Signal source identification device, method, program, recording medium

Abstract

To improve measurement accuracy of a signal of a magnetic field and the like.SOLUTION: A signal source identification device 1 receives a signal expressed by a vector a having a prescribed direction from a plurality of signal sources S1, S2, and receives measurement results of a plurality of sensors MS1-MS64 which measure components of three-axes X, Y, Z which are orthogonal each other, to identify positions of signal sources S1, S2 and the vector a. The signal source identification device 1 comprises: a relationship matrix recording part 13 for recording, a relationship matrix (lead field matrix) indicating a relationship between the measurement results which are collected for the number of the sensors for each axis and the vector; and a position and vector deriving part 15 for deriving the positions of the signals S1, S2 and the vector a where a cost function becomes minimum, on the basis of a measurement result b and a relationship matrix H. In the vector a, the components of the same are collected by the number of lattice points V in a space where the signal sources are provided for each of X, Y, Z axes.SELECTED DRAWING: Figure 2

Description

Technical Field

[0001] The present invention relates to the measurement of signals such as magnetic fields.

Background Art

[0002] Conventionally, methods for estimating the position of a signal source from the measurement result of a magnetic field (for example, LORETA method, MUSIC method (see Patent Document 3), Lasso method, etc.) are known (see Patent Documents 1, 2, and 3).

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Patent Document 2

Patent Document 3

Summary of the Invention

Problems to be Solved by the Invention

[0004] However, in the LORETA method, since the current source distribution with a Laplacian filter is minimized, it is possible to estimate to a deep position, but the signal source distribution is blurred and estimated. As a result, according to the LORETA method, it becomes difficult to estimate the positions of a plurality of signal sources.

[0005] In addition, although the MUSIC method can estimate the positions of a plurality of signal sources, it is difficult to estimate the positions of a plurality of signal sources (hereinafter referred to as "coherent signal sources") that output signals of the same frequency and the same phase (or DC (direct current) signals).

[0006] Furthermore, the Lasso method is only known to use a uniaxial magnetic sensor such as a SQUID, and the accuracy of estimating the positions of a plurality of signal sources (including coherent signal sources) is low.

[0007] Therefore, the present invention aims to improve the accuracy of position estimation for multiple signal sources. [Means for solving the problem]

[0008] The signal source identification device according to the present invention receives signals represented by vectors having a predetermined direction from a plurality of signal sources, and identifies the position of the signal sources and the vectors by receiving measurement results from a plurality of sensors that measure components of three mutually orthogonal axes. The device comprises a relation matrix recording unit that records a relation matrix representing the relationship between the measurement results, which are grouped for each of the sensors for each axis, and the vectors, and a position / vector derivation unit that derives the position of the signal sources and the vectors that minimize the cost function based on the measurement results and the relation matrix. In the vectors, the components are grouped for each of the grid points in the space where the signal sources are located for each axis, the cost function is the sum of an error function and a regularization term, the error function represents the error between the true value of the position of the signal sources and the vectors and a candidate value of the true value, and the regularization term is a function of a regularization parameter and the L1 norm of the vectors. The device is configured to identify the position of the signal sources and the vectors based on the derivation results of the position / vector derivation unit.

[0009] The signal source identification device configured as described above receives signals from multiple signal sources represented by vectors having a predetermined direction, and receives measurement results from multiple sensors that measure components of three mutually orthogonal axes to identify the position of the signal source and the vector. The relation matrix recording unit records a relation matrix representing the relationship between the measurement results, which are grouped for each of the sensors for each axis, and the vector. The position-vector derivation unit derives the position of the signal source and the vector that minimize the cost function based on the measurement results and the relation matrix. In the vector, its components are grouped for each of the grid points in the space where the signal source is located for each axis. The cost function is the sum of the error function and the regularization term. The error function represents the error between the true value of the position of the signal source and the vector and a candidate value of the true value. The regularization term is a function of the regularization parameter and the L1 norm of the vector. Based on the derivation results of the position-vector derivation unit, the position of the signal source and the vector are identified.

