A near-field incoherent distributed source positioning method

Abstract

The application belongs to the technical field of signal processing, and relates to a near-field incoherent distributed source positioning method, which comprises the following steps: receiving a near-field incoherent distributed source signal by using a sensor array, and estimating a covariance estimation quantity of the near-field incoherent distributed source signal; constructing a covariance model of the near-field incoherent distributed source signal according to the covariance estimation quantity; discretizing the angle and distance distribution of the near-field incoherent distributed source to obtain a near-field incoherent distributed source signal covariance model containing a spatial spectrum matrix; constructing a low-rank minimization problem of spatial spectrum estimation according to the near-field incoherent distributed source signal covariance model; solving the low-rank minimization problem to obtain a spatial spectrum estimation quantity; extracting key parameters of the angle and distance distribution of the near-field distributed source in the spatial spectrum according to the spatial spectrum estimation quantity, and obtaining the position of the near-field incoherent distributed source according to the key parameters; the application does not need a parameterized model of the spatial distribution of the near-field incoherent distributed source, and can directly position and estimate the angle and distance distribution of the source.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of signal processing, and particularly relates to a near-field incoherent distributed source positioning method. BACKGROUND

[0002] In the fields of sonar, airborne sound source positioning, and mobile car radar positioning, the closer the target source is to the detection sensor array, the more dispersed the received source signal appears in space. In this case, the near-field target source signal should be modeled as a near-field distributed source. Unlike the array direction vector of a far-field distributed source, which is mainly related to the angle of arrival, the array direction vector of a near-field distributed source is related to both the angle of arrival and the distance. Therefore, the angle of arrival estimation method of a far-field distributed source cannot be directly used for near-field distributed source positioning. According to the different degrees of correlation of signals from different spatial positions, a near-field distributed source can also be divided into a near-field coherent distributed source and an incoherent distributed source. For the same incoherent distributed source, signals from different spatial positions are incoherent.

[0003] Currently, the main method for near-field distributed source positioning is to extend the far-field distributed source subspace method to the near-field distributed source to estimate the parameters of the angle distribution of the distributed source, such as the near-field subspace NF-DISPARE method (reference: Meng Y, Stoica P, Wong K M. Estimation of the directions of arrival of spatially dispersed signals in array processing [J]. IEE Proceedings-Radar, Sonar and Navigation, 1996, 143(1): 1-9.). This method assumes that the angle distribution shape of all sources is known and the same, but in actual scenarios, the spatial distribution of each source is unknown and different. In order to overcome the shortcomings of the NF-DSPE method, some research has proposed a joint angle, distance, spread, shape estimator (JADSSE) method (reference: Abou Chaaya J, Picheral J, Marcos S. Localization of spatially distributed near-field sources with unknown angular spread shape [J]. Signal Processing, 2015, 106: 259-265.). This method adds a shape parameter to estimate the type of angle distribution. The NF-DISPARE method and the JADSSE method are essentially based on a parameterized angle distribution model, assuming that the angle distribution is of several specific distribution types, and by using a matching search algorithm, the most matching spatial distribution angle and distance key parameters, i.e. distance, central angle of arrival, angle spread and shape of angle distribution, are found. However, in actual application scenarios, the accurate angle distribution type is often unknown, and the assumed several distribution types may not be able to better match various complex near-field distributed source scenarios. In addition, due to the need for multi-dimensional parameter search, the computational complexity is high.

[0004] In summary, the existing near-field distributed source positioning method is mainly based on a parameterized model of the angle distribution, i.e. the type (shape) of the angle distribution is known, which is difficult to meet the positioning of sources with different angle distributions in complex scenarios. At the same time, due to the need for multi-dimensional parameter search, the algorithm complexity is too high, so there is an urgent need for a near-field distributed source positioning method that does not require the type of angle distribution to be known and has low algorithm complexity. SUMMARY

[0005] To solve the problems in the prior art, the present application provides a near-field incoherent distributed source positioning method, which comprises the following steps: receiving a near-field incoherent distributed source signal by using a sensor array and estimating a covariance estimation of the near-field incoherent distributed source signal; constructing a covariance model of the near-field incoherent distributed source signal according to the covariance estimation; discretizing an angle and distance distribution of the near-field incoherent distributed source to obtain a near-field incoherent distributed source signal covariance model containing a spatial spectrum matrix; constructing a low-rank minimization problem of spatial spectrum estimation according to the near-field incoherent distributed source signal covariance model containing the spatial spectrum matrix; solving the low-rank minimization problem to obtain a spatial spectrum estimation; extracting key parameters of the angle and distance distribution of the near-field distributed source in the spatial spectrum according to the spatial spectrum estimation, and obtaining the position of the near-field incoherent distributed source according to the key parameters.

