A finite snapshot near-field source localization method based on SPICE method

Abstract

The present disclosure relates to the field of modern signal processing, and specifically to a limited snapshot near-field source positioning method based on the SPICE method. The method includes: the sensor array collects data of the source signal, pre-processes the data, and represents it in the form of an overcomplete dictionary and a sparse matrix, that is, X=ΨW+E; based on the difference between the sample covariance matrix and the covariance matrix of the received signal, the covariance matrix of the sparse matrix is ​​estimated using a solvable optimization problem form; the covariance matrix of the received signal and the solution of the optimization problem are calculated, and the calculation is iteratively solved until the covariance matrix of the received signal and the sample covariance matrix converge to an estimated error less than the termination set threshold; the spatial spectrum of the near-field source positioning model is restored according to the covariance matrix elements of the sparse matrix; the present invention proposes a near-field source positioning method based on sparse iterative covariance estimation, which is used in scenes with insufficient snapshots, and overcomes the problem that traditional methods cannot effectively reconstruct spatial spectra under a limited number of snapshots.

Description

Technical Field

[0001] The invention belongs to the field of modern signal processing, and in particular relates to a finite snapshot near-field source positioning method based on a SPICE method. Background Art

[0002] In the field of modern signal processing, array signal processing stands out as an important technology. It uses spatial sampling signals captured by sensors distributed in different spatial positions to effectively suppress interference and extract valuable information. Therefore, it has been widely used in fields such as sonar and radar. In the study of source localization, researchers divide the source localization problem into near-field source estimation and far-field source estimation according to the distance between the source and the receiving array. When the source is located in the far-field area, that is, r<2D 2 / λ, where r is the distance from the source to the array reference element, D is the array aperture, and λ is the wavelength of the spatial carrier. Under this assumption, the propagation of the signal in space can be approximated as plane wave propagation. This far-field source positioning problem is equivalent to the well-known direction of arrival (DOA) estimation problem. The target source and the receiving array meet 0.62 (D 3 / λ)1 / 2≤r≤2D 2 / λ, the source is located in the Fresnel region of the array aperture. In this case, the signal from the source arrives at the array as a spherical wavefront, rather than being approximated as a plane wave. The problem of locating such a source is called near-field source localization. It involves not only solving the DOA angle parameter of the source, but also solving the distance parameter between the source and the array. Therefore, near-field source localization is a complex two-dimensional parameter estimation problem. In addition, solving this problem becomes challenging due to the spherical wavefront and nonlinear phase differences between sensors.

[0003] At present, most near-field source parameter estimation methods rely on simplified approximate signal models. They use the Fresnel approximation to deal with the time delay of source signals arriving at different array elements, resulting in the usual approximate phase difference including only the linear term in DOA and the quadratic term related to the distance. Through this approximation, the algorithm suitable for far-field source localization can also be used for near-field source localization problems. Therefore, under the approximate model, the 2D-MUSIC (2-dimensional Multiple Signal Classification) algorithm based on the subspace method can show good performance in the near-field source localization problem.

[0004] Subspace-based methods require accurate prior knowledge to ensure accurate source separation and avoid confusion between noise and signal subspaces. In addition, the performance of traditional covariance matrix-based methods will degrade significantly due to the small number of available snapshot data. Summary of the invention

[0005] To solve the above problems, the present invention proposes a near-field source localization method based on sparse iterative covariance estimation (SPICE), which is used in scenes with insufficient snapshots. The method includes:

[0006] The sensor array receives echo signal data from the near-field source and represents it in the form of an overcomplete dictionary and a sparse matrix, that is, X = ΨW + E; where X is the received signal matrix, E is the noise matrix, and Ψ∈C (2M+1)×IJ is an overcomplete dictionary matrix, a sparse matrix W∈C IJ×L , where each column vector of the sparse matrix is ​​ideally composed of the signal received by 2M+1 receiving sensors from the Kth near-field target source at time t, t=1,2,....,L,K<<IJ;