[0010] Furthermore, the signal source identification device according to the present invention may be configured to identify the derivation result of the position / vector derivation unit as the position of the signal source and the vector.

[0011] Furthermore, the signal source identification device according to the present invention may include a clustering unit that classifies the positions of the signal sources derived by the position / vector derivation unit into clusters of the number of signal sources, a centroid derivation unit that derives the centroid of the signal source for each cluster, and a weighted average unit that averages the vectors derived by the position / vector derivation unit for each cluster in inverse proportion to the distance between the signal source and the centroid, thereby identifying the position of the signal source as the centroid and identifying the vector as the result of the weighted average unit's derivation.

[0012] Furthermore, the signal source identification device according to the present invention may be configured such that the classification into clusters is performed in accordance with the K-means method.

[0013] Furthermore, the signal source identification device according to the present invention may be configured such that the measurement result is the product of the relation matrix and the vector.

[0014] Furthermore, the signal source identification device according to the present invention may be configured such that the k-th power of the measurement result is the product of the k-th power of the relation matrix and the vector (where k > 1).

[0015] Furthermore, in the signal source identification device according to the present invention, the relation matrix may be a read field matrix.

[0016] Furthermore, in the signal source identification device according to the present invention, the measurement results, which are grouped according to the number of sensors for each axis, may be arranged in a single-column matrix.

[0017] Furthermore, in the signal source identification device according to the present invention, the vector may be a single-column matrix.

[0018] Furthermore, the signal source identification device according to the present invention may be configured such that the error function is a function of the measurement result, the relation matrix, and the candidate value.

[0019] Furthermore, the signal source identification device according to the present invention has an error function such that, when the measurement result is b, the relation matrix is ​​H, and the candidate value is a, the error function is (1 / 2)(b-Ha) T It may also be (b-Ha).

[0020] Furthermore, in the signal source identification device according to the present invention, the regularization term may be the product of the regularization parameter and the L1 norm of the vector.

[0021] Furthermore, the signal source identification device according to the present invention may be configured such that the vector is a magnetic dipole moment or an electric dipole moment.

[0022] The present invention is a signal source identification method that receives signals represented by vectors having a predetermined direction from a plurality of signal sources, receives measurement results of a plurality of sensors that measure components of three axes orthogonal to each other, and identifies the position of the signal source and the vector. The method includes a relationship matrix recording step of recording a relationship matrix representing the relationship between the measurement results grouped by the number of sensors for each axis and the vector, and a position and vector derivation step of deriving the position of the signal source and the vector such that a cost function is minimized based on the measurement results and the relationship matrix. In the vector, its components are grouped by the number of lattice points in the space where the signal source is located for each axis. The cost function is the sum of an error function and a regularization term. The error function represents the error between the true values of the position and the vector of the signal source and the candidate values of the true values. The regularization term is a function of a regularization parameter and the L1 norm of the vector. Based on the derivation result of the position and vector derivation step, it is a signal source identification method for identifying the position of the signal source and the vector.

[0023] The present invention is a program for causing a computer to perform a signal source identification process to identify the position of a signal source and the vector, based on the input of a signal represented by a vector having a predetermined direction from a plurality of signal sources and the measurement results of a plurality of sensors that measure components of three mutually orthogonal axes, wherein the signal source identification process comprises a relation matrix recording step of recording a relation matrix representing the relationship between the measurement results, which are grouped for the number of sensors for each axis, and the vector, and a position / vector derivation step of deriving the position of the signal source and the vector that minimizes the cost function based on the measurement results and the relation matrix, wherein the components of the vector are grouped for the number of grid points in the space where the signal source is located for each axis, the cost function is the sum of an error function and a regularization term, the error function represents the error between the true value of the position of the signal source and the vector and a candidate value of the true value, the regularization term is a function of a regularization parameter and the L1 norm of the vector, and the program identifies the position of the signal source and the vector based on the derivation result of the position / vector derivation step.

