnetic field is generated when the internal state of the device 1 is changed, for example, when the magnitude of the current flowing through the component mounted on the device 1 is changed, or when the magnetization state of the component mounted on the device 1 is changed. It changes with it. Since the external magnetic field is a non-uniform magnetic field, it changes as the device 1 moves. Therefore, accurate geomagnetism can be measured by periodically performing the offset update.

In step S100, initialization processing and magnetic data acquisition processing are performed. In the initialization process, the buffer management module 71 is called and the magnetic data stored in the RAM 20 is discarded. In the present embodiment, all of the magnetic data is discarded, but only a certain percentage of the data stored in the RAM 20 from the oldest may be discarded. Then, the magnetic data acquisition process, the N number of the magnetic data q ₁ to q _N output from a 3D magnetic sensor 60 is stored in the RAM 20 (N is the provision of magnetic data required to derive accurately offset A natural number of 5 or more representing the number of measurements).
In step S101, magnetic data distribution determination processing is performed. Magnetic data distribution determination process, N pieces of the magnetic data q ₁ to q _N stored in the RAM20 and the like in step S100, is appropriate as data to be used in the center point calculation process performed in a subsequent step S102 That is, it is determined whether the distribution has an appropriate distribution for calculating the center point. If the determination result is appropriate, the process proceeds to step S102, and if it is not appropriate, the process ends.

In step S102, a center point calculation process is performed. The center point calculation process assumes that the _N magnetic data q _{1 to} q _N are probabilistically distributed in the vicinity of a spherical surface (center point calculating spherical surface) S, and the center point x ₀ of the spherical surface S is offset. Calculate as a candidate.
In step S103, distortion determination processing is performed. In the distortion determination process, based on the N pieces of magnetic data q _{1 to} q _N , the distribution shape of the N pieces of data is in the vicinity of a spherical surface centered on a certain point as shown in FIGS. Judge whether it is distributed. Specifically, the distortion determination process determines whether the N pieces of magnetic data q _{1 to} q _N are distributed in the vicinity of the spherical surface S centered on the center point x ₀ calculated in the center point calculation process. To do. If it is determined that those distributed in the vicinity of the spherical surface S of the magnetic data q ₁ to q _N is centered at the center point x _0, i.e., magnetic data q ₁ to q _N are shown in FIGS. 2 and 4 to employ a center point x ₀ as an offset c when it is determined that distributed in the vicinity of the surface of the near shape of the solid in such sphere as. On the other hand, when it is determined that the magnetic data q _{1 to} q _N are distributed in the vicinity of the surface of a solid having a shape other than the spherical surface as shown in FIG. 3, the center point x ₀ is not adopted as the offset c, and the process ends. To do.

In the present embodiment, if it is determined in step S101 or S103 that it is not appropriate, the process is terminated, but the present invention is not limited to this.
For example, if it is determined in step S101 or S103 that it is not appropriate, the process may be returned to step S100, or after a message is output to the display unit 50, the process is temporarily stopped and an instruction from the user is waited for. The processing may be resumed from step S100.
When acquiring N pieces of magnetic data q _{1 to} q _N , if the user does not hold and rotate the device 1 with his hand, but only change the posture of the device 1 while fixing the position, The influence of the external magnetic field Bx can be kept low (see FIG. 4B). Therefore, when it is determined in step S103 that it is not appropriate, the user may be instructed to rotate the device 1 while the position of the device 1 is fixed. The user may be instructed by displaying an image, a moving image, or the like on the display unit 50 of the device 1 or using a voice or the like.

Details of the magnetic data distribution determination process, the center point calculation process, and the distortion determination process performed in steps S101 to S103 will be described below.
For convenience of explanation, the center point calculation process in step S102 will be described first, and then the magnetic data distribution determination process in step S101 will be described.

[3.1. Center point calculation process]
The center point calculation process in step S102 will be described with reference to FIG.
In the center point calculation process, if the magnetic data q _{1 to} q _N output from the three-dimensional magnetic sensor 60 detect only the geomagnetism Bg and the internal magnetic field Bi and are not affected by the non-uniform external magnetic field Bx or extremely small. The process is assumed. Specifically, the center point calculation process assumes that a plurality of magnetic data q _{1 to} q _N are probabilistically distributed in the vicinity of the spherical surface S with the radius r in the sensor coordinate system Σ _S. a process of calculating the point x _0.
Note, if you are not affected by the non-uniform external magnetic fields Bx, or when the influence of an external magnetic field Bx is small, the radius r denotes the magnitude of the geomagnetism Bg, sphere S and the center point x ₀ is geomagnetism equal to the spherical _{S G} and the center point _{x 0G} represents a bg.
Even if there is a non-uniform external magnetic field Bx, a plurality of pieces of magnetic data q ₁ are obtained while changing only the posture while fixing the position of the device 1 (strictly, the position of the three-dimensional magnetic sensor 60). when measured to q _N, the radius r denotes the magnitude of the vector obtained by addition of a vector representing the vector with the external magnetic field Bx representing the geomagnetism Bg, the center point x ₀ of the sphere S, the sphere representing the geomagnetism Bg It becomes almost equal to the center point _{x0G of} S _G.
In the following, unless otherwise specified, are vectors and coordinates and the like, and those expressed in the sensor space sigma _S.

When it is assumed that a plurality of magnetic data q _{1 to} q _N are present on the spherical surface S having a radius r, the distance between each magnetic data q _i and the center point x ₀ of the spherical surface S is r. (1) to (3) are established.

Here, the center of gravity of the plurality of magnetic data q ₁ to q _N is defined as q _c . The center of gravity q _c is expressed by Expression (4).
Also, introducing a barycentric coordinate system sigma _C to the center of gravity q _c origin. In this case, between the magnetic data q _i and the center point x ₀ expressed in the sensor coordinate system Σ _S and the magnetic data ^C q _i and the center point ^C x ₀ expressed in the centroid coordinate system Σ _C , the following The relationship of Formula (6) and Formula (7) is materialized.

Equation of sphere S in the sensor coordinate system sigma _S (1) is expressed as Equation (8) in the centroid coordinates sigma _C. Then, Expression (9) is obtained by substituting Expressions (6) and (7) into Expression (8).

The following formula (10) can be obtained by dividing the result of substituting each of the magnetic data q _{1 to} q _N for q _{i in} formula (9) by the number N of magnetic data. Then, by taking the difference between the expression (10) and the expression (11) obtained by expanding the expression (9), a term that does not depend on the variable q _i can be eliminated and the expression (12) can be obtained.

