JP2007240270A - Magnetic data processor, processing method, and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a magnetic data processor capable of correcting an offset from an accumulated magnetic data group by simple processing. <P>SOLUTION: The magnetic data processor comprises an input means for the input of magnetic data sequentially output from a three-dimensional magnetometric sensor. The magnetic data processor also comprises an offset deriving means that requires as a constraint condition that a new offset as the sum of the old offset and a corrective vector when the corrective vector is assumed to be a primary junction of a second basic vector group that is a positional vector of a temporary offset derived from the population data group without using the offset and uses, as a coefficient, a weighted value of each coefficient of the positional vector according to the ratio of the main value of the distribution of the population data group, and derives the new offset based on the old offset and the population data group. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a magnetic data processing apparatus, method, and program, and more particularly to a technique for correcting an offset of a three-dimensional magnetic sensor.

  Conventionally, a three-dimensional magnetic sensor that is mounted on a mobile body such as a mobile phone or a vehicle and detects the direction of geomagnetism is known. In general, a three-dimensional magnetic sensor includes three magnetic sensor modules for detecting a scalar quantity by decomposing a magnetic field vector into three orthogonal components. The magnetic data that is the output of the three-dimensional magnetic sensor is a combination of the outputs of the three magnetic sensor modules, and is three-dimensional vector data that is a linear combination of unit vectors orthogonal to each other. The direction and magnitude of the magnetic data are the direction and magnitude of the magnetic field detected by the three-dimensional magnetic sensor. When the direction or magnitude of the geomagnetism is specified based on the output of the three-dimensional magnetic sensor, a process for correcting the output of the three-dimensional magnetic sensor in order to cancel measurement errors due to magnetization of the moving body and temperature characteristics of the magnetic sensor itself is performed. is necessary. The operation value of this correction process is called offset. The offset is vector data representing a magnetic field generated by magnetization of the moving body detected by the three-dimensional magnetic sensor, and the measurement error is canceled by subtracting the offset from the magnetic data that is the output of the three-dimensional magnetic sensor. The offset can be calculated by obtaining the center of the spherical surface on which the magnetic data group is distributed.

  By the way, the distribution of magnetic data is not a perfect sphere in reality. This is because the output of the three-dimensional magnetic sensor itself has a measurement error according to a Gaussian distribution, and in reality there is no completely uniform magnetic field, so magnetic data necessary for calculating the offset is accumulated. This is because the magnetic field measured by the three-dimensional magnetic sensor fluctuates during the period, and there is a calculation error until the output of the three-dimensional magnetic sensor is extracted as a digital value.

Conventional magnetic sensor offset derivation methods accumulate a large amount of magnetic data and derive the offset by statistical processing. Therefore, unless the user consciously changes the posture of the moving object, the offset is accurately obtained. A magnetic data group necessary for updating is not accumulated, and it takes a long time to be updated after the offset needs to be updated. Further, since the attitude of the magnetic sensor mounted on the vehicle rarely changes greatly in three dimensions, usually only magnetic data distributed in a plane is accumulated. Therefore, in order to accurately update the offset of the magnetic sensor mounted on the vehicle, it is not desirable to wait for a magnetic data group uniformly distributed in a spherical shape to be accumulated.
Patent Document 1 discloses an algorithm that can correct an offset even if the distribution of a magnetic data group is planar. However, since the program according to the algorithm described in Patent Document 1 is complicated, implementation is not easy.

International Publication No. 2005/061990

  An object of the present invention is to provide a magnetic data processing apparatus, method and program, and a magnetic measurement apparatus capable of correcting an offset from an accumulated magnetic data group by a simple process regardless of the distribution of the magnetic data group.

  (1) A magnetic data processing apparatus for achieving the above object is an input means for inputting magnetic data sequentially output from a three-dimensional magnetic sensor, which is three-dimensional vector data that is a linear combination of the first basic vector group. Storage means for storing a plurality of magnetic data as a population data group in order to update the old offset of the magnetic data to a new offset, and a temporary offset derived from the population data group without using the old offset A ratio of the principal value of the distribution of the population data group to each coefficient of the position vector that is a linear combination of the second basic vector group in the principal axis direction of the distribution of the population data group and the position vector with respect to the old offset When the linear combination of the second basic vector group having a coefficient weighted according to the coefficient is used as a correction vector, the old offset and the correction vector are used. As a constraint condition that obtains the new offset is the sum of the torque, and a offset derivation means for deriving the new offset based on said old offset and the data set of statistical population.

The algorithm employed in this apparatus will be described in detail with reference to FIG. The main point of this algorithm is that the magnetic data group distributed in the main axis direction with a larger variance is evaluated more heavily as the population element used to update the offset, and the magnetic data group distributed in the main axis direction with a smaller variance. It is to be lightly evaluated as a population element. Specifically, it is as follows. The old offset c ₀ , the new offset c, and the temporary offset (the position of the end point of g with respect to the origin 0) are three-dimensional position vector data that is a linear combination of basic vectors of magnetic data. That is, these are vector data represented by a coordinate system called xyz. The new offset c is derived based on the magnetic data group stored to update the old offset c ₀ to the new offset c and the old offset c ₀ .