[0024] The present invention is a computer-readable recording medium recording a program for causing a computer to execute a signal source identification process for receiving signals represented by vectors having a predetermined direction from a plurality of signal sources, receiving measurement results of a plurality of sensors that measure components of three axes orthogonal to each other, and identifying the positions of the signal sources and the vectors. The signal source identification process includes a relationship matrix recording step of recording a relationship matrix representing the relationship between the measurement results grouped by the number of sensors for each axis and the vector, and a position-vector derivation step of deriving the position of the signal source and the vector such that a cost function is minimized based on the measurement results and the relationship matrix. In the vector, its components are grouped by the number of lattice points in the space where the signal source is located for each axis. The cost function is the sum of an error function and a regularization term. The error function represents the error between the true values of the position and the vector of the signal source and the candidate values of the true values. The regularization term is a function of a regularization parameter and the L1 norm of the vector. It is a recording medium for identifying the position of the signal source and the vector based on the derivation result of the position-vector derivation step.

Brief Description of Drawings

[0025] [Figure 1] It is a perspective view of a voxel V and a magnetic sensor MS according to a first embodiment of the present invention. [Figure 2] It is a functional block diagram showing the configuration of a signal source identification device 1 according to a first embodiment of the present invention. [Figure 3] It is a functional block diagram showing the configuration of a signal source identification device 1 according to a second embodiment of the present invention. [Figure 4] It is a diagram showing clustering of the positions of signal sources S1 to S4 by a clustering unit 18a (FIG. 4(a)), derivation of the centroid of the cluster by a centroid derivation unit 18b (FIG. 4(b)), and derivation of the weighted average of the vectors by a weighted average unit 18c (FIG. 4(c)).

Modes for Carrying Out the Invention

[0026] Embodiments of the present invention will be described below with reference to the drawings.

[0027] First Embodiment Figure 1 is a perspective view of a voxel V and magnetic sensor MS according to a first embodiment of the present invention. Figure 2 is a functional block diagram showing the configuration of a signal source identification device 1 according to a first embodiment of the present invention.

[0028] Referring to Figure 1, signal sources S1 and S2 output signals. The signals are represented by a vector a having a predetermined direction. Vector a is, for example, a magnetic dipole moment. The number of signal sources is, for example, two, but there may be three or more, as long as it is less than the number of magnetic sensors MS. The signals output by each signal source may have different frequencies or phases, or they may not. That is, the signals output by each signal source may have the same frequency and phase. Furthermore, the signals output by each signal source may be DC (direct current) signals.

[0029] Furthermore, the spatial positions of signal sources S1 and S2 are represented by voxels V (for example, 10 × 10 × 10 = 1000 voxels). Signal sources S1 and S2 are located in different voxels V. Note that each of the 1000 voxels V will be denoted as V1 to V1000.

[0030] Multiple magnetic sensors (for example, 64 sensors arranged in an 8x8 grid) receive a signal (for example, a magnetic dipole moment) and measure the components bx, by, and bz of the three mutually orthogonal axes X, Y, and Z. Each of the 64 magnetic sensors is denoted as MS1 to MS64. The signal is represented by a vector a with a predetermined direction. The multiple magnetic sensors receive signals from multiple signal sources S1 and S2.

[0031] Here, if vector r is the direction vector from the signal source (magnetic dipole) to the magnetic sensor MS, then the magnetic flux density B (a function of vector r) measured by the magnetic sensor MS is expressed by the Biot-Savart law as shown in equation (1). Here, μ0 is the magnetic constant. Furthermore, vector r can be said to represent the positional relationship between each of the voxels V (V1 to V1000) and each of the magnetic sensors MS1 to MS64.

[0032]

number

[0033]

number

[0034] From equation (1), by can be expressed as shown in equation (3) below.

[0035]

number

[0036] From equation (1), bz can be expressed as shown in equation (4) below.

[0037]

number

[0038] Here, bx, by, and bz are expressed as shown in equation (5) below.

[0039]

number

[0040] Here, the measurement results b, aggregated for each of the X, Y, and Z axes (64 magnetic sensors), are a single-column matrix consisting of bx, by, and bz. (See the left-hand side of equation (8) and equation (8').

[0041] Furthermore, ax, ay, and az can be expressed as shown in equation (6) below.