Thus, equation (1), which is a spherical formula indicating that the variable q _i that is magnetic data exists on the spherical surface S, is composed of the magnetic data q _i , the center of gravity q _c , and the center point x _0. (12). For the variable _{q i} of Equation (12), the N equations obtained by substituting the N magnetic data _q 1 to q _N respectively, is expressed as equation (13) using the matrix X .

Expression (13) has a solution when the coordinates of all the magnetic data q _{1 to} q _N completely coincide on the spherical surface S centered on the center point x ₀ . However, in consideration of the measurement error of the three-dimensional magnetic sensor 60, the coordinates of all the magnetic data q _{1 to} q _N do not exist at positions that completely coincide with the spherical surface S. Does not have.
Therefore, in order to obtain a plausible solution by a statistical method, a vector δ1 that absorbs the error represented by Expression (17) is introduced.

このように、球面近傍に磁気データｑ_１〜ｑ_Ｎが確率的に分布すると仮定して、複数の磁気データｑ_１〜ｑ_Ｎで示される３軸の座標と球面との誤差を最小化することで算出された球面Ｓの中心点ｘ_０が、オフセットｃの候補となる。 Vector x for such a norm of a vector .delta.1 minimized, in other words, it can be said that (.delta.1) vector x that minimizes the ^{T (.delta.1)} is what plausible as the center point x ₀ of the spherical S .
Here, when the objective function f ₁ (x) represented by the following equation (19) is defined, x that minimizes the objective function f ₁ (x) is a plausible value as the center point x ₀ of the spherical surface S. . The center point x _0, if the matrix A shown in Equation (21) is non-singular, it can be obtained by equation (20).

As described above, assuming that the magnetic data q _{1 to} q _N are probabilistically distributed in the vicinity of the spherical surface, the error between the three-axis coordinates indicated by the plurality of magnetic data q _{1 to} q _N and the spherical surface is minimized. The center point x0 of the spherical surface S calculated in ( ₁₎ is a candidate for the offset c.

[3.2. Magnetic data distribution judgment process]
Next, the magnetic data distribution determination process in step S101 will be described.
Aforementioned, the method for determining the center point x ₀ at the center point calculation process, the magnetic data q ₁ to q _N is assumed to have a sufficiently three-dimensionally spread in the sensor coordinate system sigma _S. However, since the orientation θs of the three-dimensional magnetic sensor 60 changes when the user moves the device 1 by hand, if the method of moving the device 1 is inappropriate, the magnetic data q _{1 to} q _N are it may not have a three-dimensional expanse in the sensor coordinate system sigma _S.
For example, as shown in FIG. 8, when the magnetic data q ₁ to q _N are distributed two-dimensionally on the plane π of the sensor coordinate system sigma _S is unable to calculate the center point x _0. If there is a magnetic data _q 1 to q _N in the vicinity of the circle [pi _C on the plane [pi, the center point _{x 0} of the sphere S is to may be a center point _{x 01} spherical S _.pi.1, the center point of the spherical surface S _.pi.2 This is because it may be x ₀₂ and it is not possible to specify which position on the straight line π _{L the} center point x ₀ is.

Therefore, in order to calculate the center point x _0, as shown in FIG. 9, it requires that the magnetic data q ₁ to q _N is in the sensor coordinate system sigma _S, are distributed with a three-dimensionally spread It becomes. The determination as to how three-dimensionally the magnetic data q _{1 to} q _N are distributed can be made using the matrix A shown in Expression (21).
The matrix A is a matrix corresponding to N times the variance-covariance matrix of the magnetic data q _{1 to} q _N. The eigenvalues of the matrix A are λ ₁ , λ ₂ , and λ ₃ in descending order, and the eigenvectors of size 1 corresponding to the respective eigenvalues are u ₁ , u ₂ , and 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. 9, to place 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 the value obtained. That is, it can be determined by the magnitude of the corresponding eigenvalue λ _j how much the magnetic data q _{1 to} q _N have a spread with respect to the direction of the eigenvector u _j when the center of gravity q _C is the origin.

Since the direction of the eigenvector u ₃ corresponding to the minimum eigenvalue λ ₃ is the direction in which the spread is the smallest, it can be said that the magnetic data q _{1 to} q _N are three-dimensionally distributed, the minimum eigenvalue λ ₃ values may be any predetermined threshold value lambda ₀ or more.
In the magnetic data distribution determination process, the minimum eigenvalue λ ₃ of the matrix A shown in Expression (21) is used as an evaluation value for evaluating the distribution of the magnetic data. If the value is equal to or greater than the threshold λ ₀ , the magnetic data q _{1 to} q It is determined that the distribution of _N is sufficiently three-dimensional, the process proceeds to step S102, and the above-described center point calculation process is performed. On the other hand, when the minimum eigenvalue λ ₃ is less than the threshold λ _0, it is determined that the distribution of the magnetic data q _{1 to} q _N is a two-dimensional distribution having no three-dimensional spread. In this case, the process ends.

[3.3. Distortion judgment processing]
Next, the distortion determination process in step S103 will be described.
As shown in FIG. 3, when the external magnetic field Bx is not uniform and the influence of the external magnetic field Bx is large, the magnetic data q _{1 to} q _N output from the three-dimensional magnetic sensor 60 are obtained in step S102. calculated the center point x ₀ in the vicinity of the sphere S having its center is not distributed, it will be distributed in the vicinity of the surface of the three-dimensional SD of different distorted shape than spherical. In this case, the center point x ₀ of the spherical S calculated by the center point calculating process in step S102, since the different coordinate with the center point x _0G spherical S _G representing the geomagnetism Bg, have a meaning as an offset not, it is necessary to avoid adopting a center point x ₀ of sphere S as the offset c (see FIG. 10).