The population data group, which is a magnetic data group stored for updating to the new offset c, may be composed of a magnetic data group stored within a predetermined period, or a predetermined number of magnetic data It may be configured by a group, or may be configured by an arbitrary number of magnetic data groups accumulated at a certain timing (for example, timing when an offset update request is generated).
The old offset c ₀ may be derived by the same method as the new offset c, or may be determined in advance.

The temporary offset is defined to be derived from the population data group without using the old offset c ₀ , but this definition is a definition for defining a constraint condition for deriving the new offset c, and is actually derived. It is not data that must be present. Since the temporary offset is derived from the population data group without using the old offset c ₀ , if the temporary offset is actually derived, the center of the spherical surface in which the population data group is distributed in the vicinity is assumed. This is a position vector. However, if the population data group is distributed to a part of the sphere derived from it, the error included in each of the population data groups strongly affects the derivation result of the sphere. There is a high possibility that a temporary offset far from the offset is derived. For example, as shown in FIG. 1, a population data group is distributed in a donut shape in which eigenvectors orthogonal to each other are u ₁ , u ₂ , u _3, and the population is determined in the direction of the eigenvector u ₃ corresponding to the smallest principal value. Consider the case where the variance of the data group is minimized. In this case, since the variance of the population data group is small in the direction of the eigenvector u ₃ of the distribution, the temporary offset derived from such a population data group and the position of the true offset are in the direction of the eigenvector u _3. Is likely to be far away. On the other hand, in this case, since the variance of the population data group is large in the direction of the eigenvector u ₁ of the distribution, the positions of the temporary offset and the true offset derived from such a population data group are in the direction of the eigenvector u _1. And is likely to be close.

Because dispersion of the principal axis direction of the distribution may be represented principal value lambda ₁ of the distribution, lambda _2, lambda ₃ as an index, in this apparatus, each according to principal values λ _1, λ _2, λ ₃ ratio of distribution Evaluate population elements distributed in the direction corresponding to the principal value. Specifically, the coordinate axis α which first matches the main axis direction of the distribution, beta, in a coordinate system with gamma, the correction vector f and the temporary offset relative to the old offset c ₀ is the position vector of the new offset c relative to the old offset c ₀ A position vector g can be defined. In other words, the correction vector f and the position vector g can be defined as a linear combination of basic vectors in the main axis direction of the distribution. This corresponds to the spindle conversion. Then, each component g _α , g _β , g _γ of the temporary offset position vector g with respect to the old offset c ₀ is weighted according to the magnitudes of the corresponding main values u ₁ , u ₂ , u _{3 in} the distribution, and the correction vector When the components f _α , f _β , and f _γ of f are derived, the correction vector f is derived by increasing the reliability of the population element in the direction of large variance and decreasing the reliability of the population element in the direction of small variance. can do. However, the definition of the correction vector f and the position vector g is also a definition for defining a constraint condition for deriving the new offset c, and is not data that needs to be actually derived.

Eventually, by deriving the new offset c with the constraint that the new offset c is obtained as the sum of the correction vector f and the old offset c ₀ defined in this way, the magnetic field is distributed in the direction of the major axis. New offsets can be derived while evaluating data groups more heavily as population elements used to update offsets and magnetic data groups with smaller variances in the main axis direction as lighter evaluations as population elements. . As a technique for deriving a new offset in this way, for example, there is a technique for formulating a distribution into an optimization problem. When deriving a new offset as a distribution optimization problem with constraints, the new offset can be derived by solving a simple simultaneous linear equation as described below as an embodiment. That is, according to this apparatus, the most probable new offset that can be derived from the population data group can be derived by simple processing regardless of the distribution of the population data group.

  (2) In the offset deriving device for a magnetic sensor for achieving the above object, the constraint condition is that a ratio of the intermediate main value to the maximum main value is larger than a first threshold value, and the maximum main When the ratio of the minimum principal value to the value is equal to or smaller than the second threshold value, the weight coefficient of the position vector is 0 for the coefficient of the second basic vector in the principal axis direction corresponding to the minimum principal value. Yes, the ratio of the intermediate main value to the maximum main value is less than or equal to the first threshold value, and the ratio of the minimum main value to the maximum main value is less than or equal to the second threshold value The position vector weighting factor for the second basic vector coefficient in the principal axis direction corresponding to the minimum principal value and the second basic vector coefficient in the principal axis direction corresponding to the intermediate principal value. Both can be 0 .

In this apparatus, the distribution of the population data group is discretely evaluated, and each coefficient of the temporary offset position vector g with respect to the old offset c ₀ is discretely weighted according to the result of the discrete evaluation. That is, the weight of the coefficient of the position vector g is 0 in the direction in which the variance becomes the minimum value. Also, when the variance is small in the direction where the variance becomes an intermediate value, the weight of the coefficient of the position vector g is also 0 in that direction. That is, in this apparatus, magnetic data is not evaluated at all in the direction where the dispersion is relatively smaller than a certain threshold value.

