A dictionary matrix iterative optimization sOMP off-grid direct positioning method

Abstract

The application discloses a SOMP off-grid direct positioning method with dictionary matrix iterative optimization, and belongs to the technical field of passive positioning. The application uses a uniform linear array as a base station receiving device, monitors a signal source by using a distributed base station structure, and collects signal source receiving data. The application carries out noise reduction preprocessing on the signals received by the array, and then uses the noise-reduced signals to carry out matching search on a spatial grid to obtain the position of the signal source. The application uses a Taylor iterative optimization dictionary matrix in a matching process, and reduces the compensation deviation of a traditional off-grid algorithm. Compared with the traditional off-grid algorithm, the estimation result of the application is more accurate, and the application has important application value.

Description

Technical Field

[0001] This invention belongs to the field of passive localization technology, and relates to a direct localization method that combines Simultaneous Orthogonal Matching Pursuit (SOMP) and Taylor iterative compensation, and particularly to a SOMP off-grid direct localization method that utilizes Taylor iterative compensation to optimize the dictionary matrix. Background Technology

[0002] Passive localization technology is an important research direction in the field of modern radar signal processing. It eliminates the need for high-power active equipment for target detection, estimating the source location solely by intercepting non-cooperative signals with a receiver. Therefore, it boasts excellent concealment and low energy consumption, leading to its widespread application in an increasing number of scenarios.

[0003] Direct localization (DRT) is a passive localization technique that uses multiple base stations to receive source signals and directly processes the raw sampled signals to obtain the source's location estimate. Compared to traditional two-step localization, DRT can better reduce information loss, has good robustness, and has great development potential. However, DRT requires synchronous processing of data from multiple base stations and grid traversal search, resulting in high computational load and grid mismatch issues. In recent years, the introduction of compressed sensing theory has provided new ideas for DRT. Sparse methods have effectively reduced the computational load of DRT algorithms, but the grid mismatch problem still exists. In array signal processing, off-grid methods are one approach to solve the grid mismatch problem, but directly applying off-grid methods to DRT results in multi-station compensation conflicts. Therefore, researching off-grid sparse representation methods applicable to DRT is of great significance. Summary of the Invention

[0004] This invention addresses the shortcomings of existing technologies by providing a SOMP off-grid direct localization method based on dictionary matrix iterative optimization. This method, based on the synchronous orthogonal matching method, utilizes Taylor iterative compensation to optimize the dictionary matrix, achieving accurate estimation of the source location.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A dictionary matrix iterative optimization method for SOMP off-mesh direct localization, characterized by the following steps:

[0007] Step 1: A distributed base station composed of a uniform linear array collects multi-shot signals;

[0008] Step 2: Calculate the covariance matrix of the received signals from multiple times, perform eigenvalue decomposition, and take the signal subspace as the initial received signal;

[0009] Step 3: Divide the area enclosed by the distributed base stations into spatial grids, and construct a dictionary matrix based on the grid.

[0010] Step 4: Detect the correlation of the spatial grid using the received signal;

[0011] Step 5: Normalize the correlation detection results;

[0012] Step 6: Select the grid points with the highest correlation and assign them to the support base;

[0013] Step 7: Optimize the grid point positions using Taylor iteration and update the dictionary matrix;

[0014] Step 8: Estimate the corresponding source signal using the support basis and dictionary matrix, and subtract the estimated source signal from the initial received signal to obtain the updated residual;

[0015] Step 9: Use the residual as the received signal. If the number of supporting elements is less than the number of sources, go to step 4; otherwise, go to step 10.

[0016] Step 10: Select the source location from the updated grid points using the support base.

[0017] To optimize the above technical solution, the specific measures also include:

[0018] Furthermore, in step 1, the base stations are distributed around the areas where the K signal sources are located. The effective direction-finding space of the uniform linear array covers the area enclosed by multiple base stations. The collected signal of base station h is represented as:

[0019] X h (t)=A h S h (t)+N h (t), 1≤h≤N

[0020] In the formula, X h (t) represents the data collected by the h-th base station, A h S represents the array manifold of the h-th base station. h (t) represents the source vector consisting of the transmitted signals sent from the source to the h-th base station, N h (t) is the noise vector formed by the noise data received by the h-th base station, and N represents the number of base stations.