However, the shape of the three-dimensional SD is, if sufficiently close to the shape of the spherical surface may be employed center point x ₀ of sphere S as an offset c. For example, as shown in FIG. 4 (A), when the influence of an external magnetic field Bx is small, in the sensor coordinate system sigma _S, the magnetic data _q 1 to q _N for outputting the three-dimensional magnetic sensor 60, at step S102 will be distributed calculated the center point x ₀ in the vicinity of the sphere S having its center, and, the spherical surface S and the center point x ₀ is approximately a sphere S _G and the center point x _0G representing the geomagnetism Bg (See FIG. 11C).
Further, as shown in FIG. 4B, the magnetic data q _{1 to} q _N are acquired by changing only the position of the device 1 (strictly speaking, the three-dimensional magnetic sensor 60) while the position is fixed. near the outside when the magnetic field Bx is detected as substantially uniform magnetic field by the three-dimensional magnetic sensor 60, the magnetic data q ₁ to q _N is sphere S centered on the center point x ₀ calculated in step S102 Will be distributed. In this case, the spherical S is different from the sphere _{S G} representing the geomagnetism Bg, the center point _{x 0} of the sphere S is substantially equal to the center point _{x 0G} spherical _{S G} (see FIG. 11 (B)).
The strain determination process evaluates how close the shape of the solid SD is to the shape of the spherical surface , assuming that the magnetic data q _{1 to} q _N are distributed near the surface of the solid SD, and the shape of the solid SD There, if evaluated to sufficiently close to the shape of the spherical surface, it is a process of employing the center point x ₀ of sphere S as an offset c.

In the above-mentioned center point calculation process, using the objective function f ₁ of the error between the coordinates and spherical S of the magnetic data q ₁ to q _N when the magnetic data q ₁ to q _N is to be distributed in the vicinity of the sphere S Evaluation did.
On the other hand, in the distortion determination process, first, it is assumed that the magnetic data q _{1 to} q _N are distributed near the surface of the three-dimensional SD having a distorted shape different from the spherical surface, and the magnetic data q ₁ shown in Expression (22). An objective function f ₂ (E, x) representing an error between ˜q _N and the solid SD is introduced.
This objective function f ₂ (E, x) has a component k (E) representing a curved surface shown in Expression (23) in addition to a component “X (x−q _c ) −j” representing a spherical surface. That is, the solid SD is a superposition of the spherical surface and the component k (E) representing the curved surface. By evaluating the influence of the component k (E) representing the curved surface, the shape of the solid SD can be compared with the spherical shape. It can be evaluated whether it is close to the extent.
Note that the magnitude of the influence of the component k (E) representing the curved surface (that is, how close the shape of the solid SD is to the shape of the spherical surface ) is shown by equations (28) and (29) described later. The evaluation value f ₃ (E) can be evaluated. If the evaluation value f ₃ (E) is equal to or less than the threshold value, the shape of the solid SD is within the range that can be regarded as the spherical surface S, and the center point x ₀ calculated by the center point calculation process is adopted as the offset c. On the other hand, when the evaluation value f ₃ (E) exceeds the threshold value, the center point x ₀ is not adopted as the offset c.

As shown in Expression (23), the component k (E) representing the curved surface is an n-dimensional vector. The element ke (q _i −x ₀ ) of the i-th row of the component k (E) representing the curved surface has the center point x ₀ as the origin with respect to the function ke (p) represented by the following equation (25). Is a value given by substituting a vector (q _i −x ₀ ) representing magnetic data q _i viewed from the coordinate system. The function ke (p) is expressed in a quadratic form of three variables p = (p _x , p _y , p _z ) shown in the equation (26), with the evaluation matrix E shown in the equation (24) as a coefficient matrix. It is a function. The evaluation matrix E is a symmetric matrix as shown in the equation (24).

In the equations (17) to (19) described above, the error between the coordinates of the magnetic data q _{1 to} q _N and the spherical surface S is to be absorbed by the vector δ1. Each element of the first to Nth rows constituting the vector δ1 is an independent variable. Accordingly, when the error is absorbed by the vector δ1, each of the errors between the magnetic data q _{1 to} q _N and the spherical surface S becomes an independent value without any restriction. That is, the N errors represented by the vector δ1 are expressed on the assumption that each of them is independently determined probabilistically, and the N errors have symmetry as a whole. The white noise has no direction dependency.
Therefore, in the equations (17) and (19), the error between the coordinates of the magnetic data q _{1 to} q _N and the spherical surface S is regarded as white noise that has symmetry and does not depend on the direction. The solution was to minimize some error.

On the other hand, the objective function f ₂ (E, x) represented by the equation (22) represents an error between the coordinates of the magnetic data q _{1 to} q _N and the spherical surface in the secondary form represented by the equation (25). It is intended to be absorbed by the component k (E) representing the curved surface, which is a vector having the function ke (p) as each component. The quadratic form of the three variables is a function in which the variable is composed of quadratic terms. By such a function, various curved surfaces in a three-dimensional space, for example, straight lines, planes, columnar surfaces, spherical surfaces, elliptical surfaces A conical surface, a 1-leaf hyperboloid, a 2-leaf hyperboloid, various parabolas, and the like can be drawn. That is, Expression (22) absorbs an error between the coordinates of the magnetic data q _{1 to} q _N and the spherical surface by a curved surface in a three-dimensional space represented by a quadratic form.
Thus, each magnetic data q ₁ to q _N, each of the error between the sphere is mutually independent and not, each magnetic data q ₁ to q all N error corresponding to the _N identical function ke ( It is expressed as a value having a constraint that it exists on the curved surface represented by p).
A component that represents a smooth curved surface separately from the case of white noise in which N errors corresponding to each of the magnetic data q _{1 to} q _N are independently stochastically determined by the objective function f ₂ (E, x). An error having the property of distortion from a spherical surface due to k (E) can also be expressed. That is, by introducing the objective function f ₂ (E, x), the error between each magnetic data q _{1 to} q _N and the spherical surface is changed to the error caused by white noise and the distortion caused by the component k (E) representing the curved surface. It became possible to separate into errors caused by.

Incidentally, formula (19) is the objective function _f 1 (x) and indicating, the objective function _f 2 (E, x) indicated by the equation (22), in the equation purely representative of the geometric shape in the sensor coordinate system sigma _S Absent. Equation (19) is an equation (1) that is an average value obtained by substituting the values of a plurality of magnetic data q _{1 to} q _{N into} Equation (1) that is a spherical equation having a purely geometric meaning. 10) is an expression obtained as a result of the operation in accordance with the above and the like, and has a statistical meaning as well as a geometric meaning. Therefore, the expression (22) is an expression having both a geometric meaning and a statistical meaning, and the function ke (p) that is an element of the component k (E) representing the curved surface appearing in the expression (22) is It does not directly represent the curved surface in the sensor coordinate system sigma _S.
However, since the equations (19) and (22) are only derived by operations based on spherical equations, it is possible to reproduce purely geometrical equations from these equations. is there. That is, the function ke (p) can be regarded as representing the curved surface in the sensor coordinate system sigma _S.