[0007] Based on the difference between the sample covariance matrix and the covariance matrix of the received signal, estimating the covariance matrix of the sparse matrix using a solvable optimization problem form, wherein the covariance matrix of the sparse matrix expresses the position information of the received signal in the overcomplete dictionary;

[0008] Calculate the covariance matrix of the received signal and the solution of the optimization problem, iteratively solve and calculate until the covariance matrix of the received signal and the sample covariance matrix converge to an estimated error less than a termination setting threshold, and the solution of the optimization problem is the optimization variable p when the estimated error is less than the termination setting threshold n With the value of σ, the p n is the covariance matrix element of the sparse matrix, and σ is the variance of the noise matrix;

[0009] Restoring the near-field source localization model spatial spectrum according to the covariance matrix elements of the sparse matrix to obtain an explicit solution of the target source position, wherein the non-zero elements of the sparse matrix correspond to the respective positions in the dictionary matrix;

[0010] The optimization problem can be solved by solving the following equation:

[0011]

[0012] The R is the covariance matrix of the received signal, the is the sample covariance matrix, and h is the estimation error in the case of finite snapshots.

[0013] In the case of sufficient snapshots, the optimization problem can be solved by solving the following equation:

[0014]

[0015] The R is the covariance matrix of the received signal, the is the sample covariance matrix, and g is the estimation error in the case of sufficient snapshots.

[0016] The received signal is represented as an overcomplete dictionary and a sparse matrix in the form of:

[0017] Represents the received signal vector x(t)=As(t)+e(t), where represents the noise term vector, represents the target source signal vector. The direction matrix is ​​expressed as

[0018] The set of possible locations of near-field sources is defined as

[0019] Construct an overcomplete dictionary matrix as Ψ=[Ψ1,…,Ψ J ]=[ψ1,…,ψ N ]∈C( 2M+1)×N , where Ψ j =[a(θ1,r j ),…,a(θ I ,r j )],ψ n ∈C 2M+1 ,n=1,…,N,N=IJ;

[0020] The received signal vector is represented as X = ΨW + E; for each t, ​​w(t) contains only K non-zero elements, corresponding to K parameter pairs And K<<N.

[0021] The explicit solution, when the number of snapshots is insufficient, is:

[0022]

[0023] The p n The covariance matrix of the sparse matrix corresponds to (θ i ,r j ) position, C is the auxiliary optimization variable in the solution process, and ψ n is the element in the overcomplete dictionary matrix.

[0024] The explicit solution, when there are sufficient snapshots, is:

[0025]

[0026] The p n The covariance matrix of the sparse matrix corresponds to (θ i ,r j ) position, C is the auxiliary optimization variable in the solution process, and ψ nis an element in the overcomplete dictionary matrix, is the covariance matrix of the sample matrix.

[0027] The present invention proposes a near-field source localization method based on sparse iterative covariance estimation, which is used in scenes with insufficient snapshots, and overcomes the problem that traditional methods cannot effectively reconstruct spatial spectrum under a limited number of snapshots. Through experiments of specific embodiments, it can be seen that compared with 2D-MUSIC, the near-field source localization method based on SPICE can obtain better localization results, especially when snapshots are limited, and a higher reconstructed spatial spectrum resolution can be achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 A flow chart of a finite snapshot near-field source positioning method based on the SPICE method disclosed in the present invention;

[0029] Figure 2 is a schematic diagram of a near-field source positioning system used in an embodiment of the present invention;

[0030] Figure 3 The spatial spectrogram reconstructed by the MUSIC method and the method of the present invention under the condition of sufficient snapshots in the embodiment of the present invention;

[0031] Figure 4 The spatial spectrum reconstructed by the MUSIC method and the method of the present invention under the limited snapshot condition in the embodiment of the present invention;

[0032] Figure 5 RMSE variation curves of the MUSIC method and the method of the present invention with respect to SNR under the condition of sufficient snapshots in the embodiment of the present invention;