[0021] Furthermore, in step 2, the covariance matrix of the multiple received signals is calculated using the following formula, eigenvalue decomposition is performed, and the signal subspace is obtained:

[0022]

[0023]

[0024] In the formula, X h (t l ) represents t l The signal collected by the base station in the snapshot moment, R h The covariance matrix representing the signal collected by the h-th base station is derived from the data X collected by the h-th base station. h (t) is obtained, E(·) represents the expectation, and L represents the number of snapshots of the acquired signal; eigenvalue decomposition is performed on the covariance matrix. Let represent a K×K dimensional diagonal matrix whose diagonal elements are composed of the K largest eigenvalues ​​obtained from eigenvalue decomposition. It is a diagonal matrix composed of MK smallest eigenvalues, where M represents the number of elements of a uniform linear matrix, and the matrix formed by the eigenvectors corresponding to the K largest eigenvalues ​​is the signal subspace. The matrix formed by the eigenvectors corresponding to the MK smallest eigenvalues ​​is the noise subspace. Initial received signal

[0025] Furthermore, step 3 is specifically as follows:

[0026] The area enclosed by the distributed base stations is divided into X. m Line Y m Column X m ×Y m There are _ _ grid points, and the coordinates of the i-th grid point are denoted as P. i =(x i y i ), where 1≤i≤X m ×Y m ;

[0027] Construct the dictionary matrix Φ for each base station h Its expression is as follows:

[0028]

[0029]

[0030] In the formula, the trigonometric function value of the relative angle between each grid point and the base station. Let θ be the coordinates of the h-th base station. h θ represents the angle between the direction of the uniform linear array normal of the h-th base station and the due north direction. h The value range of θ is -90° to 90°, and it is defined that when the normal is in the clockwise direction from true north, θ...h For a positive value, the element spacing d = λ / 2, where λ represents the wavelength and M represents the number of elements in the uniform linear array.

[0031] Furthermore, step 4 is specifically as follows:

[0032] The correlation of the i-th grid point in the signal measurement domain of the h-th base station is calculated using the following formula.

[0033]

[0034] In the formula, r h (t l ) represents t l The residual of the snapshot moment, during the first execution of step 4, is the residual r. h equal to the initial received signal K represents the number of snapshots, which is equal to the number of information sources.

[0035] Furthermore, in step 5, the correlation of the i-th grid point in the signal measurement domain of the h-th base station is calculated using the following formula. Normalize:

[0036]

[0037] In the formula, g h It is the set of correlations of grid points in the signal measurement domain of the h-th base station. max(·) means taking the maximum value in the set, and min(·) means taking the minimum value in the set.

[0038] Furthermore, in step 6, the grid point number i with the largest sum of correlations in all base station signal measurement domains is selected as the j-th supporting base m using the following formula. j :

[0039]

[0040] In the formula, j represents the number of times the step is executed.

[0041] Furthermore, step 7 specifically includes the following sub-steps:

[0042] Step 71: For Φ h The mth j The column elements are expanded using a two-dimensional Taylor series to obtain:

[0043]

[0044] This component is approximated by the following formula. The expression is as follows:

[0045]

[0046] In the formula, S h for At grid points The reconstructed signal at ξ x ξ is the lateral compensation value for the grid. y This is the longitudinal compensation value for the grid;

[0047] Let H h，1 =S h H h，2 =ξ x S h H h，3 =ξ y S h ,(·) + The Moore-Penrose pseudo-inverse operation yields:

[0048]

[0049] Find S h =H h，1 ,use For the mth j The coordinates of each grid point Perform Taylor iteration updates to further approximate the region where the information source is located. and These are the updated coordinate values ​​from this step. and These are the coordinate values ​​before the update in this step;

[0050] Step 72: Repeat step 71 until... in Indicates Y after this iteration h (t), Represents Y after the last iteration h (t), the first iteration equal to the initial received signal This indicates that the signal subspace is at snapshot time t. l The corresponding data, ε, represents an arbitrarily small value, typically 10. -6 ;

[0051] Step 73: Calculation Update m j The corresponding dictionary matrix columns.

[0052] Furthermore, step 8 specifically includes the following sub-steps:

[0053] Step 81: Place the support base m jStored in the supporting basis set Ω, which is initialized to an empty set;

[0054] Step 82: Through Reconstructed signal, Indicates the reconstructed signal. This represents the corresponding dictionary matrix column of the grid points corresponding to the support basis in Ω in the h-th base station signal measurement domain;

[0055] Step 83: From the initial received signal Subtract the estimated signal value from the middle As residual r h ,

[0056] Furthermore, in step 9, if the number of elements in Ω is less than the number of signal sources K, then proceed to step 4; otherwise, proceed to step 10.