(3) In the magnetic data processing apparatus for achieving the above object, the constraint condition is obtained by weighting the position vector coefficient by a weight coefficient that continuously corresponds to a ratio of principal values of the distribution of the population data group. The value may be a coefficient of the correction vector.
According to this apparatus, since the continuous correspondence with respect to the variance is in the weight coefficient, the substantial utilization rate of the population data group can be improved. Further, according to this apparatus, the new offset can be derived without changing the process according to the distribution of the population data group, so that the offset update process can be simplified.

(4) In the magnetic sensor offset deriving device for achieving the above object, the position vector weighting coefficient is 1 for the coefficient of the second basic vector in the principal axis direction corresponding to the maximum principal value. As described above, the weighting coefficient of each coefficient may be normalized.
In the case of introducing a distribution evaluation index other than the ratio of the main values of the distribution of the population magnetic data group, it is not necessary to normalize each weighting coefficient by setting the maximum weighting coefficient to 1. For example, the principal axis direction corresponding to the largest principal value (ie, the principal direction) with respect to the radius of the spherical surface derived as a spherical surface whose distribution is approximated to a part of the population magnetic data group based on the population magnetic data group The maximum weighting factor can be made less than 1 depending on the ratio of the maximum distance between the magnetic data for).

この装置によると、制約条件付の分布の最適化問題として新オフセットを導出するため、実施形態として後述するような単純な連立一次方程式を解くことにより、新オフセットを導出することができる。つまり、この装置によると、母集団データ群の分布に関わらず、その母集団データ群から導出できる最も確からしい新オフセットを簡素な処理で導出することができる。 (5) In the magnetic data processing apparatus for achieving the above object, the offset deriving means may derive c that minimizes the following objective function f (c) under the constraint condition.

According to this apparatus, since a new offset is derived as a distribution optimization problem with constraints, the new offset can be derived by solving a simple simultaneous linear equation as will be described later as an embodiment. That is, according to this apparatus, the most probable new offset that can be derived from the population data group can be derived by simple processing regardless of the distribution of the population data group.

(6) A magnetic measurement apparatus for achieving the above object includes the magnetic data processing apparatus described in (1) to (5) above and the three-dimensional magnetic sensor.
According to this apparatus, the most probable new offset that can be derived from the population data group can be derived by simple processing regardless of the distribution of the population data group.

  Each function of the plurality of means provided in the present invention is realized by hardware resources whose functions are specified by the configuration itself, hardware resources whose functions are specified by a program, or a combination thereof. Further, the functions of the plurality of means are not limited to those realized by hardware resources that are physically independent of each other. The present invention can be specified not only as an apparatus invention but also as a program invention, a recording medium recording the program, and a method invention. In addition, the order of each operation of the method described in the claims is not limited to the order of description unless there is a technical impediment, and may be executed in any order, and may be executed simultaneously. Also good.

Hereinafter, embodiments of the present invention will be described in the following order.
A. First embodiment [1. Overall explanation]
1-1. Hardware configuration 1-2. Software configuration [2. Process flow]
2-1. Overall flow 2-2. Buffer update 2-3. Evaluation of distribution 2-4. Derivation of new offset by optimization problem 2-5. Restriction when distribution is planar 2-6. Restriction when distribution is slightly linear 2-7. Derivation of new offset when distribution is three-dimensional 2-8. Summary B. Second Embodiment-Outline-Evaluation of Distribution-Derivation of New Offset C.I. Other embodiments

[1. Overall explanation]
1-1. Hardware Configuration FIG. 2 is a schematic diagram showing an appearance of a mobile phone 3 which is an example of a mobile body to which the present invention is applied. A three-dimensional magnetic sensor 4 is mounted on the mobile phone 3. The three-dimensional magnetic sensor detects the direction and strength of the magnetic field by detecting the strength of the magnetic field in three directions of x, y, and z orthogonal to each other. Various information such as characters and images is displayed on the display 2 of the mobile phone 3. For example, the display 2 displays a map and an arrow or character indicating the direction.

  FIG. 3 is a block diagram showing a magnetic measurement device including the three-dimensional magnetic sensor 4 and the magnetic data processing device 1. The three-dimensional magnetic sensor 4 includes an x-axis sensor 30, a y-axis sensor 32, and a z-axis sensor 34 that respectively detect an x-direction component, a y-direction component, and a z-direction component of a magnetic field vector due to geomagnetism. The x-axis sensor 30, the y-axis sensor 32, and the z-axis sensor 34 are all configured by a magnetoresistive element, a Hall element, etc., and may be any one as long as it has directivity. The x-axis sensor 30, the y-axis sensor 32, and the z-axis sensor 34 are fixed so that their sensitivity directions are orthogonal to each other. Outputs of the x-axis sensor 30, the y-axis sensor 32, and the z-axis sensor 34 are time-divisionally input to a magnetic sensor I / F (Inter Face) 22. In the magnetic sensor I / F 22, input from the x-axis sensor 30, the y-axis sensor 32, and the z-axis sensor 34 is amplified and then AD converted. Digital magnetic data output from the magnetic sensor I / F 22 is input to the magnetic data processing device 1 via the bus 5.