[0042]

number

[0043] Here, vector a is a single-column matrix. Moreover, in vector a, its components ax, ay, and az are grouped together for each of the X, Y, and Z axes, corresponding to the number of grid points in the space where the signal source is located (1000 points) (see the matrix on the right side of the right-hand side in equations (8) and (8')).

[0044] Referring to Figure 2, the signal source identification device 1 according to the first embodiment includes a relative position recording unit 11, a read field matrix derivation unit 12, a read field matrix recording unit 13, and a position vector derivation unit 15.

[0045] The signal source identification device 1 receives measurement results from multiple sensors MS1 to MS64 and identifies the positions and vectors a of signal sources S1 and S2.

[0046] The relative position recording unit 11 records a vector r, which is the relative position between each of the 1000 voxels V and each of the magnetic sensors MS1MS64.

[0047] The read-field matrix derivation unit 12 reads the vector r from the relative position recording unit 11 and calculates hxx, hxy, hxz, hyx, hyy, hyz, hzx, hzy, hzz (with the vector r as the argument) (components of the relation matrix H (e.g., the read-field matrix) described later) (see equations (2) to (4) and (2') to (4').

[0048] For example, hxx can be expressed as shown in equation (7) below.

[0049]

number

[0050] Similarly, hxy, hxz, hyx, hyy, hyz, hzx, hzy, and hzz can each take on 1000 × 64 possible values.

[0051] Here, equations (2') to (4') can be expressed as equation (8) below.

[0052]

number

[0053] Furthermore, let the matrix on the right side of the right-hand side of equation (8) be vector a (in vector a, its components ax, ay, and az are grouped together for each of the X, Y, and Z axes, corresponding to the number of grid points in the space where the signal sources S1 and S2 are located (1000)). Vector a is a single-column matrix.

[0054] Furthermore, let H be the matrix on the left side of the right-hand side in equation (8). H is a relation matrix (for example, a read field matrix) that represents the relationship between the measurement result b and the vector a.

[0055] Then, equation (8) can be expressed as equation (8'). That is, the measurement result b is the product of the relation matrix H and the vector a.

[0056] As explained earlier, the lead field matrix derivation unit 12 finds the components of the relation matrix H and further derives the relation matrix (lead field matrix) H.

[0057] The lead field matrix recording unit 13 receives the relation matrix (lead field matrix) H from the lead field matrix derivation unit 12 and records it.

[0058] The position / vector derivation unit 15 derives the positions and vectors a of signal sources S1 and S2 that minimize the cost function, based on the measurement result b and the relation matrix H.

[0059] In other words, the position vector derivation unit 15 derives a vector a that satisfies the following equation (9).

[0060]

number

[0061] The error function represents the error between the true value of the vector a and a candidate value of the true value, based on the positions of signal sources S1 and S2. The error function is a function of the measurement result b, the relation matrix H, and the candidate value a (of the true value of the vector). For example, the error function can be expressed as (1 / 2)(b-Ha). T (b-Ha)

[0062] The regularization term is a function of the regularization parameter λ and the L1 norm of vector a. For example, the regularization term is the product of the regularization parameter λ and the L1 norm of vector a.

[0063] Based on the derivation result a of the position / vector derivation unit 15, the positions and vectors a of signal sources S1 and S2 are identified. For example, the derivation result a of the position / vector derivation unit 15 is identified as the position and vector of the signal source. For example, if signal source S1 is located at voxel V500 and signal source S2 is located at voxel V600, then (ax500, ay500, az500) in the derivation result a is the vector of the signal output by signal source S1, and (ax600, ay600, az600) is the vector of the signal output by signal source S2.

[0064] Next, the operation of the first embodiment will be described.

[0065] The read-field matrix derivation unit 12 reads the vector r from the relative position recording unit 11, and derives the components hxx, hxy, hxz, hyx, hyy, hyz, hzx, hzy, and hzz of the relation matrix (read-field matrix) H (see equations (2) to (4) and (2') to (4')).

[0066] The read field matrix recording unit 13 receives the relation matrix H from the read field matrix derivation unit 12 and records it.