[0057] The beneficial effects of this invention are as follows: Compared with the prior art, this invention makes full use of the low complexity and fast convergence of the synchronous orthogonal matching tracking algorithm, thereby improving the speed of direct positioning calculation; in the iterative process of the synchronous orthogonal matching tracking algorithm, the Taylor iterative compensation method is used for single-point optimization, which avoids the grid mismatch problem and improves the accuracy of grid point position optimization. Attached Figure Description

[0058] Figure 1 This is a flowchart of a SOMP off-mesh direct localization method based on dictionary matrix iterative optimization proposed in this invention;

[0059] Figure 2 This is a scene diagram of the SOMP off-mesh direct localization method proposed in this invention, which uses dictionary matrix iterative optimization.

[0060] Figure 3 This is a comparison chart of the simulation results of the present invention and the mesh method;

[0061] Figure 4 This is a comparison chart of the source location estimation performance of the present invention and the traditional off-grid method under different signal-to-noise ratios. Detailed Implementation

[0062] The invention will now be described in further detail with reference to the accompanying drawings.

[0063] In this embodiment, the symbols are represented as follows: E(·) represents the expectation, (·) represents the expectation. H This indicates the conjugate transpose operation, (·). ·j Let (·) represent the j-th column of the matrix. +The pseudo-inverse operation is represented by max(·), which means taking the maximum value in the set, and min(·) means taking the minimum value in the set. The pseudo-inverse calculation uses the pinv(·) function algorithm in MATLAB. For ease of description, the position vector [x, y] is represented as the coordinate representation (x, y) in the Cartesian coordinate system.

[0064] This embodiment proposes a dictionary matrix iterative optimization method for SOMP off-mesh direct localization, the detailed process of which is as follows: Figure 1 As shown. This method uses a uniform linear array as a base station detection device to estimate the source location within the area enclosed by all base stations. The specific implementation process is as follows:

[0065] Step 1: The base station collects the source signal.

[0066] There are N base stations, where N is 4 or more, and the coordinates of each base station are... Each base station consists of a uniform linear array of M elements, with M ranging from 13 to 20 elements. The element spacing is d = λ / 2, where λ represents the wavelength. Assume there are K signal sources from... The signal radiates outwards, and the number of snapshots L for acquiring the signal is 100 or more. The signal acquired by the array can be represented as:

[0067] X h (t)=A h S h (t)+N h (t), 1≤h≤N

[0068] In the formula, For signal vectors, For noise vectors, Represents the direction matrix. Representative position The direction vector of the source relative to the base station h is expressed as:

[0069]

[0070] In the formula, For the k-th source location θ h θ represents the angle between the direction of the uniform linear array normal of the h-th base station and the due north direction. h The value range of θ is -90° to 90°, and it is defined that when the normal is in the clockwise direction from true north, θ... h It is a positive value.

[0071] Step 2: Noise reduction processing.

[0072] Based on the data model, information about the acquired signals can be obtained, and the covariance matrix can be calculated:

[0073]

[0074] In the formula, L represents the number of snapshots of the data. For R... h Eigenvalue decomposition of the covariance matrix can be expressed as:

[0075]

[0076] In the formula, Let represent a K×K dimensional diagonal matrix whose diagonal elements are composed of the K largest eigenvalues ​​obtained from eigenvalue decomposition. It is a diagonal matrix composed of MK smallest eigenvalues. The matrix formed by the eigenvectors corresponding to the K largest eigenvalues ​​is the signal subspace. The matrix formed by the eigenvectors corresponding to the MK smallest eigenvalues ​​is the noise subspace.

[0077] Will Assign to As the initial received signal input, it reduces the impact of noise in the initial received signal on the algorithm's results.

[0078] Step 3: Divide the space into a grid and construct a dictionary matrix.

[0079] Select grid point P in the area enclosed by all base stations i (1≤i≤X m ×Y m The distribution of grid points can be approximated as X. m Line Y m In each column, following the order from top to bottom and from left to right in each row, the grid points are labeled with index i and grid point P. i =(x i y i ).