[0033] Figure 6 RMSE variation curves of the MUSIC method and the method of the present invention with respect to SNR under limited snapshot conditions in an embodiment of the present invention; DETAILED DESCRIPTION

[0034] The best mode of implementation of the present invention is described below by way of example. It should be understood that the specific embodiments herein are used to explain the present invention in detail and should not be construed as limiting the present invention. It should be noted that various changes and modifications may be made under the premise of following the principles and core scope of the present invention, and these changes should all be deemed to be within the scope of protection of the present invention. In conjunction with the accompanying drawings, the specific implementation steps of the present invention are described in detail.

[0035] The following specifically introduces a finite snapshot near-field source positioning method based on the SPICE method provided by the present invention.

[0036] Step 1: The sensor array receives echo signal data from the near-field source and represents it in the form of an overcomplete dictionary and a sparse matrix, i.e., X = ΨW + E;

[0037] Consider K independent narrowband near-field uncorrelated signal sources, the signals emitted by these signal sources are incident on a symmetrical uniform linear array (ULA) with an element spacing of d, such as Figure 2 As shown. k and r k denote the DOA and range of the kth source respectively, where k = 1, 2, …, k.

[0038] Where m = -M, ..., -1, 0, 1, ..., M, t = 1, ..., L, the received signal of K near-field source targets received by the mth sensor at time t can be expressed as:

[0039]

[0040] Where L is the number of snapshots, i.e. the number of received signals, and s k (t) represents the signal received from the kth near-field target source at time t, e m (t) represents the additive Gaussian white noise of the mth sensor, with a variance of σ 2 , with a mean of zero. k ∈(-π / 2, π / 2) represents the incident angle of the kth target source. k ∈(0.62(D 3 / λ) 1 / 2 ,2D 2 / λ), indicating that the target is within the Fresnel region, r k Represents the range from the kth light source to the reference point. Where D = 2Md represents the array aperture, λ is the wavelength of the incident signal, and D < λ / 4.

[0041] Using the second-order Taylor expansion to approximate the phase difference in (1), (1) is simplified to

[0042]

[0043] The received signal is expressed as a matrix, Represents the received signal vector at time t, x(t) can also be expressed as:

[0044] x(t)=As(t)+e(t) (3)

[0046] in, represents the noise term vector, Represents the target source signal vector.

[0047] The direction matrix is ​​expressed as The steering vector is defined as

[0048]

[0049] The set of locations where near-field sources may appear is defined as an I×J grid, that is, there are IJ points, which can be defined as:

[0050]

[0051] where θ i ∈(-π / 2,π / 2) represents the angle range of the signal received by the receiving array, r j ∈(0.62(D 3 / λ) 1 / 2 ,2D 2 / λ) represents the range of the Fresnel region, and the number of grid points is much larger than the number of target sources, that is, I, J>>K.

[0052] Using the steering vector generated by the near-field source localization mathematical model in (4), an overcomplete dictionary matrix is ​​constructed as

[0053] Ψ=[Ψ1,…,Ψ J ]=[ψ1,…,Ψ N ]∈C 2M+1)×N (6)

[0055] Among them Ψ j =[a(θ1,r j ),…,a(θ I ,r j )],ψ n ∈C 2M+1 ,n=1,…,N,N=IJ. This is equivalent to constructing an I×J grid and placing K steering vectors in the grid. For the dictionary matrix Ψ, (3) can be equivalently expressed as:

[0056] X=ΨW+E

[0057] (7) Indicates the L snapshot signals received by the receiving array, The noise component in the received L snapshot signals.

[0058] Each column vector w(t) of W is composed of the target source signal vector s(t) in an ideal situation. Specifically, when the dictionary grid point element (θ i ,r j ) satisfies (θ i ,r j )=(θk ,r k ), the nth element w of w(t) n (t) = s k (t), otherwise it is 0, where n=(j-1)I+i, t=1,…,L.