ここで、図１０及び図１１を参照しながら、磁気データｑ_１〜ｑ_Ｎが立体ＳＤの表面と完全に一致することを示す式（２７）が成立する場合と、磁気データｑ_１〜ｑ_Ｎが球面Ｓと完全に一致することを示す式（１３）が成立する場合とについて検討する。 When the value of the objective function f ₂ (E, x) is 0, that is, when the following equation (27) is satisfied, the magnetic data q _{1 to} q _N are set so as to completely coincide with the surface of the solid SD. Distributed.

Here, with reference to FIG. 10 and FIG. 11, the case where the formula (27) indicating that the magnetic data q _{1 to} q _N completely coincides with the surface of the solid SD is established, and the magnetic data q _{1 to} q _N. Let us consider the case where the formula (13) indicating that the S is completely coincident with the spherical surface S is satisfied.

When Expression (27) is established, the magnetic data q _{1 to} q _N are distributed so as to completely coincide with the surface of the solid SD as shown in FIG. When the external magnetic field Bx is and its impact greater in nonuniform, three-dimensional SD is a superposition of the curved surface SX representing the spherical S _G and the external magnetic field Bx representing the geomagnetism Bg is significantly different shape from the spherical Therefore, the shape of the solid SD is significantly different from the shape of the spherical surface S, and the influence of the component k (E) representing the curved surface in the equation (27) becomes large.
In such a case, it cannot be considered that the magnetic data q _{1 to} q _N distributed on the solid SD are distributed on the spherical surface S, and the value of the center point x ₀ of the spherical surface S means It becomes the value without. Furthermore, in such a case, since there is high possibility that different from the sphere S and the sphere S _G, possibly the center point x _0G the center point x ₀ and sphere S _G of the spherical S does not match high.
Thus, established formula (27), and, when the influence of component k (E) representing the curved surface is large, the center point x _0G the center point x ₀ and sphere S _G of the spherical S do not match more likely, it is necessary to avoid adopting a center point x ₀ of sphere S as an offset c.

On the other hand, even if Expression (27) holds, if Expression (13) also holds simultaneously, that is, if the component k (E) representing the curved surface in Expression (27) is “0”. it can employ the center point x ₀ of sphere S as an offset c.
For example, consider the case where the external magnetic field Bx does not exist as shown in FIG. In this example, because there is no curved SX representing the external magnetic field Bx, stereoscopic SD is a superposition of the curved surface SX representing the spherical S _G and the external magnetic field Bx representing the geomagnetism Bg is equal to the spherical S _G, the shape Becomes a spherical surface. Accordingly, the component k (E) representing the curved surface in Expression (27) is “0”, and Expression (13) and Expression (27) are equal. That is, the spherical S and steric SD is equal to the sphere _{S G} representing the geomagnetism Bg.
In this case, since the center point x _0G the center point x ₀ and sphere S _G of the spherical S coincide, it is possible to adopt a center point x ₀ of sphere S as an offset c.

Further, even when Expression (27) is satisfied, it can be considered that Expression (13) is also satisfied at the same time, that is, when the component k (E) representing the curved surface is small (component k representing the curved surface). (E) in this case) to be ≒ 0, the center point x ₀ of the spherical S can be employed regarded as offset c.
For example, as shown in FIG. 11B, consider a case where the external magnetic field Bx is detected as a substantially uniform magnetic field by the three-dimensional magnetic sensor 60 . In this example, the shape of the curved surface SX representing the external magnetic field Bx, it is possible to consider a spherical surface centered on the center point x _0G, sphere S _G and shape of the three-dimensional SD is a superposition of the curved surface SX Is also almost spherical. Therefore, the influence of the component k (E) representing the curved surface in the expression (27) representing the solid SD is reduced. That is, it can be considered that Expression (13) is simultaneously established simultaneously with Expression (27), and the solid SD and the spherical surface S are substantially equal.
Therefore, since the magnetic data q _{1 to} q _N distributed on the solid SD can be considered to be distributed on the spherical surface S, the value of the center point x ₀ of the spherical surface S is a meaningful value. Further, the spherical surface S and the center point stereo SD having a shape close to a sphere centered at x _0G, since it becomes approximately equal, the center point x ₀ of sphere S, the center point x _0G spherical S _G is The coordinates are almost the same.
Therefore, even if, as shown in FIG. 11 (B), it can be employed center point x ₀ of sphere S as an offset c.

Further, even if the equation (27) is satisfied, it can be considered that the equation (13) is also satisfied at the same time, and is detected by the three-dimensional magnetic sensor 60 as shown in FIG. Consider the case where the magnitude of the non-uniform external magnetic field Bx is sufficiently small.
In this example, the influence of the curved surface SX representing the external magnetic field Bx can be ignored. That is, since the three-dimensional SD is a superposition of the curved surface SX representing the spherical S _G and the external magnetic field Bx representing the geomagnetism Bg can be regarded as substantially equal to the spherical S _G representing the geomagnetism Bg, solid SD shape Becomes close to a spherical surface. Therefore, the influence of the component k (E) representing the curved surface in the expression (27) representing the solid SD is reduced. That is, it can be considered that Expression (13) is simultaneously established simultaneously with Expression (27), and the solid SD and the spherical surface S are substantially equal.
Therefore, since the magnetic data q _{1 to} q _N distributed on the solid SD can be considered to be distributed on the spherical surface S, the value of the center point x ₀ of the spherical surface S is a meaningful value. Also, since the spherical surface S and the spherical surface S _G centered on the central point x _0G are substantially equal, the central point x ₀ of the spherical surface S and the central point x _0G of the spherical surface S _G are substantially the same coordinates. become.
Therefore, even if, as shown in FIG. 11 (C), it can be employed center point x ₀ of sphere S as an offset c.

Thus, when the influence of the component k (E) representing the curved surface is small, it can be considered that the magnetic data q _{1 to} q _N distributed on the solid SD is also distributed on the spherical surface S. the center point x ₀ can be adopted as the offset c. Hereinafter, a method for evaluating the magnitude of the influence of the component k (E) representing the curved surface will be described.