[0067] The position / vector derivation unit 15 derives the positions and vectors a of signal sources S1 and S2 that minimize the cost function, based on the measurement result b and the relation matrix H (see equation (9)).

[0068] According to the first embodiment, the accuracy of position estimation for multiple signal sources (including coherent signal sources) is improved. That is, since the first embodiment is based on the Lasso method, position estimation is possible even for coherent signal sources. Moreover, according to the first embodiment, the measurement result b and vector a are summarized for each of the X, Y, and Z axes (see equations (8) and (8')), and the measurement results for all three axes can be used, thus improving the accuracy of position estimation for multiple signal sources.

[0069] Second Embodiment The signal source identification device 1 according to the second embodiment differs from the signal source identification device 1 according to the first embodiment in that it includes a clustering unit 18a, a centroid derivation unit 18b, and a weighted average unit 18c.

[0070] Figure 3 is a functional block diagram showing the configuration of a signal source identification device 1 according to a second embodiment of the present invention. The signal source identification device 1 according to the second embodiment includes a relative position recording unit 11, a read field matrix derivation unit 12, a read field matrix recording unit 13, a position vector derivation unit 15, a clustering unit 18a, a centroid derivation unit 18b, and a weighted average unit 18c.

[0071] The relative position recording unit 11, the read field matrix derivation unit 12, the read field matrix recording unit 13, and the position / vector derivation unit 15 are the same as in the first embodiment and will not be described.

[0072] Figure 4 shows the clustering of the signal sources S1 to S4 by the clustering unit 18a (Figure 4(a)), the derivation of the centroid of the cluster by the centroid derivation unit 18b (Figure 4(b)), and the derivation of the weighted average of the vectors by the weighted average unit 18c (Figure 4(c)). However, in Figures 4(b) and 4(c), the signal sources S1 and S2 are omitted from the illustration.

[0073] Referring to Figure 4(c), position G1 is the true position of the signal source, and the signal vector is ag1. However, if position G1 does not coincide with a voxel, the signal source positions are derived to be S1 and S2. Furthermore, the signal vectors are also derived to be A1 and A2.

[0074] Furthermore, position G2 is the true position of the signal source, and the signal vector is ag2. However, if position G2 does not coincide with a voxel, the signal source positions are derived to be S3 and S4. Furthermore, the signal vectors are also derived to be A3 and A4.

[0075] From the derivation results of the position vector derivation unit 15 (S1-S4 and A1-A4), the true signal source positions G1 and G2 and the true signal vectors ag1 and ag2 are determined.

[0076] First, referring to Figure 4(a), the clustering unit 18a classifies the signal source positions S1 to S4, derived by the position vector derivation unit 15, into clusters equal to the number of signal sources (2). In the example in Figure 4(a), signal source positions S1 and S2 are classified into cluster C1, and signal source positions S3 and S4 are classified into cluster C2. The distance between signal source positions S1 and S2 is D1, and the distance between signal source positions S3 and S4 is D2.

[0077] Next, referring to Figure 4(b), the centroid derivation unit 18b derives the centroid of the signal source for each cluster. The centroid G1 of the signal source in cluster C1 lies on the line segment connecting the signal source positions S1 and S2. Note that S1G1 / S2G1 = size of A2 / size of A1. The centroid G2 of the signal source in cluster C2 lies on the line segment connecting the signal source positions S3 and S4. Note that S3G2 / S4G2 = size of A4 / size of A3.

[0078] Furthermore, the clustering can be performed according to the K-means method. In this case, first, two centroids are randomly placed, and then the locations S1 to S4 of the signal sources are classified into clusters according to the proximity of the centroids to the locations S1 to S4 of the signal sources.

[0079] Furthermore, the centroid of the signal source is derived for each cluster, and then the signal source locations S1 to S4 are classified into clusters according to the proximity of the derived centroid to the signal source locations S1 to S4. This derivation of the centroid and classification into clusters is repeated until the derived centroid is in the same position as the centroid immediately before derivation.

[0080] The location of the signal source is identified as the centroids G1 and G2 derived in this manner.

[0081] Furthermore, referring to Figure 4(c), the weighted average unit 18c averages the vector a derived by the position vector derivation unit 15 for each cluster, inversely proportional to the distance between the signal source and the centroid.