[0080] Assuming that a source may exist at each grid point, construct the dictionary matrix Φ according to the grid point index. h The expression is:

[0081]

[0082] Among them, the elements in the overcomplete dictionary Trigonometric function values ​​of the relative angle between each grid point and the base station

[0083] Step 4: Calculate the correlation between grid points.

[0084] The correlation of each grid point is calculated in the signal measurement domain of each base station, as shown in the following expression:

[0085]

[0086] In the formula, r represents the correlation of grid point i in the signal measurement domain of base station h. h (t) represents the residual updated during algorithm execution. Before entering the algorithm, the residual r is... h (t) is initialized to the noise-reduced received signal.

[0087] Step 5: Normalize the correlation of grid points.

[0088] Since the inconsistency in the correlation value range within each base station signal measurement domain leads to an increase in the number of ambiguous points estimated by the algorithm, the correlation in each base station signal measurement domain is normalized, and its range is constrained to 0 to 1, as shown in the following expression:

[0089]

[0090] In the formula, the signal measurement domain of the h-th base station This represents the correlation of the grid point with index i in the signal measurement domain of the h-th base station.

[0091] Step 6: Select the grid point with the highest correlation as the support base.

[0092] In each base station signal measurement domain, the grid points near the signal source have the highest correlation. Therefore, after summing the correlation of each grid point in different base station signal measurement domains, the grid point with the highest correlation is located near the signal source, as shown in the following expression:

[0093]

[0094] In the formula, m j It is the j-th support base, representing the grid point number i with the largest sum of correlations in all base station signal measurement domains.

[0095] Step 7: Use Taylor iteration to compensate and optimize the grid points, and update the dictionary matrix.

[0096] The traditional SOMP algorithm reduces the magnitude of the difference between the sum of known components and the target quantity by finding appropriate weights, and maintains approximate orthogonality between the difference and the matched components using least squares throughout the sequential matching process. However, in scenarios involving direct positioning away from the mesh, the dictionary matrix Φ... h Since there is a discrepancy between the dictionary matrix and the ideal dictionary matrix, this embodiment adds an optimization step for the selected columns of the dictionary matrix based on the traditional SOMP algorithm.

[0097] In Φ h The mth jThe column elements can be obtained by performing a two-dimensional Taylor expansion:

[0098]

[0099] Therefore, this component can be approximated by the received signal using the following formula. The expression is as follows:

[0100]

[0101] In the formula, S h for At grid points The reconstructed signal at ξ x ξ is the lateral compensation value for the grid. y This is the longitudinal compensation value for the grid.

[0102] Let H h，1 =S h H h，2 =ξ x S h H h，3 =ξ y S h We can obtain:

[0103]

[0104] So right Update the following formula:

[0105]

[0106] Repeat the above steps until... in Indicates Y after this iteration h (t), Represents Y after the last iteration h (t), the first iteration Equal to the initial received signal vector of base station h ε represents an arbitrarily small value, typically ranging from 10 to 6.

[0107] At the same time, for the m-th dictionary matrix j The column is updated:

[0108]

[0109] The resulting dictionary matrix can narrow the gap with the ideal matrix.

[0110] Step 8: Recalculate the residuals.

[0111] Through Ωnew =Ω old ∪{m j Update the supporting basis set Ω, which is initialized to an empty set at the start of the algorithm. new For the updated set of supporting bases, Ω old This is the set of supporting bases before the update. Then, it is processed by least squares. Reconstruct the signal. Indicates only The estimation of the signal when a source is present at the location, and the least squares in this step also ensures that after the least squares in step 7, the sum of the signal components will still approximate the initial received signal.

[0112] Next, calculate the residual r. h The difference vector between the estimated signal and the initial received signal is obtained, expressed as follows:

[0113]

[0114] Step 9: Conditional judgment.

[0115] The algorithm is then iterated to determine whether to continue. If the number of elements in Ω is less than the number of signal sources K, it means that the estimation of the signal source components has not yet ended. In this case, the algorithm is executed in step 4. Otherwise, the algorithm is executed in step 10.

[0116] Step 10: Output the coordinates of the grid points corresponding to the support base.

[0117] Output the grid point P with the element index in the support basis set Ω. Ω Location coordinates,

[0118] To verify the effectiveness of this invention, the following demonstration is performed using MATLAB simulation analysis. The performance estimation metric is the root mean square error (RMSE), defined as:

[0119]

[0120] In the formula, J represents the number of Monte Carlo simulations, and K represents the number of information sources. This indicates the actual location of the k-th information source. This represents the estimated position of the k-th source in the nth simulation experiment.