Here, the evaluation value f ₃ (E) shown in the following equations (28) and (29) is defined as an evaluation value for evaluating the magnitude of the influence of the component k (E) representing the curved surface.
When the value of the evaluation value f ₃ (E) is 0, Expression (27) matches Expression (13), and the solid SD is equal to the spherical surface S. Even if the value of the evaluation value f ₃ (E) does not become 0, it can be determined that the solid SD has a shape close to the spherical surface S if it is equal to or less than the certain threshold value δe. In these cases, since the magnetic data q _{1 to} q _N are distributed in the vicinity of the spherical surface S, the center point x ₀ of the spherical surface S obtained by the center point calculation process described above can be used as the offset c.
When the evaluation value f ₃ (E) is equal to or less than the threshold value δe, the solution x = x ₀₂ that minimizes the objective function f ₂ (E, x) is almost the same as the center point x ₀ of the spherical surface S. Therefore, instead of using the center point x ₀ as the offset c, a solution x = x ₀₂ that minimizes the objective function f ₂ (E, x) may be used as the offset c.

A method for obtaining the evaluation value f ₃ (E) will be described below.
First, since the function ke (p) shown in Expression (25) is a function expressed in a quadratic form, it can be expressed as an inner product of vectors as in Expression (30) below.
Further, the i-th row element ke components k (E) representing the curved surface is a n-dimensional vector _(q i -x _0), relative to the variable p in equation (30), the vector _(q i -x ₀ )), the equation is obtained by using the vector ke ₂ (i) represented by the equation (32) and the vector e in which the components of the evaluation matrix E represented by the equation (33) are arranged. It can be expressed as (31).

We introduce the matrix _{X 2} represented by the formula (34). The matrix X ₂ is a matrix in which the transposed vector ke ₂ (i) represented by Expression (32) and the transposed vector (q _i −x ₀ ) are arranged in the _i-th row.

By using the matrix X ₂ represented by the equation (34), the objective function f ₂ (E, x) represented by the equation (22) is changed to the objective function f ₄ (e) represented by the equation (35). It can be deformed.
The vector e in Expression (35) is a vector in which the vector e ₂ shown in Expression (33) and the vector e ₃ shown in Expression (37) are arranged. Further, the vector e ₃ in Expression (37) is obtained by subtracting the center of gravity q _c shown in Expression (4) from the variable x shown in Expression (18).

The solution e ₀ for minimizing the objective function f ₄ (e) represented by the equation (35) is obtained by using a Gaussian elimination method or a Cholesky decomposition method with respect to the simultaneous equations represented by the following equation (38). And so on by applying.

Based on the solution e ₀ obtained in this way, the evaluation matrix E is restored by equation (24). Then, the value of the evaluation value f ₃ (E) shown in Expression (28), that is, the norm of the evaluation matrix E is obtained. Since the norm of the evaluation matrix E is equal to the maximum absolute value of the eigenvalues of the evaluation matrix E, it can be obtained by the Jacobian method or the power method.
As described above, when the evaluation value f ₃ (E) is less than or equal to the threshold δe, the center point x ₀ of the spherical surface S obtained by the center point calculation process or the objective function f ₂ (E, x) the none of the solutions x = x ₀₂ for minimizing, can be adopted as the offset c. Solution _{x 02} is out of the solution _{e 0,} the portion corresponding to _{e 3} of the formula (36) obtained by substituting the equation (37).

[4. simulation]
In order to verify the effectiveness of the center point calculation process and the distortion determination process, a simulation was performed. In the following, the preconditions of the simulation and the results are described.
The simulation is performed using a two-dimensional magnetic sensor instead of the three-dimensional magnetic sensor 60 described above. The two-dimensional magnetic sensor includes two magnetic sensor modules for detecting the scalar quantity by decomposing the magnetic field vectors of the geomagnetism Bg, the external magnetic field Bx, and the internal magnetic field Bi into two orthogonal components. Two-dimensional vector data having two components each of the scalar quantities output by the two magnetic sensor modules is output, and the same as the three-dimensional magnetic sensor 60 except that the Z-axis sensor 63 is not provided. Composed.

[4.1. Two-dimensional center point calculation process and distortion determination process]
Offset derivation processing (initialization processing, magnetic data acquisition processing, magnetic data distribution determination processing, center point calculation processing, and distortion determination processing) when using a two-dimensional magnetic sensor is performed using two-dimensional vector data instead of three-dimensional vector data. Except for using vector data, this is the same as the offset derivation process described above. That is, the offset derivation process in the case of using the two-dimensional magnetic sensor, in the above formulas (1) to (38), the calculation process in the two-dimensional sensor coordinate system sigma _S2 excluding the z-axis component.
In this case, the center point calculation process assumes that the magnetic data q _{1 to} q _{N that} are two-dimensional vector data are distributed in the vicinity of the circumference S in the two-dimensional plane, and the center point x _{0 of the} circumference S. Is a process for calculating. Further, in the strain determination process, when it is assumed that the magnetic data q _{1 to} q _{N that} are two-dimensional vector data are distributed in the vicinity of the curve SD in the two-dimensional plane, the shape of the curve SD is determined from the shape of the circumference. This is a process for determining whether or not the degree is different. Further, in the magnetic data distribution determination process, since the matrix A representing the dispersion of the magnetic data q _{1 to} q _N is a 2-by-2 matrix, the smaller eigenvalue of the two eigenvalues of the matrix A is less than the threshold value. Is a process of determining that the distribution of the magnetic data q _{1 to} q _{N is} a one-dimensional distribution having no two-dimensional spread.
Hereinafter, modifications of the equations necessary for applying the above-described equations (1) to (38) in two dimensions will be described.

First, in the center point calculation process, magnetic data q _i and magnetic data used in Expression (19) representing the objective function f ₁ (x) and Expression (20) for determining the center point x ₀ of the circumference S are used. The center of gravity q _c and the center point x ₀ are expressed by the following equations (40) to (42) in the two-dimensional space. Here, the variable x is a two-dimensional vector represented by x = (x, y) T.

In the distortion determination process, the evaluation matrix E used in Expression (22) representing the objective function f ₂ (E, x) is expressed by the following Expression (43) in the two-dimensional space.

Then, the function ke (p), the vector ke ₂ (i), the matrix used in the process of deriving the evaluation value f ₃ (E) of Expression (28) and the objective function f ₄ (e) of Expression (35) X ₂ and the vector e are expressed by the following equations (44) to (49) in the two-dimensional space.