[0059] For each t, ​​w(t) contains only K non-zero elements, corresponding to the K parameter pairs And K<<N, so w(t) appears as a sparse vector. In addition, w(t) is jointly sparse. Although each signal may not be sparse individually, they show overall sparsity in the common representation space, that is, W contains only a few non-zero rows and is a row sparse matrix.

[0060] Therefore, equation (7) expresses the sparse framework form of the near-field source localization problem (3).

[0061] Step 2: Based on the difference between the sample covariance matrix and the covariance matrix of the received signal, a covariance matrix of a sparse matrix is ​​estimated using a solvable optimization problem form, wherein the covariance matrix of the sparse matrix expresses the position information of the received signal in the overcomplete dictionary;

[0062] The received signal matrix X can be viewed as encoded by a row sparse matrix W, that is, the matrix X is represented by a sparse matrix W, which is constrained by a small number of support vectors in the dictionary matrix Ψ. Once these support vectors are recovered, the dictionary basis vectors actually used to represent the signal are identified from the sparse representation, and the estimated parameter pair for near-field source localization can be obtained. Therefore, the near-field source localization problem can be transformed into a sparse signal recovery problem.

[0063] In addition, assuming that the signals and noise at different times are uncorrelated, the matrix of uncorrelated signals is multiplied by its own transpose and then averaged to obtain a diagonal matrix, namely the covariance matrix of the signal matrix, whose diagonal elements represent the variance of each signal. This means

[0064] E{e(t)e H (t)}=σI

[0065] E{w(t)w H (t)}=P=diag(p) (8)

[0067] Where P is the covariance matrix of the sparse matrix W, p n ≥0 represents the nth element of vector p, n=1,…,N, diag(p) ​​represents the construction of a diagonal matrix for vector p, E{·} represents the calculation of mathematical expectation, σ is the variance of the noise signal, and I is the identity matrix.

[0068] Under this assumption, the covariance matrix of the received signal is expressed as

[0069] R = E{x(t)x H (t)}=ΨPΨ H +σI=Ψ'P'Ψ' H (9)

[0071] Where Ψ'=[Ψ,I], P'=diag(P,σI), and the covariance matrix of the received signal is linearly related to the covariance matrix P of the sparse matrix W and the variance σ of the noise signal.

[0072] The sample covariance matrix is:

[0073] The goal of the traditional SPICE algorithm (used to estimate the covariance matrix) is to optimize iteratively, given Minimize to estimate R, that is, the sample covariance matrix contains the noise component, and the received signal covariance matrix is ​​estimated by minimizing the difference between the sample covariance matrix and the received signal covariance matrix, which is usually achieved by minimizing the Frobenius norm. The Frobenius norm is a specific matrix norm used to measure the size of the matrix. It can be regarded as flattening the matrix into a vector and then calculating its Euclidean norm, which is equivalent to the sum of the squares of all elements in the matrix.

[0074] Consider minimizing the following function:

[0075]

[0076] Among them, p n ,σ is the optimization variable, p n is the element in the covariance matrix P of the sparse matrix W, σ is the variance of the noise signal, and the covariance matrix R of the received signal is linearly related to it. The optimization problem is solved to find the value of the optimization variable that minimizes the difference between the sample covariance matrix and the received signal covariance matrix and satisfies all constraints.

[0077] In order to standardize the covariance matrix and simplify the problem, the square root of the received signal matrix is ​​introduced. By standardizing the covariance matrix, the influence of different scales can be eliminated, numerical stability can be enhanced, and the problem can be transformed into a more tractable form. That is:

[0078]

[0079] In non-convex optimization problems, a local optimum is not necessarily a global optimum. A local optimum is a solution that is optimal within a small neighborhood, while a global optimum is a solution that is optimal in the entire solution space. Non-convex problems are often more difficult to solve because they may contain multiple local optima, saddle points, or discontinuous solution spaces, which makes it more complicated to find the global optimum.