[0082] Taking cluster C2 as an example, if vector A3 is (P, Q, 0) and vector A4 is (R, S, 0), then the true signal vector ag2 is ((P*D22+R*D21) / D2, (Q*D22+S*D21) / D2, 0). The same applies to cluster C1, so the explanation is omitted.

[0083] The signal vector is identified as the weighted average ((P*D22+R*D21) / D2, (Q*D22+S*D21) / D2, 0) derived in this way.

[0084] Next, the operation of the second embodiment will be described.

[0085] First, the operation of the relative position recording unit 11, the read field matrix derivation unit 12, the read field matrix recording unit 13, and the position vector derivation unit 15 is the same as in the first embodiment, so we will omit the explanation.

[0086] The output of the position vector derivation unit 15 is given to the clustering unit 18a, and clustering of the positions of signal sources S1 to S4 is performed (see Figure 4(a)). Next, the centroid derivation unit 18b derives the centroids of clusters C1 and C2 (see Figure 4(b)). These centroids G1 and G2 are the true signal source positions. Finally, the weighted average unit 18c derives the weighted average of the vectors (see Figure 4(c)). The weighted averages ag1 and ag2 are the true signal vectors.

[0087] According to the second embodiment, the position of the signal source and the signal vector can be determined even when the position of the signal source does not coincide with a voxel.

[0088] In the above embodiment, the signal was a magnetic dipole moment, but it may also be an electric dipole moment.

[0089] Furthermore, in the above embodiment, the measurement result b was the product of the relation matrix H and the vector a, but the κ-th power of the measurement result b may be the product of the κ-th power of the relation matrix H and the vector a (where κ > 1) (see equation (10) below).

[0090]

number

[0091] Furthermore, the above embodiment can be realized as follows: A computer equipped with a CPU, a hard disk, and a media (USB memory, CD-ROM, etc.) reader is made to read a media containing a program that implements each of the above parts, for example, the relative position recording unit 11, the read field matrix derivation unit 12, the read field matrix recording unit 13, the position / vector derivation unit 15, the clustering unit 18a, the centroid derivation unit 18b, and the weighted average unit 18c, and install it on the hard disk. The above functions can also be realized by this method. [Explanation of symbols]

[0092] 1. Signal vector derivation device 11 Relative position recording unit 12. Lead field matrix derivation section 13 Read Field Matrix Recording Section 15 Position Vector Derivation Section 18a Clustering section 18b Center of gravity derivation part 18c Weighted average part MS Magnetic Sensor V-Voxel B Magnetic flux density H relation matrix (readfield matrix) S1, S2 signal source a. Vector (magnetic dipole moment)

Claims

1. A signal source identification device that receives signals represented by vectors having a predetermined direction from multiple signal sources, and identifies the vectors based on measurement results from multiple sensors that measure components of three mutually orthogonal axes, A relation matrix recording unit records a relation matrix that represents the relationship between the measurement results, which are grouped for each of the three axes according to the number of sensors, and the vector. A vector derivation unit that derives the vector that minimizes the cost function based on the measurement results and the relation matrix, Equipped with, The aforementioned vector is a matrix vector in which its components are arranged consecutively for each of the three axes, corresponding to the number of grid points in the space where the signal source is located. The aforementioned cost function is the sum of the error function and the regularization term. The error function represents the error between the true value of the vector and a candidate value for the true value. The regularization term is a function of the regularization parameter and the L1 norm of the vector. Based on the derivation results of the vector derivation unit, the vector is identified, The vector represents the signal output from each of the plurality of signal sources. Signal source identification device.

2. A signal source identification device according to claim 1, The derivation result of the vector derivation unit is identified as the vector. Signal source identification device.

3. A signal source identification device according to claim 1 or 2, The measurement result is the product of the relation matrix and the vector. Signal source identification device.

4. A signal source identification device according to any one of claims 1 to 3, The k-raised value of the measurement result is the product of the k-raised value of the relation matrix and the vector (where k > 1). Signal source identification device.