[4.2. Simulation data]
With reference to FIG. 12, a method for generating magnetic data q _{1 to} q _N used in the simulation and its preconditions will be described.
First, as case A, as shown in FIG. 12 (1), magnetic data q _{1A to} q _NA were prepared assuming no observation error and no magnetic field inhomogeneity due to the external magnetic field Bx. . Specifically, the magnetic data q _1A to the magnetic data q _1A to so that the angle φ from the x axis is in increments of 1 degree on the circumference S _sim having the radius r _sim with the center point c _sim = (0,0) ^T The case where _qNA was observed was assumed. The number of data N is N = 181 (that is, the angle φ is 0 ≦ φ ≦ 180), and the magnetic data q _{1A to} q _NA are evenly distributed in the upper half of the circumference S _sim .
The center point c _sim is a true offset, that is, a value given as a precondition in simulation that there is no sensor measurement error and that the external magnetic field Bx does not exist at all or is completely uniform. Such a center point c _sim cannot be calculated from magnetic data obtained by actual observation, but is set as a precondition in the simulation. The center point c _sim means a coordinate value of a vector representing the internal magnetic field Bi, but in the simulation, the coordinate of the center point c _sim is (0, 0) ^T for convenience.

Next, as case B, as shown in FIG. 12 (2), normal random values in the x-axis direction and the y-axis direction with respect to the coordinates of the magnetic data q _{1A to} q _NA prepared in case A, respectively. Are prepared as magnetic data q _{1B to} q _NB . These magnetic data q _{1B to} q _NB assume a case where white noise, which is an observation error, is added to the magnetic data q _{1A to} q _NA .

Further, as shown in FIG. 12C, as the case C, the coordinates on the circumference S _sim can be obtained by appropriately shifting the coordinates of the magnetic data q _{1A to} q _NA prepared in the case A in the radial direction. Magnetic data q _{1C to} q _NC that draw different smoothly distorted curves SD were prepared.

[4.3. Indicator calculation]
The center point calculation process and the distortion determination process described above were performed on the plurality of magnetic data set in cases A to C. Specifically, for each of cases A to C, first, it is assumed that a plurality of magnetic data exist on a certain circumference S, and the center point x ₀ of the circumference S is determined using equation (20). Then, the value of the evaluation value f ₃ (E) given by the equation (28) was calculated.

For comparison, the applicant was calculated evaluation value _{f 5} represented by formula (51) which is disclosed in JP-A-2007-107921. The evaluation value f ₅ is used to determine how much the magnetic data q _{1 to} q _N have an error from the circumference (or spherical surface) of the radius r having the center point x ₀ . Incidentally, the radius r to be used in this evaluation value _{f 5} is the center point _{x 0} described above, based on the distance between each magnetic data _q 1 to q _N, is calculated by the equation (52).

Further, an error δx representing the distance between the center point x ₀ calculated by the center point calculating means and the center point c _sim = (0, 0) ^T representing the true offset given as a precondition for the simulation, It calculated based on Formula (53).
The error δx is a value that can be calculated only in a simulation in which the center point c _sim that is a true offset is known. Based on the error δx, the validity of the evaluation value indicated by each of the evaluation value f ₃ (E) and the known evaluation value f ₅ in this embodiment is determined.

[4.4. simulation result]
The simulation result will be described below with reference to the simulation result table of FIG.
First, the error δx in cases A to C described in the first column of the simulation result table will be described. The error δx is 0.00% in case A, 2.79% in case B, and 7.78% in case C, which is a large value compared to case B. This means that in case C, the center point x ₀ calculated by the center point calculation process has a large error from the center point c _sim which is the true offset, while in case B, the center point x ₀ This means that an error between the point x ₀ and the center point c _sim which is a true offset is smaller than that in the case C.
That is, in Case C, the center point x ₀ is the error is large, whereas it is necessary to avoid adopting as an offset, the Case B, the error of the center point x ₀ is small, is adopted as an offset It means that it doesn't matter.

Next, the value of the evaluation value f ₃ (E) in cases A to C described in the second column of the simulation result table will be described. The value of the evaluation value f ₃ (E) is 4.36 × 10 ^{−14 in} case A and 6.07 × 10 ^{−2 in} case B, whereas it is 2.42 × 10 ^{−1 in} case C. Compared to Case B, it was a large value. That is, in the case C where the error δx is large, the evaluation value f ₃ (E) also shows a large value, and in the case B where the error δx is small, the evaluation value f ₃ (E) also shows a small value. That is, based on the evaluation value f ₃ (E), the error δx between the center point x ₀ and the center point c _sim that is the true offset could be evaluated.

Listed in the third column of the simulation result table, the value of the known evaluation value f ₅ in Case A to C will be described. The value of the evaluation value f ₅ is 7.25 × 10 ⁻¹⁴ in case A, 3.14 × 10 ^{−3 in} case B, and 3.01 × 10 ^{−3 in} case C. .
Than Case C error δx is a larger value, towards the case B where the error δx exhibits a small value, the evaluation value f ₅ showed a large value. That is, depending on the evaluation value f ₅ , it is impossible to evaluate the error δx between the center point x ₀ and the center point c _sim which is a true offset.

Thus, in case C where the error δx shows a large value, both the evaluation value f ₃ (E) and the evaluation value f ₅ showed a large value, whereas in case B where the error δx shows a small value, The evaluation value f ₃ (E) showed a small value, whereas the evaluation value f ₅ showed a large value.
From this, it was found that the evaluation value f ₃ (E) is a function that can evaluate the error δx between the center point x ₀ and the center point c _sim that is the true offset.
In other words, the evaluation value f ₃ (E) is distributed on the curve having the distorted shape different from the case where the magnetic data q _{1 to} q _N are distributed with noise from the periphery. It turned out that it is a function which can judge the case where it is a thing.

[5. Conclusion]
As described above, in the present embodiment, as the offset derivation process, the magnetic data distribution determination process for determining whether or not the plurality of magnetic data q _{1 to} q _N have an appropriate distribution, and the plurality of magnetic data q _{1 to} q A center point calculation process for calculating a center point x ₀ that is a candidate for offset from _N , and whether it is appropriate to employ the center point x ₀ calculated from a plurality of magnetic data q _{1 to} q _N as an offset. distortion determination process of determining, by providing the three processes, to prevent adopting incorrect offsets, to adopt as an offset only suitable central point x ₀ which indicates a value close to the internal magnetic field Bi It was possible.
That is, the offset derivation process of the present embodiment has an advantage that an accurate geomagnetism value can be calculated with an accurate offset.