  The magnetic data processing device 1 is a so-called computer including a CPU 40, a ROM 42, and a RAM 44. The CPU 40 is a processor that performs overall control of the mobile phone 3, for example. The ROM 42 is a non-volatile storage medium that stores a magnetic data processing program executed by the CPU 40 and various programs for realizing the function of the moving body, for example, a navigation program. The RAM 44 is a volatile storage medium that temporarily holds data to be processed by the CPU 40. The magnetic data processing device 1 and the three-dimensional magnetic sensor 4 can be configured as a one-chip magnetic measurement device.

1-2. Software Configuration FIG. 4 is a block diagram showing the configuration of the magnetic data processing program 90. The magnetic data processing program 90 is a program for providing azimuth data to the navigation program 98, and is stored in the ROM 42. The azimuth data is two-dimensional vector data indicating the direction of geomagnetism. The orientation data may be provided to other application programs as, for example, three-dimensional vector data for recognizing the posture of the moving body. The magnetic data processing program 90 is composed of a module group such as a buffer management module 92, an offset derivation module 94, and an orientation derivation module 96.

  The buffer management module 92 is a program component that inputs magnetic data sequentially output from the magnetic sensor 4 and accumulates the input magnetic data in a buffer for use in offset updating. The CPU 40, the RAM 44, and the ROM 42 are input means and It functions as a storage means. The buffer may be configured by hardware or software. The magnetic data group stored in this buffer is referred to as a population data group.

  The offset derivation module 94 is a program component that derives a new offset based on the population data group held by the buffer management module 92 and the old offset held by itself and updates the old offset to the new offset. Thus, the CPU 40, the RAM 44, and the ROM 42 are caused to function as offset deriving means. Since the new offset becomes the old offset when the old offset is updated to the new offset, the old offset is simply referred to as an offset in a context without misunderstanding. Actually, the offset used to correct the azimuth data is set to one variable, the new offset is derived as a variable different from that variable, and is set to the variable used to correct the azimuth data when it is derived. Therefore, the variable used for correcting the azimuth data is a variable in which the old offset is stored.

  The azimuth derivation module 96 is a program part that generates azimuth data by correcting the magnetic data sequentially output from the magnetic sensor 4 with the offset held by the offset derivation module 94. The azimuth derivation module 96 derives the direction of the CPU 40, the RAM 44, and the ROM 42. It functions as a means. Specifically, the azimuth derivation module 96 outputs two or all three of the three components obtained by subtracting each offset component from each component of magnetic data that is three-dimensional vector data as azimuth data. .

  The navigation program 98 is a well-known program that searches for a guidance route to a destination and displays the guidance route on a map. For ease of map recognition, the map is displayed on the screen so that the orientation on the map matches the actual orientation. Therefore, for example, when the mobile phone 3 rotates, the map displayed on the display 2 rotates with respect to the display 2 so as not to rotate with respect to the ground. Direction data is used for such map display processing. Of course, the azimuth data may be used only for displaying east, west, south, and north with characters or arrows.

[2. Process flow]
2-1. Overall Flow FIG. 5 is a flowchart showing a flow of processing for deriving a new offset. The process shown in FIG. 5 proceeds when the CPU 40 executes the offset derivation module 94 when an offset update request is generated.

2-2. In the buffer update step S100, all the magnetic data stored in the buffer for storing the magnetic data group (population data group) used for deriving the new offset is deleted. That is, at this time, the population data group used to derive the old offset is deleted.
In step S102, magnetic data used to derive a new offset is input and stored in a buffer. When the magnetic data is sequentially input from the magnetic sensor 4 at short time intervals in a situation in which the posture of the mobile phone 3 is hardly changed, the distance between the two magnetic data that are continuously input becomes close. A plurality of magnetic data that are close to each other are stored in a buffer having a limited capacity, which is a waste of memory resources and causes an unnecessary buffer update process. In addition, when a new offset is derived based on a magnetic data group that is close to each other, a new offset with low accuracy may be derived based on a population data group having a biased distribution. Therefore, the necessity for updating the buffer may be determined as follows. For example, if the distance between the magnetic data stored in the buffer immediately before and the last input magnetic data is smaller than a certain threshold value, it is determined that there is no need to update the buffer, and the last input magnetic data is Discarded without being stored in the buffer.

  In step S104, it is determined whether a specified number of magnetic data necessary for deriving a new offset with high accuracy has been accumulated in the buffer. That is, the number of elements in the population data group is determined in advance. By setting the number of elements of the population data group determined in advance to be small, the response to the offset update request is improved. Steps S102 and S104 are repeated until a prescribed number of magnetic data is accumulated in the buffer.

ただし、

2-3. Distribution Evaluation When a prescribed number of magnetic data is accumulated in the buffer, the distribution of the population data group is evaluated (steps S106 and S108). The distribution is evaluated based on the main value of the distribution.
When the magnetic data group is expressed by the following equation (1),
q _i = (q _ix , q _iy , q _iz ) (i = 0,1,2 ...) (1)
The main value of the distribution is a symmetric matrix A defined by equations (2), (3), and (4) using the sum of vectors starting from the center of gravity (average) of the population data group and ending with each magnetic data. Is the eigenvalue of.

However,

The matrix A can also be written as equation (5).