[0121] Here, K represents the number of signal sources and also the number of columns in the signal subspace. In this invention, the signal subspace is processed as the output signal, and the number of snapshots in the signal subspace is K. In array signal processing theory, after the signal covariance matrix is ​​decomposed into eigenvalues, M eigenvalues ​​are generated. Each eigenvalue corresponds to an eigenvector (with 1 column). The K largest eigenvalues ​​and the K eigenvectors corresponding to them constitute the signal subspace.

[0122] like Figure 2 The diagram shown illustrates a scenario of the present invention, where the base station uses a uniform linear array to sense orientation, and the effective direction-finding area of ​​the linear array covers the area enclosed by the base station.

[0123] Figure 3 The simulation results are shown below. In the simulation, the base station array elements selected are M=15, and the element spacing is d=λ / 2. The grid area is 100m long and 100m wide, with a grid spacing of 5m. The source locations are (23.8m, 32.7m), (67.3m, 70.1m), and the four base station locations are (100m, 100m), (0m, 100m), (0m, 0m), and (100m, 0m). The number of snapshots is set to 500, and the signal-to-noise ratio is set to 20dB. The simulation results show that compared to the SOMP grid method, the method of this invention can correct the grid bias of the grid method and accurately estimate the source location.

[0124] Figure 4 This is a comparison of the source location estimation performance of the method of the present invention under different signal-to-noise ratios. In the simulation, the base station array elements selected were M=15, and the element spacing was d=λ / 2. The grid range was 100m long and 100m wide, with a grid spacing of 5m. The source locations were (29.8m, 30.7m), (67.3m, 82.1m), and the four base station locations were (100m, 100m), (0m, 100m), (0m, 0m), and (100m, 0m). The number of snapshots was set to 500, and the number of Monte Carlo experiments was 100. The simulation results show that, compared with the MUSIC, JSOMP, and SBL off-grid methods, the method of the present invention can estimate the source location more accurately.

[0125] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A SOMP off-grid direct localization method based on dictionary matrix iterative optimization, characterized in that, Includes the following steps: Step 1: A distributed base station composed of a uniform linear array collects multi-shot signals; Step 2: Calculate the covariance matrix of the received signals from multiple times, perform eigenvalue decomposition, and take the signal subspace as the initial received signal; Step 3: Divide the area enclosed by the distributed base stations into spatial grids, and construct a dictionary matrix based on the grid. Step 4: Detect the correlation of the spatial grid using the received signal; Step 5: Normalize the correlation detection results; Step 6: Select the grid points with the highest correlation and assign them to the support base; Step 7: Optimize the grid point positions using Taylor iteration and update the dictionary matrix; Step 8: Estimate the corresponding source signal using the support basis and dictionary matrix, and subtract the estimated source signal from the initial received signal to obtain the updated residual; Step 9: Use the residual as the received signal. If the number of supporting elements is less than the number of sources, go to step 4; otherwise, go to step 10. Step 10: Select the source location from the updated grid points using the support base.

2. The SOMP off-mesh direct localization method based on dictionary matrix iterative optimization as described in claim 1, characterized in that: In step 1, the base stations are distributed around the areas where the K signal sources are located. The effective direction-finding space of the uniform linear array covers the area enclosed by multiple base stations. The signal collected by base station h is represented as follows: X h (t)=A h S h (t)+N h (t),1≤h≤N In the formula, X h (t) represents the data collected by the h-th base station, A h S represents the array manifold of the h-th base station. h (t) represents the source vector consisting of the transmitted signals sent from the source to the h-th base station, N h (t) is the noise vector formed by the noise data received by the h-th base station, and N represents the number of base stations.