Further, at the center point calculation process, by a plurality of magnetic data q ₁ to q _N is assumed to be distributed in the vicinity of the sphere S around the center point x _0, the center of a plurality of magnetic data q ₁ to q _N calculating a point x _0, which was used as a candidate of an offset.
Such a center point calculation process has the advantage that offset candidates can be calculated by a simple calculation, and has the advantage of improving the processing speed.

Further, in the center point calculation process, in calculating the center point x ₀ , in the center of gravity coordinate system Σ _C with the center of gravity q _c of the plurality of magnetic data q _{1 to} q _N as the origin, the plurality of magnetic data q _{1 to} q _N is calculated. Calculations were performed by expressing values.
Accordingly, the output value of the three-dimensional magnetic sensor 60, as compared with the case of calculating using as the value of the magnetic data q ₁ to q _N in the sensor coordinate system sigma _S, it is possible to reduce the size of the data, This has the advantage of saving the size of the memory required for processing and improving the processing speed.

Also, well in magnetic data distribution determining processing, for determining the minimum eigenvalue lambda ₃ of the matrix A, by determining that the value is the threshold value lambda ₀ or more, the magnetic data q ₁ to q _N is in the sensor coordinate system sigma _S It is possible to prevent the center point calculation process based on the magnetic data q _{1 to} q _{N from} being able to derive an accurate center point x ₀ by determining that the center point has a three-dimensional spread. It was possible.
Thus, by avoiding to adopt an incorrect central point x ₀ as an offset, which has the advantage that it is possible to prevent detecting a value of a large geomagnetic errors, improper magnetic data q ₁ to make the center point calculation process for deriving an incorrect center point x ₀ which is based on to q _N is possible to prevent, with the advantage that it is possible to shorten the time to adopt the correct offset.

Also, in the distortion determination process, by introducing the evaluation value f ₃ (E), how close the shape of the solid SD having the magnetic data q _{1 to} q _N near the surface is to the shape of the spherical surface I was able to evaluate. Thereby, in the center point calculation process, it is possible to evaluate the validity of adopting the center point x ₀ derived on the assumption that the magnetic data q _{1 to} q _N are distributed in the vicinity of the spherical surface S as an offset. Thus, it is possible to effectively prevent an inappropriate offset from being employed.

The evaluation value f ₃ (E) is a three-dimensional SD having a distorted shape different from the spherical surface when the magnetic data q _{1 to} q _N are distributed from a certain spherical surface with an error corresponding to white noise. It also has the meaning that it is possible to distinguish the case where it is distributed in the vicinity of the surface.
For example, in the conventional evaluation value f ₅ , when the magnetic data q _{1 to} q _N are distributed with an error from the spherical surface S, the error is due to white noise or a non-uniform external magnetic field. It could not be judged whether it was due to Bx. That is, even when the magnetic data q _{1 to} q _N are distributed in the vicinity of the surface of the three-dimensional SD having a shape greatly distorted from the spherical surface, it is merely evaluated as an error as white noise from the spherical surface. It was.
On the other hand, the evaluation value f ₃ (E) of the present embodiment can distinguish between an error due to white noise and an error due to the influence of the non-uniform external magnetic field Bx. Therefore, the error is the center point x ₀ which is calculated when it is just white noise is employed as the offset for error between the vector representing the internal magnetic field Bi is small. Meanwhile, the center point x ₀ which is calculated when the error due to non-uniform external magnetic field Bx is present, it is possible to prevent the adoption of an offset for a large error between the vector ^S Bi representing the internal magnetic field Bi.
As a result, the offset derivation process of the present embodiment enables the reduction in the number of measurements until the correct offset is calculated, and also prevents the inaccurate value from being adopted as an offset beforehand. Have

In the distortion determination process, a component k (E) representing a curved surface that is an n-dimensional vector is introduced into the objective function f ₂ (E, x). The element in the i-th row of the component k (E) representing the curved surface is a vector (q _i −x ₀ ) obtained by subtracting the center point x ₀ from the magnetic data q _{i with} respect to the function ke (p) that is a quadratic form. ) Is a value given by substituting.
Conventionally, an error between the coordinates of the magnetic data q _{1 to} q _N and the spherical surface S is absorbed by a vector δ 1 as shown in Expression (17). Since each element in the first to Nth rows constituting the vector δ1 is an independent variable, each of the N errors expressed by the vector δ1 is an independent value without any restriction. That is, N errors represented by the vector δ1 are each determined independently and probabilistically, and the N errors as a whole are white noise having symmetry and no direction dependency. Met.
On the other hand, in the present embodiment, each of the magnetic data q _{1 to} q _N is represented by a component k (E) representing a curved surface that is an n-dimensional vector having a function ke (p) that is a quadratic form as an element, By expressing each of the errors with the spherical surface , each of the N errors corresponding to each of the magnetic data q _{1 to} q _N has a restriction that it exists on the curved surface represented by the function ke (p). Expressed as a value. That, N number of errors corresponding to each magnetic data q ₁ to q _N is the case of white noise, each determined probabilistically independently separately, an error having the property that the distortion from the spherical by a smooth curved surface It became possible to express some cases. This makes it possible to separate a portion caused by white noise and a portion caused by distortion caused by a curved surface from an error from a spherical surface.
Therefore, the offset derivation process of the present embodiment can determine the magnitude of the influence of distortion due to the external magnetic field Bx among the errors between the magnetic data q _{1 to} q _N and the spherical surface, and is calculated in the center point calculation process. and the case where distortion is present due to external magnetic field Bx which can not be adopted as the offset of the center point x _0, it has become possible to accurately determine.

1 ... apparatus, 2 ... object, 10 ... CPU, 60 ... 3-dimensional magnetic sensor, Bg ... geomagnetism, Bi ... internal magnetic field, Bx ... external magnetic field, sigma _G ... ground coordinate system, sigma _S ... sensor coordinate system, _{q i} ... Magnetic data, x ₀ ... center point, x _0G ... center point (geomagnetic), E ... evaluation matrix, Ps ... position, θs ... attitude, S ... spherical surface, S _G ... spherical surface (geomagnetic), SX ... curved surface, SD ... solid R, radius of the spherical surface, f ₁ (x), objective function, f ₂ (E, x), objective function, f ₃ (E), evaluation value, k (E), a component representing a curved surface.