The eigenvalues of the matrix A are λ ₁ , λ ₂ , and λ _{3 in} descending order. In addition, eigenvectors corresponding to λ ₁ , λ ₂ , and λ ₃ and normalized by a magnitude of 1 and orthogonal to each other are denoted by u ₁ , u ₂ , and u ₃ . In the range handled in this specification, λ ₁ > 0, λ ₂ > 0, and λ ₃ ≧ 0. When two or more eigenvalues are 0, in other words, when the rank of the matrix A is 1 or less, the number of elements of the population data group is 1 or the distribution is a complete straight line, so it is necessary to consider Absent. Since the matrix A is a non-negative definite matrix from its definition, the eigenvalue is always 0 or a positive real number.
The distribution of the population data group is evaluated based on λ ₃ / λ ₁ that is the ratio of the minimum eigenvalue to the maximum eigenvalue and λ ₂ / λ ₁ that is the ratio of the intermediate eigenvalue to the maximum eigenvalue.

In step S106, it is determined whether the distribution of the population data group is sufficiently three-dimensional. Specifically, an affirmative determination is made when the following expression (6) is satisfied, and a negative determination is made when it is not satisfied.
λ ₃ / λ ₁ > t ₁ and λ ₂ / λ ₁ > t ₂ (6)
t ₁ and t ₂ are predetermined constants. How to set the values of t ₁ and t ₂ is a design matter, and can be arbitrarily set depending on how the derivation characteristic of the offset is determined. When Expression (6) is satisfied, the population data group is isotropically distributed from the center of gravity of the population data group. The fact that the population data group is isotropically distributed from the center of gravity of the population data group means that the population data group is distributed evenly around a specific spherical surface.

In step S108, it is determined whether the distribution of the population data group is sufficiently planar. Specifically, an affirmative determination is made when the following expression (7) is satisfied, and a negative determination is made when it is not satisfied.
λ ₃ / λ ₁ ≦ t ₁ and λ ₂ / λ ₁ > t ₂ (7)
When Expression (7) is satisfied, the population data group is isotropically distributed from the center of gravity of the population data group within a range limited to a specific plane vicinity. The fact that the population data group is isotropically distributed from the center of gravity of the population data group within the range limited to the vicinity of a specific plane means that the population data is biased to the vicinity of the circumference of the cross-section circle of the specific spherical surface. It means that the group is distributed.

  When a negative determination is made in step S108, the distribution of the population data group is somewhat linear. The distribution of the population data group is somewhat linear because the population data group is unevenly distributed in the short arc of the cross-section circle of a specific spherical surface, or the population data group is distributed at both ends of the diameter of the cross-section circle. It means that it is unevenly distributed.

ただし、

2-4. Derivation of New Offset by Optimization Problem Here, the optimization problem for deriving the new offset will be described.
When the population data group is composed of four magnetic data that are not on the same plane, the spherical surface on which the population data group is distributed is uniquely identified without using a statistical method. The position vector c = (c _x , c _y , c _z ) at the center of the spherical surface can be obtained by solving simultaneous equations (8). There are four equality constraints for three variables, but one of the equality constraints is redundant, so equation (8) always has a solution.

However,

このとき、ｃについての連立一次方程式（１１）が解を持てば、その解は、母集団データ群が分布する球面の中心である。
Ｘｃ=ｊ・・・（１１） When the number of elements in the population data group is 5 or more, j is defined by the following equation (10).

At this time, if the simultaneous linear equations (11) for c have a solution, the solution is the center of the spherical surface on which the population data group is distributed.
Xc = j (11)

However, considering the measurement error of the three-dimensional magnetic sensor 4 itself, in reality, the equation (11) cannot have a solution. Therefore, in order to obtain a plausible solution by a statistical method, a vector e defined by the following equation (12) is introduced.
e = Xc−j (12)

It can be said that c that minimizes || e || ₂ ² (that is, e ^T e) is plausible as the center of the spherical surface in which the population data group is distributed closest. The problem of obtaining c that minimizes || e || ₂ ² is an optimization problem that minimizes the objective function of the following equation (13) when the matrix A is regular.

2-5. Restriction when distribution is planar When the distribution of the population data group is planar as shown in FIG. 6, the new offset is derived by limiting the correction direction for the old offset to two directions orthogonal to each other. (Step S112). When the population data group is distributed near a specific plane and is distributed discretely when viewed from the normal direction of the plane, the population data group can be sufficiently reliable in the direction parallel to the plane. The population data group cannot be trusted for the normal direction of the plane. In such a case, it is possible to prevent the offset from being updated based on unreliable information by not correcting the old offset for the normal direction of the plane.

Distributed near a specific plane in which the data set of statistical population, if you are discretely distributed when viewed from the normal direction of the plane, the normal direction of the plane, the eigenvector u ₃ corresponding to the minimum eigenvalue lambda ₃ The directions parallel to the plane and orthogonal to each other coincide with the directions of u ₁ and u ₂ corresponding to the maximum eigenvalue λ ₁ and the intermediate eigenvalue λ ₂ , respectively. Therefore, in order to derive the new offset without correcting the old offset in the normal direction of the plane, the new offset c that minimizes the objective function of the equation (13) under the constraint condition of the following equation (14) is obtained. Ask.
c = c ₀ + β ₁ u ₁ + β ₂ u ₂ (β ₁ and β ₂ are real numbers) (14)
Expression (14) is equivalent to the following expression (15).