3. The SOMP off-grid direct localization method based on dictionary matrix iterative optimization as described in claim 1, characterized in that: In step 2, the covariance matrix of the multiple received signals is calculated using the following formula, eigenvalue decomposition is performed, and the signal subspace is obtained: In the formula, X h (t l ) represents t l The signal collected by the base station in the snapshot moment, R h The covariance matrix representing the signal collected by the h-th base station is derived from the data X collected by the h-th base station. h (t) is obtained, E(·) represents the expectation, and L represents the number of snapshots of the acquired signal; eigenvalue decomposition is performed on the covariance matrix. Let represent a K×K dimensional diagonal matrix whose diagonal elements are composed of the K largest eigenvalues ​​obtained from eigenvalue decomposition. It is a diagonal matrix composed of MK smallest eigenvalues, where M represents the number of elements of a uniform linear matrix, and the matrix formed by the eigenvectors corresponding to the K largest eigenvalues ​​is the signal subspace. The matrix formed by the eigenvectors corresponding to the MK smallest eigenvalues ​​is the noise subspace. Initial received signal 4. The SOMP off-mesh direct localization method based on dictionary matrix iterative optimization as described in claim 1, characterized in that: Step 3 is described in detail below: The area enclosed by the distributed base stations is divided into X. m Line Y m Column X m ×Y m There are _ _ grid points, and the coordinates of the i-th grid point are denoted as P. i =(x i y i ), where 1≤i≤X m ×Y m ; Construct the dictionary matrix Φ for each base station h Its expression is as follows: In the formula, the trigonometric function value of the relative angle between each grid point and the base station. Let θ be the coordinates of the h-th base station. h θ represents the angle between the direction of the uniform linear array normal of the h-th base station and the due north direction. h The value range of θ is -90° to 90°, and it is defined that when the normal is in the clockwise direction from true north, θ... h For a positive value, the element spacing d = λ / 2, where λ represents the wavelength and M represents the number of elements in the uniform linear array.

5. The SOMP off-mesh direct localization method based on dictionary matrix iterative optimization as described in claim 4, characterized in that: Step 4 is described in detail below: The correlation of the i-th grid point in the signal measurement domain of the h-th base station is calculated using the following formula. In the formula, r h (t l ) represents t l The residual of the snapshot moment, during the first execution of step 4, is the residual r. h equal to the initial received signal K represents the number of snapshots, which is equal to the number of information sources.

6. The SOMP off-mesh direct localization method based on dictionary matrix iterative optimization as described in claim 5, characterized in that: In step 5, the correlation of the i-th grid point in the signal measurement domain of the h-th base station is calculated using the following formula. Normalize: In the formula, g h It is the set of correlations of grid points in the signal measurement domain of the h-th base station. max(·) means taking the maximum value in the set, and min(·) means taking the minimum value in the set.

7. The SOMP off-mesh direct localization method based on dictionary matrix iterative optimization as described in claim 6, characterized in that: In step 6, the grid point number i with the largest sum of correlations in all base station signal measurement domains is selected as the j-th support base m using the following formula. j : In the formula, j represents the number of times the step is executed.

8. The SOMP off-mesh direct localization method based on dictionary matrix iterative optimization as described in claim 7, characterized in that: Step 7 specifically includes the following sub-steps: Step 71: For Φ h The mth j The column elements are expanded using a two-dimensional Taylor series to obtain: This component is approximated by the following formula. The expression is as follows: In the formula, S h for At grid points The reconstructed signal at ξ x ξ is the lateral compensation value for the grid. y This is the longitudinal compensation value for the grid; Let H h，1 =S h H h，2 =ξ x S h H h，3 =ξ y S h ,(·) + The Moore-Penrose pseudo-inverse operation yields: Find S h =H h，l ,use For the mth j The coordinates of each grid point Perform Taylor iteration updates to further approximate the region where the information source is located. and These are the updated coordinate values ​​from this step. and These are the coordinate values ​​before the update in this step; Step 72: Repeat step 71 until... in Indicates Y after this iteration h (t), Represents Y after the last iteration h (t), the first iteration equal to the initial received signal This indicates that the signal subspace is at snapshot time t. l The corresponding data, ε, represents an arbitrarily small value, taking a value of 10. -6 ; Step 73: Calculation Update m j The corresponding dictionary matrix columns.

9. The SOMP off-mesh direct localization method based on dictionary matrix iterative optimization as described in claim 1, characterized in that: Step 8 specifically includes the following sub-steps: Step 81: Place the support base m j Stored in the supporting basis set Ω, which is initialized to an empty set; Step 82: Through Reconstructed signal, Indicates the reconstructed signal. This represents the corresponding dictionary matrix column of the grid points corresponding to the support basis in Ω in the h-th base station signal measurement domain; Step 83: From the initial received signal Subtract the estimated signal value from the middle As residual r h , 10. The SOMP off-mesh direct localization method based on dictionary matrix iterative optimization as described in claim 8, characterized in that: In step 9, if the number of elements in Ω is less than the number of signal sources K, then proceed to step 4; otherwise, proceed to step 10.

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