Claims (10)

A three-dimensional magnetic sensor that is incorporated in a device including a component that generates a magnetic field and detects magnetic components in three directions orthogonal to each other;
Storage means for storing magnetic data sequentially output from the three-dimensional magnetic sensor when the posture of the device is changed ;
Assuming that the coordinates indicated by the plurality of magnetic data stored in the storage means are probabilistically distributed near the surface of an aspheric solid obtained by superimposing a spherical surface and a curved surface, the plurality of magnetic data A first evaluation value based on a component representing the curved surface in the objective function when minimizing an error value represented by the objective function using an objective function representing an error between the coordinates indicated by 3 and the surface of the solid And a distortion determination means for determining whether or not the first evaluation value is equal to or smaller than a predetermined magnitude ;
An offset update means for updating an offset that is a coordinate of three axes representing a magnetic field component generated by the component in the magnetic data when the determination result of the distortion determination means is affirmative;
A geomagnetism measuring device. When the first evaluation value is larger than the predetermined size, there is provided means for urging the user to change the posture of the device without changing the position of the device. Item 2. The geomagnetism measuring device according to item 1. The geomagnetism measuring device is
Assuming that the coordinates indicated by the plurality of magnetic data stored in the storage means are probabilistically distributed near the center point calculation spherical surface, the three-axis coordinates indicated by the plurality of magnetic data and the center point Center point calculating means for calculating the center point of the center point calculating sphere so as to minimize an error from the calculation sphere,
In addition,
The component representing the curved surface in the objective function is a vector composed of elements corresponding to each of the plurality of magnetic data,
For each element, a 3-axis value representing the magnetic data in a coordinate system with the center point as the origin is substituted for a function expressed in a three-variable quadratic form with the first evaluation matrix as a coefficient matrix. Is the value obtained by
The first evaluation value, Ri norm der of the first evaluation matrix,
The offset is the center point.
The geomagnetism measuring apparatus according to claim 1 or 2. The center point calculating means includes
A second evaluation value for evaluating that the coordinates indicated by the plurality of magnetic data are distributed with a three-dimensional spread is calculated, and when the second evaluation value is equal to or larger than a predetermined size, The geomagnetic measurement apparatus according to any one of claims 1 to 3, wherein the center point is calculated. The center point calculation means calculates x, which minimizes the value of the following second objective function f ₁ (x), as the center point. 5. The geomagnetic measuring device described.

The objective function is represented by f ₂ (E, x), where E is a variable, where E is the first evaluation matrix and x ₀ is the center point.
The geomagnetic measurement apparatus according to claim 5, wherein the first evaluation value is a norm of E that minimizes f ₂ (E, x).

The geomagnetic measurement apparatus according to claim 5 or 6, wherein the second evaluation value is a minimum eigenvalue of the following matrix A.

A two-dimensional magnetic sensor that is incorporated in a device including a component that generates a magnetic field and detects magnetic components in two directions orthogonal to each other;
Storage means for storing magnetic data sequentially output from the two-dimensional magnetic sensor when the posture of the device is changed;
Assuming that the coordinates indicated by the plurality of magnetic data stored in the storage means are probabilistically distributed in the vicinity of the circumference centered on the coordinates indicating the magnetic field component generated by the component, Center point calculating means for calculating a center point of the circumference so as to minimize an error between the coordinates of the two axes indicated by the magnetic data and the circumference;
Assuming that the coordinates indicated by the plurality of magnetic data are probabilistically distributed in the vicinity of the second curve having a shape other than the circumference obtained by superimposing the circumference and the first curve, the plurality of magnetic data The first curve in the third objective function when the error value represented by the third objective function is minimized by using the third objective function representing the error between the coordinates indicated by the data and the second curve. And a distortion determination unit that calculates a third evaluation value based on a component representing, and adopts the center point as an offset of the two-dimensional magnetic sensor when the third evaluation value is equal to or smaller than a predetermined size. Geomagnetic measuring device. A three-dimensional magnetic sensor that is incorporated in a device including a component that generates a magnetic field and detects magnetic components in three directions orthogonal to each other;
Storage means for storing magnetic data sequentially output from the three-dimensional magnetic sensor when the posture of the device is changed;
An offset determination method used in a geomagnetism measuring apparatus comprising:
Assuming that the coordinates indicated by the plurality of magnetic data stored in the storage means are probabilistically distributed in the vicinity of the center point calculation spherical surface with the coordinates indicating the magnetic field component generated by the component as the center point , Calculating a center point of the center point calculating sphere so as to minimize an error between the three-axis coordinates indicated by the plurality of magnetic data and the center point calculating sphere ;
Assuming that the coordinates indicated by the plurality of magnetic data are probabilistically distributed near the surface of an aspheric solid obtained by superimposing a spherical surface and a curved surface, the coordinates indicated by the plurality of magnetic data and the A first evaluation value based on a component representing the curved surface in the objective function when the error value represented by the objective function is minimized is calculated using an objective function representing an error with the surface of the solid, When the evaluation value is equal to or smaller than a predetermined size, the center point is employed as an offset of the three-dimensional magnetic sensor.
An offset determination method characterized by the above. A three-dimensional magnetic sensor that is incorporated in a device including a component that generates a magnetic field and detects magnetic components in three directions orthogonal to each other;
Storage means for storing magnetic data sequentially output from the three-dimensional magnetic sensor when the posture of the device is changed;
An offset determination program used in a geomagnetism measuring device comprising:
Assuming that the coordinates indicated by the plurality of magnetic data stored in the storage means are probabilistically distributed in the vicinity of the center point calculation spherical surface with the coordinates indicating the magnetic field component generated by the component as the center point , so as to minimize the error between the coordinates and the center point calculation spherical three axes indicated by the plurality of magnetic data, the processing for calculating the center point of the center point calculation spherical,
Assuming that the coordinates indicated by the plurality of magnetic data are probabilistically distributed near the surface of an aspheric solid obtained by superimposing a spherical surface and a curved surface, the coordinates indicated by the plurality of magnetic data and the A first evaluation value based on a component representing the curved surface in the objective function when the error value represented by the objective function is minimized is calculated using an objective function representing an error with the surface of the solid, A process of adopting the center point as an offset of the three-dimensional magnetic sensor when one evaluation value is a predetermined size or less;
An offset determination program to be executed by a computer.

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