とすると、ｘの連立一次方程式（１７）がその方程式となる。

ただし

The equation that solves the optimization problem of Equation (13) under the constraint of Equation (15) can be transformed into an equivalent simultaneous equation by Lagrange's undetermined constant method. Indeterminate constant ρ is introduced,

Then, the simultaneous linear equation (17) of x becomes the equation.

However,

As understood from the above description, when the distribution of the population data group is planar, the process of deriving the new offset in step S112 is to solve the simultaneous linear equations (17). Since the rank of the matrix B ₄ is always 4, the solution x is always uniquely specified.

2-6. Restriction when distribution is slightly linear As shown in Fig. 7, when the distribution of the population data group is slightly linear, the new offset is derived by limiting the correction direction for the old offset to the main direction of the distribution. (Step S110). If the population data group is distributed near a certain straight line and is distributed discretely in the direction of the straight line, the population data group is sufficiently reliable for the direction of the straight line, and the population data group for other directions. The group data group cannot be trusted. In such a case, it is possible to prevent the offset from being updated based on unreliable information by not correcting the old offset in directions other than the direction of the straight line.

When the population data group is distributed in the vicinity of a certain straight line and distributed in the straight line direction, the direction of the straight line coincides with the direction of the eigenvector u ₁ corresponding to the maximum eigenvalue λ ₁ , The vectors in the other directions are linear combinations of the eigenvectors u ₂ and u ₃ corresponding to the intermediate eigenvalue λ ₂ and the minimum eigenvalue λ ₃ , respectively. Therefore, in order to derive the new offset by correcting the old offset only for the direction of the straight line, the new offset c that minimizes the objective function of the equation (13) is obtained under the constraint condition of the following equation (20).

Expression (20) is equivalent to the following expression (21).

とすると、ｘの連立一次方程式（２３）がその方程式となる。

ただし

The equation that solves the optimization problem of Equation (13) under the constraint condition of Equation (21) can be transformed into an equivalent simultaneous equation by Lagrange's undetermined constant method. Indeterminate constants ρ ₁ and ρ ₂ are introduced,

Then, the simultaneous linear equation (23) of x becomes the equation.

However,

As understood from the above description, when the distribution of the population data group is slightly linear, the process of deriving the new offset in step S110 is to solve the simultaneous linear equations (23). Since the rank of the matrix B ₅ is always 5, the solution x is always uniquely specified.

2-7. Derivation of a new offset when the distribution is three-dimensional When the distribution is three-dimensional, a new offset is derived without limiting the correction direction for the old offset (step S114). When the distribution is three-dimensional, that is, when the population data group is distributed to some extent in all directions as seen from the center of gravity of the population data group, the population data group is sufficiently reliable in all directions. Therefore, in such a case, it is not always necessary to use the old offset in order to derive the new offset, and the new offset can be derived based on the population data group without using the old offset. Various algorithms for deriving a new offset based on a population data group without using an old offset have been proposed, and may be an algorithm using a statistical method, or a patent application already filed by the applicant. An algorithm that does not use a statistical method may be used as disclosed in Japanese Patent Application No. 2005-337412 and Japanese Patent Application No. 2006-44289.
In this embodiment, a new offset is derived by a statistical method. That is, in step S114, a new offset c is derived as a solution to the optimization problem that minimizes the objective function of equation (13) without any constraint.

2-8. Summary Here, based on FIGS. 1, 6, and 7, the processing of steps S110, S112, and S114 will be described using a spatial concept. Assuming that the data set of statistical population completely reliable, for old offset c _0, the position vector g of the center of the spherical surface derived from only the data set of statistical population, the new offset c as the sum of the old offset c ₀ Considering, the new offset c is defined by the following equation (26).
c = c ₀ + g (26)

The position vector g obtained as a solution to the optimization problem that minimizes the objective function of Equation (13) without any constraint is a linear combination of basic vectors in the same direction as the eigenvectors u ₁ , u ₂ , u ₃ of the distribution. . Therefore, by weighting the coefficients g _α , g _β , and g _γ of the position vector g according to the reliability of the population data group in the corresponding main axis direction, the position vector g is set according to the reliability of each component. Thus, a correction vector f corresponding to the corrected vector can be obtained (see FIG. 1).

As shown in FIG. 6, in step S112, which is executed when the distribution of the population data group is planar, the following constraint conditions are used for deriving the new offset based on the old offset c ₀ and the population data group. It is attached. The constraint condition is that the distribution main axis direction component g _α corresponding to the maximum principal value of the distribution, that is, the maximum eigenvalue λ _1, and the main axis direction component g _α corresponding to the intermediate main value of the distribution, that is, the intermediate eigenvalue λ _{2. A} correction vector f obtained by setting the weighting coefficient of the position vector g to 1 and setting the weighting coefficient of the position vector g to 0 for the component g _{γ in the} principal axis direction corresponding to the minimum main value of the distribution, that is, the minimum eigenvalue λ _3. And the new offset c as the sum of the old offset c ₀ .