[0080] However, the optimization problem (10) is non-convex with respect to the variable R, and thus lacks the guarantee of global minimization. To solve this problem, the SPICE algorithm of the present invention gives a convex version of the problem (10) to convert the problem into a solvable form.

[0081] Specifically, when there are enough snapshots, i.e., L ≥ 2M + 1 and It is non-singular (full rank, reversible). For a non-singular sample matrix, its inverse matrix exists and is stable. It can be minimized by solving the following optimization problem:

[0082]

[0083] In matrix operations, the Frobenius norm can also be expressed as the trace of the matrix, that is:

[0084]

[0085] Therefore, in the present invention, formula (11) can be:

[0086]

[0087] Substituting the covariance matrix representation of the received signal into problem (11), the optimization problem can be solved by iteratively solving the following problem:

[0088]

[0089] The matrix C is an auxiliary optimization variable, C H Represents the conjugate transpose of C.

[0090] Obviously, to obtain the minimum value of (12) we need to satisfy

[0091]

[0092] Among them, in matrix calculation, the Frobenius norm of a matrix is ​​equal to the Euclidean norm after it is expanded into a vector. In other words, the Frobenius norm of a matrix can be directly regarded as the Euclidean norm after all elements of the matrix are regarded as a vector, that is, ||C|| F =||C n ||2.

[0093] Therefore, when C is determined, it is easy to obtain the explicit solution of problem (12) as

[0094]

[0095] Among them C n Represents the nth row vector of matrix C.

[0096] When the number of snapshots is limited, that is, L≤2M+1, due to The singularity of , its inverse matrix may not exist or be numerically unstable, and some eigenvalues ​​are zero or close to zero, which makes the condition number of the matrix very large, thus affecting the numerical stability and calculation accuracy, and the optimization problem (11) becomes infeasible.

[0097] In order to solve this problem, the present invention provides a new optimization problem form:

[0098]

[0099] Correspondingly, (15) also has its iterative solution form, which can be expressed as:

[0100]

[0101] Substituting the covariance matrix of the received signal into the problem, the first term of the objective function in (16) can be rewritten as

[0102]

[0103] Among them, the matrix C is an auxiliary optimization variable.

[0104] Obviously, to obtain the minimum value of (16) we need to satisfy

[0105]

[0106] Therefore, problem (16) becomes

[0107]

[0108] After the above transformation, problem (19) is a solvable optimization problem that satisfies global minimization and has an explicit solution:

[0109]

[0110] Since the objective function is monotonically decreasing during the iteration process, the SPICE algorithm can converge to the global minimum.

[0111] Step 3: Calculate the covariance matrix of the received signal and the solution of the optimization problem, and iteratively solve and calculate until the covariance matrix of the received signal and the sample covariance matrix converge to an estimation error less than the termination set threshold;

[0112] In a specific embodiment, the above principle can be implemented by the following algorithm:

[0113] If the number of snapshots is insufficient:

[0114] 1. Construct the dictionary Ψ, set the termination threshold ∈, and initialize the covariance matrix P of the sparse matrix (1) for I, σ (1) is 0.05, set the current iteration number i = 0, h (0) Initialize to infinity;

[0115] 2. Calculate the receiving covariance matrix R by using equation (9) and equation (18) respectively (0) and optimize auxiliary variable C (0) The initial value of

[0116] 3. Use the criterion given in the optimization problem (15) to calculate the minimization problem h (1) ;

[0117] 4. When |h (i) -h (i-1) When | is greater than or equal to the threshold, use (20) to update P based on C (i) and σ (i) ;

[0118] Using the updated P (i) and σ (i) Update R by (9) and (18) (i) and C (i) Using the criterion given in the optimization problem (15), h is calculated (i) , until |h (i) -h (i-1) |Less than the threshold;

[0119] When |h (i) -h (i-1) |When it is less than the threshold, continue to run;

[0120] 5. According to the convergent P (i) The elements in recover the spatial spectrum of the near-field source localization model, which correspond to their respective positions in the dictionary matrix. n represents the value corresponding to (θ i ,r j ) position energy.