5. A signal source identification device according to any one of claims 1 to 4, The aforementioned relation matrix is ​​a read-field matrix. Signal source identification device.

6. A signal source identification device according to any one of claims 1 to 4, The measurement results, grouped for each of the three axes according to the number of sensors, are in a single-column matrix. Signal source identification device.

7. A signal source identification device according to any one of claims 1 to 4, The aforementioned vector is a one-column matrix. Signal source identification device.

8. A signal source identification device according to any one of claims 1 to 4, The error function is a function of the measurement result, the relation matrix, and the candidate value. Signal source identification device.

9. A signal source identification device according to claim 8, The error function is such that when the measurement result is b, the relation matrix is ​​H, and the candidate value is a, (1 / 2)(b-Ha) T (b-Ha) A signal source identification device.

10. A signal source identification device according to any one of claims 1 to 4, A signal source identification device in which the regularization term is the product of the regularization parameter and the L1 norm of the vector.

11. A signal source identification device according to any one of claims 1 to 4, The aforementioned vector is a magnetic dipole moment or an electric dipole moment. Signal source identification device.

12. A signal source identification method that identifies a vector by receiving signals represented by vectors having a predetermined direction from multiple signal sources and receiving measurement results from multiple sensors that measure components of three mutually orthogonal axes, wherein the vector is identified by receiving signals represented by vectors having a predetermined direction from multiple signal sources, A relation matrix recording step involves recording a relation matrix that represents the relationship between the measurement results, which are grouped for each of the three axes according to the number of sensors, and the vector. A vector derivation step is performed to derive the vector that minimizes the cost function based on the measurement results and the relation matrix, Equipped with, The aforementioned vector is a matrix vector in which its components are arranged consecutively for each of the three axes, corresponding to the number of grid points in the space where the signal source is located. The aforementioned cost function is the sum of the error function and the regularization term. The error function represents the error between the true value of the vector and a candidate value for the true value. The regularization term is a function of the regularization parameter and the L1 norm of the vector. Based on the derivation results of the vector derivation process, the vector is identified, The vector represents the signal output from each of the plurality of signal sources. Signal source identification method.

13. A program for causing a computer to perform a signal source identification process that identifies a vector by receiving signals represented by vectors having a predetermined direction from multiple signal sources and receiving measurement results from multiple sensors that measure components of three mutually orthogonal axes, wherein the vector is identified. The aforementioned signal source identification process, A relation matrix recording step involves recording a relation matrix that represents the relationship between the measurement results, which are grouped for each of the three axes according to the number of sensors, and the vector. A vector derivation step is performed to derive the vector that minimizes the cost function based on the measurement results and the relation matrix, Equipped with, The aforementioned vector is a matrix vector in which its components are arranged consecutively for each of the three axes, corresponding to the number of grid points in the space where the signal source is located. The aforementioned cost function is the sum of the error function and the regularization term. The error function represents the error between the true value of the vector and a candidate value for the true value. The regularization term is a function of the regularization parameter and the L1 norm of the vector. Based on the derivation results of the vector derivation process, the vector is identified, The vector represents the signal output from each of the plurality of signal sources. program.

14. A computer-readable recording medium that contains a program for causing a computer to perform a signal source identification process to identify a vector, which receives signals represented by vectors having a predetermined direction from multiple signal sources and measures the components of three mutually orthogonal axes from multiple sensors, The aforementioned signal source identification process, A relation matrix recording step involves recording a relation matrix that represents the relationship between the measurement results, which are grouped for each of the three axes according to the number of sensors, and the vector. A vector derivation step is performed to derive the vector that minimizes the cost function based on the measurement results and the relation matrix, Equipped with, The aforementioned vector is a matrix vector in which its components are arranged consecutively for each of the three axes, corresponding to the number of grid points in the space where the signal source is located. The aforementioned cost function is the sum of the error function and the regularization term. The error function represents the error between the true value of the vector and a candidate value for the true value. The regularization term is a function of the regularization parameter and the L1 norm of the vector. Based on the derivation results of the vector derivation process, the vector is identified, The vector represents the signal output from each of the plurality of signal sources. Recording medium.

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