As shown in FIG. 7, in step S110 executed when the distribution of the population data group is slightly linear, the following constraint conditions are used in deriving the new offset based on the old offset c ₀ and the population data group. Is attached. The constraint condition is that the maximum principal value of the distribution, that is, the component g _{α in} the principal axis direction (main direction) of the distribution corresponding to the maximum eigenvalue λ ₁ is set to a weight coefficient of the position vector g of 1, and the intermediate principal value of the distribution That is, for the component g _β in the main axis direction corresponding to the intermediate eigenvalue λ ₂ and the minimum main value of the distribution, that is, the component g _{γ in the} main axis direction corresponding to the minimum eigenvalue λ ₃ , the weighting coefficient of the position vector g is set to 0. The new offset c is obtained as the sum of the obtained correction vector f and the old offset c ₀ .

In step S110, which is executed when the distribution of the population data group is three-dimensional, no restriction condition is applied. That is, in step S110, the new offset c is derived as the sum of the position vector g and the old offset c ₀ obtained by the objective function as the solution of the optimization problem of minimizing without constraint equation (13).

B. Second Embodiment Outline In the first embodiment, the distribution of the population data group is evaluated discretely, and when the distribution is planar, the correction vector f for the component in the principal axis direction that minimizes the principal value. When the distribution is linear and the distribution is linear, the correction vector f is set to 0 and the new offset c is derived for the components in the two main axis directions whose principal values are the intermediate value and the minimum value. In the second embodiment, unlike the first embodiment, there is no need to execute different processing according to the distribution evaluation, and a simpler new offset can be derived by efficiently using the population data group. A highly accurate algorithm is described.

  FIG. 8 is a flowchart showing a flow of processing for deriving a new offset. The processing shown in FIG. 8 proceeds as the CPU 40 executes the offset derivation module 94 when an offset update request is generated, as in the first embodiment. In addition, the process of step S200 is the same as the process of step S100 demonstrated in 1st embodiment. The process in step S202 is the same as the process in step S102 described in the first embodiment. The process of step S204 is the same as the process of step S104 described in the first embodiment.

Distribution Evaluation In step S206, a distribution index of the population data group is derived. That is, by deriving m ₂ and m ₃ defined by the following equations (27) and (28) as distribution indexes, the distribution of the population data group is evaluated as a continuous value.

k ₂ and k ₃ are positive constants determined in advance. The correspondence between the principal value and the reliability in the principal axis direction of the population data group corresponding to the principal value is determined by the values of k ₂ and k ₃ . Here, m ₂ and m ₃ always satisfy the following equation (29).
0 ≦ m ₂ <1 and 0 ≦ m ₃ ≦ 1 (29)

尚、各重み係数が主値の比に連続的に対応するように定める関係式は、式（３０）、（３１）、（３２）に限られるものではない。また、最大の主値に対応する主軸方向の成分に係る重み係数ｆ_α／ｇ_αを１未満に設定してもよい。 The spatial concept of m ₂ and m ₃ will be described with reference to FIG. The coefficients of the position vector g are set as g _α , g _β , and g _{γ in} the order of the main axis direction components of the distribution having the largest corresponding principal value, and the coefficients of the correction vector f are f _α , f in the order of the corresponding main axis direction component having the largest main value. _{When β} and f _γ are set, the relationship between the position vector g and the correction vectors f and m ₂ and m ₃ is expressed by the following equations (30), (31), and (32).

Note that the relational expressions determined so that each weighting factor continuously corresponds to the ratio of the main values is not limited to the expressions (30), (31), and (32). Further, the weighting factor f _α / g _α related to the component in the main axis direction corresponding to the maximum main value may be set to less than 1.

-Derivation of new offset When it is difficult to derive a solution for an optimization problem under a specific constraint, a relaxation problem equivalent to solving the optimization problem by loosening the constraint may be introduced. is there. In the present embodiment, by applying such a relaxation problem, the coefficient g _{α of} the position vector g (see FIG. 1) described above by the weighting coefficient corresponding to the ratio of the main value of the distribution of the population data group continuously. , G _β , and g _γ are weighted, and the process of deriving the new offset c as the sum of the correction vector f and the old offset c ₀ is realized. Specifically, it is as follows.

Indeterminate constants ρ ₁ and ρ ₂ are introduced as variables necessary for midway calculation, c, ρ ₁ and ρ ₂ are combined into one vector, and x is defined by the following equation (33).

Further, the matrix B is defined by the equation (34), and the vector b is defined by the equation (35).

The process for deriving the new offset in step S208 is a process for obtaining a solution of the following simultaneous equations (36). Since the matrix B is always regular, x is uniquely identified.
Bx = b (36)
Obtaining the solution of the simultaneous equations (36) means that the weighting factors f _α / g _α , f _β / g _β , f _γ / g _γ that continuously correspond to the ratio of the main values of the distribution of the population data group. By using the expression as a constraint, the new offset is obtained as a sum of the correction vector f having the components weighted with the coefficients of the position vector g in the principal axis direction of the distribution corresponding to each principal value and the old offset C _0. This is equivalent to solving the optimization problem (13) that minimizes the objective function.