[0121] If there are enough snapshots:

[0122] 1. Construct the dictionary Ψ, set the termination threshold ∈, and initialize the covariance matrix P of the sparse matrix (1) for I, σ (1)is 0.05, set the current iteration number i=0, g (0) Initialize to infinity;

[0123] 2. Calculate the receiving covariance matrix R by using equation (9) and equation (13) respectively (0) and optimize auxiliary variable C (0) The initial value of

[0124] 3. Use the criterion given in the optimization problem (11) to calculate the minimization problem g (1) ;

[0125] 4. When |g (i) -g (i-1) When | is greater than or equal to the threshold, use (14) to update P based on C (i) and σ (i) .

[0126] Using the updated P (i) and σ (i) Update R by (9) and (13) (i) and C (i) Using the criterion given in the optimization problem (11), we can calculate g (i) , until |g (i) -g (i-1) |Less than the threshold.

[0127] When |g (i) -g (i-1) |When it is less than the threshold, continue to run;

[0128] 5. According to the convergent P (i) The elements in recover the spatial spectrum of the near-field source localization model, which correspond to their respective positions in the dictionary matrix. n represents the value corresponding to (θ i ,r j ) position energy.

[0129] Step 4: Restore the near-field source positioning model spatial spectrum according to the covariance matrix elements of the sparse matrix, wherein the non-zero elements of the sparse matrix correspond to their respective positions in the dictionary matrix;

[0130] In a specific embodiment, the present invention uses numerical simulation experiments for analysis.

[0131] Consider a ULA with 9 isotropic sensors, where M = 4 and the element spacing is d = λ / 4. The Fresnel zone of the array is approximately (1.8λ, 8λ). Two target sources are set at (6λ, 70°) and (4λ, 50°). In the SPICE method, the grid width of the dictionary matrix Ψ is set to (0.05λ, 1°).

[0132] Under sufficient snapshot conditions, L = 200 and signal-to-noise ratio (SNR) = 25 dB, the spatial spectrum constructed by MUSIC and the proposed method is compared, as shown in Figure 3 As shown, the horizontal axis represents the azimuth and the vertical axis represents the range. Figure 3 The MUSIC spectrum shown is able to locate the target source, but its resolution is not as good as the spatial spectrum recovered by the proposed method.

[0133] In addition, the spatial spectra constructed by MUSIC and the proposed method are compared under limited snapshots with L = 6 and SNR = 25dB, as shown in Figure 4 As shown. Due to the insufficient number of snapshots, the MUSIC algorithm has a rank deficiency problem in the covariance matrix, which causes its performance to drop sharply. However, the improved SPICE algorithm of the present invention does not encounter this problem. Figure 4 The MUSIC spectrum shown in (a) cannot locate the target source, but Figure 4 (b) The spatial spectrum restored by the proposed method can still clearly and accurately locate the target source.

[0134] In addition, the embodiment of the present invention conducts A=200 Monte Carlo experiments under different signal-to-noise ratios to verify the advantages of the algorithm proposed in this article in terms of noise resistance performance.

[0135] The root mean square error (RMSE) is used as the metric, which is defined as:

[0136]

[0137] in and Represent the DOA estimate and distance estimate of the kth target in the ath experiment, θ k and r k Represent the true value of the kth DOA and the true value of the distance respectively.

[0138] Figure 5 The horizontal axis is the signal-to-noise ratio, and the vertical axis is the root mean square error. The RMSE of the two algorithms in the near-field source localization with sufficient snapshots varies with the signal-to-noise ratio from 5dB to 30dB (L=200), and the 2D-MUSIC algorithm is compared with the proposed method in this paper. It can be observed that within the signal-to-noise ratio of 5dB to 30dB, the proposed method has a lower RMSE overall compared with the 2D-MUSIC algorithm.