  As described above, in the second embodiment, since it is not necessary to branch the process for deriving the new offset according to the distribution of the population data group, the offset deriving module 94 can be easily developed and improved. The data size becomes smaller. In the second embodiment, as long as the main value of the distribution of the population data group is not 0, the old offset can be corrected in the main axis direction of the distribution by a distance that continuously corresponds to the ratio of the main value. The use efficiency of the population data group by the derivation module 94 is high, and the magnetic data can be corrected using the most likely offset in the azimuth derivation module.

C. Other Embodiments The present invention is not limited to the above-described embodiment, and can be implemented in various forms without departing from the gist thereof. For example, the present invention is naturally applicable to a magnetic sensor mounted on a PDA or a magnetic sensor mounted on a vehicle.

The schematic diagram which concerns on embodiment of this invention. The schematic diagram which concerns on embodiment of this invention. The block diagram which concerns on embodiment of this invention. The block diagram which concerns on embodiment of this invention. The flowchart which concerns on 1st embodiment of this invention. The schematic diagram which concerns on 1st embodiment of this invention. The schematic diagram which concerns on 1st embodiment of this invention. The flowchart which concerns on 2nd embodiment of this invention.

Explanation of symbols

1: magnetic data processing device, 3: mobile phone (mobile), 4: three-dimensional magnetic sensor, 90: magnetic data processing program, 92: buffer management module (input means, storage means), 94: offset derivation module ( Offset derivation means), c ₀ : old offset, c: new offset, g: position vector, f: correction vector

Claims (8)

Input means for sequentially inputting magnetic data which is three-dimensional vector data which is a linear combination of the first basic vector group and which is output from the three-dimensional magnetic sensor;
Storage means for storing a plurality of magnetic data as a population data group in order to update the old offset of the magnetic data to a new offset;
It is a position vector of the temporary offset derived from the population data group without using the old offset with respect to the old offset, and is a linear combination of the second basic vector group in the principal axis direction of the distribution of the population data group When the linear combination of the second basic vector group having a coefficient obtained by weighting each coefficient of the position vector according to the ratio of the main values of the distribution of the population data group is a correction vector, the old offset and the Offset derivation means for deriving the new offset based on the old offset and the population data group, with the constraint that the new offset that is the sum of correction vectors is obtained,
A magnetic data processing apparatus comprising: The constraints are
If the ratio of the intermediate principal value to the largest principal value is greater than the first threshold and the ratio of the smallest principal value to the largest principal value is less than or equal to the second threshold, the smallest The weighting coefficient of the position vector is 0 for the coefficient of the second basic vector in the principal axis direction corresponding to the principal value;
The ratio of the intermediate main value to the maximum main value is less than or equal to the first threshold value, and the ratio of the minimum main value to the maximum main value is less than or equal to the second threshold value. A weight coefficient of the position vector with respect to a coefficient of the second basic vector in the principal axis direction corresponding to the minimum principal value and a coefficient of the second basic vector in the principal axis direction corresponding to the intermediate principal value. Both are 0.
The magnetic data processing apparatus according to claim 1. The constraint condition is that the value of the correction vector is a value obtained by weighting the coefficient of the position vector by a weighting coefficient that continuously corresponds to the ratio of the main values of the distribution of the population data group.
The magnetic data processing apparatus according to claim 1. The weighting coefficient of the position vector is normalized by setting the weighting coefficient to 1 with respect to the coefficient of the second basic vector in the principal axis direction corresponding to the largest principal value.
The magnetic data processing apparatus as described in any one of Claims 1-3. The offset deriving means derives c that minimizes the following objective function f (c) under the constraint condition;
The magnetic data processing apparatus as described in any one of Claims 1-4.

Magnetic data processing apparatus according to any one of claims 1 to 5,
The three-dimensional magnetic sensor;
A magnetic measuring device comprising: Sequentially input magnetic data output from the three-dimensional magnetic sensor, which is three-dimensional vector data that is a linear combination of the first basic vector group;
In order to update the old offset of the magnetic data to a new offset, a plurality of the magnetic data is stored as a population data group,
It is a position vector of the temporary offset derived from the population data group without using the old offset with respect to the old offset, and is a linear combination of the second basic vector group in the principal axis direction of the distribution of the population data group When the linear combination of the second basic vector group having a coefficient obtained by weighting each coefficient of the position vector according to the ratio of the main values of the distribution of the population data group is a correction vector, Deriving the new offset based on the old offset and the population data group, with the constraint that obtaining the new offset that is the sum of the correction vectors,
Magnetic data processing method. Input means for sequentially inputting magnetic data which is three-dimensional vector data which is a linear combination of the first basic vector group and which is output from the three-dimensional magnetic sensor;
Storage means for storing a plurality of magnetic data as a population data group in order to update the old offset of the magnetic data to a new offset;
It is a position vector of the temporary offset derived from the population data group without using the old offset with respect to the old offset, and is a linear combination of the second basic vector group in the principal axis direction of the distribution of the population data group When the linear combination of the second basic vector group having a coefficient obtained by weighting each coefficient of the position vector according to the ratio of the main values of the distribution of the population data group is a correction vector, Offset derivation means for deriving the new offset based on the old offset and the population data group, with the constraint that the new offset that is the sum of the correction vectors is obtained,
A magnetic data processing program that causes a computer to function.

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