[0139] Figure 6The RMSE trends of the two algorithms with varying SNRs under limited snapshots (L=7) are described. Unlike the case with sufficient snapshots, the RMSE of the 2D-MUSIC method does not decrease significantly with increasing SNR when snapshots are limited. In contrast, the method provided by the present invention shows a significant decrease in RMSE with increasing SNR. This indicates that the proposed SPICE-based near-field source localization method is less affected by snapshot limitations and can be effectively applied to snapshot-limited scenarios.

Claims

1. A finite snapshot near-field source localization method based on the SPICE method, characterized in that: include: The sensor array receives echo signal data from the near-field source and represents it in the form of an overcomplete dictionary and a sparse matrix, that is, X = ΨW + E; where X is the received signal matrix, E is the noise matrix, and Ψ∈C (2M+1)×IJ is an overcomplete dictionary matrix, a sparse matrix W∈C IJ×L , where each column vector of the sparse matrix is ​​ideally composed of the signal received by 2M+1 receiving sensors from the Kth near-field target source at time t, t=1,2,....,L,K<<IJ; Based on the difference between the sample covariance matrix and the covariance matrix of the received signal, estimating the covariance matrix of the sparse matrix using a solvable optimization problem form, wherein the covariance matrix of the sparse matrix expresses the position information of the received signal in the overcomplete dictionary; Calculate the covariance matrix of the received signal and the solution of the optimization problem, iteratively solve and calculate until the covariance matrix of the received signal and the sample covariance matrix converge to an estimated error less than a termination setting threshold, and the solution of the optimization problem is the optimization variable p when the estimated error is less than the termination setting threshold n With the value of σ, the p n is the covariance matrix element of the sparse matrix, and σ is the variance of the noise matrix; Restoring the near-field source localization model spatial spectrum according to the covariance matrix elements of the sparse matrix to obtain an explicit solution of the target source position, wherein the non-zero elements of the sparse matrix correspond to the respective positions in the dictionary matrix; The optimization problem is obtained by solving the following equation: The R is the covariance matrix of the received signal, the is the sample covariance matrix, and h is the estimation error in the case of finite snapshots.

2. The finite snapshot near-field source localization method according to claim 1, characterized in that: Also includes: In the case of sufficient snapshots, the optimization problem can be solved by solving the following equation: The R is the covariance matrix of the received signal, the is the sample covariance matrix, and g is the estimation error in the case of sufficient snapshots.

3. The finite snapshot near-field source localization method according to claim 1, characterized in that: The method of expressing the received signal as an overcomplete dictionary and a sparse matrix includes: represents the received signal vector x(t)=As(t)+e(t) of 2M+1 receiving sensors, where represents the noise term vector, represents the target source signal vector, and the direction matrix is ​​expressed as The set of possible locations of near-field sources is defined as Construct an overcomplete dictionary matrix as Ψ=[Ψ1,…,Ψ J ]=[ψ1,…,ψ N ]∈C( 2M+1)×N , where Ψ j =[a(θ1,r j ),…,a(θ I ,r j )],ψ n ∈C 2M+1 ,n=1,…,N,N=IJ; The received signal vector is represented as X = ΨW + E; for each t, ​​w(t) contains only K non-zero elements, corresponding to K parameter pairs 4. The finite snapshot near-field source localization method according to claim 1, characterized in that: The explicit solution for the target source position, when the number of snapshots is insufficient, is: The p n The covariance matrix of the sparse matrix corresponds to (θ i ,r j ) position, C is the auxiliary optimization variable in the solution process, and ψ n is the element in the overcomplete dictionary matrix.

5. The finite snapshot near-field source localization method according to claim 1, characterized in that: The explicit solution for the target source position, when there are enough snapshots, is: The p n The covariance matrix of the sparse matrix corresponds to (θ i ,r j ) position, C is the auxiliary optimization variable in the solution process, and ψ n is an element in the overcomplete dictionary matrix, is the covariance matrix of the sample matrix.

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