[0006] The present application has the following advantages:

[0007] The present application does not need a parameterized model of the spatial distribution of the known near-field incoherent distributed source, can directly position and estimate the angle and distance distribution of the source, and can extract the key parameters of the distribution flexibly according to the needs, and the algorithm complexity of the present application is low. BRIEF DESCRIPTION OF DRAWINGS

[0008] Figure 1 A signal model diagram of the near-field incoherent distributed source of the present application;

[0009] Figure 2 A whole flow chart of the near-field incoherent distributed source positioning method of the present application;

[0010] Figure 3 A simulated actual spatial spectrum diagram under the symmetric distribution condition of the present application;

[0011] Figure 4 A simulated estimated spatial spectrum diagram of the present application;

[0012] Figure 5 A simulated actual spatial spectrum diagram under the asymmetric distribution condition of the present application;

[0013] Figure 6 A diagram showing the change of the center angle estimation RMSE with the signal-to-noise ratio of the present application;

[0014] Figure 7 A diagram showing the change of the center distance estimation RMSE with the signal-to-noise ratio of the present application;

[0015] Figure 8 A diagram showing the change of the angle extension estimation RMSE with the signal-to-noise ratio of the present application;

[0016] Figure 9 A diagram showing the change of the distance extension estimation RMSE with the signal-to-noise ratio of the present application;

[0017] Figure 10 Figure of operation time of the present application versus number of sensors. DETAILED DESCRIPTION

[0018] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present application.

[0019] A near-field incoherent distributed source positioning method, as shown in Figure 2 , the method comprises: receiving a near-field incoherent distributed source signal by using a sensor array, and estimating a covariance estimation of the near-field incoherent distributed source signal; constructing a covariance model of the near-field incoherent distributed source signal according to the covariance estimation; discretizing an angle and distance distribution of the near-field incoherent distributed source to obtain a near-field incoherent distributed source signal covariance model containing a spatial spectrum matrix; constructing a low-rank minimization problem of spatial spectrum estimation according to the near-field incoherent distributed source signal covariance model containing the spatial spectrum matrix; solving the low-rank minimization problem to obtain a spatial spectrum estimation; extracting key parameters of the angle and distance distribution of the near-field distributed source in the spatial spectrum according to the spatial spectrum estimation, and obtaining the position of the near-field incoherent distributed source according to the key parameters.

[0020] In the embodiment, a signal model of the near-field incoherent distributed source is as shown in Figure 1 , and specifically comprises: considering K near-field spatial distributed narrowband source signals incident on a uniform linear array containing N sensors in a two-dimensional space, the interval d of adjacent sensors is λ is the wavelength of the narrowband source signal. Assuming that the near-field incoherent distributed source signal simultaneously exists angle spread and distance spread, the array output signal at time t can be expressed as:

[0021]

[0022] wherein, is a complex set; θ and Θ respectively represent the azimuth angle and the angle range of the direction of arrival; l and Υ respectively represent the distance and the distance range. k (θ, l, t) represents the signal of the kth source at the spatial position (θ, l). The array direction vector wherein j is an imaginary unit, (·) T is a matrix transpose, w is the component of the signal along the direction of arrival, and φ is the phase difference. is additive white Gaussian noise.

[0023] ​Assuming that the source signals are uncorrelated with the noise, the covariance of the array output signals can be expressed as:

[0024]

[0025] where E(·) denotes expectation; (·) H denotes matrix conjugate transpose; R s and are the covariances of the source signals and the Gaussian white noise, respectively; is the noise variance, and I is the identity matrix.

[0026] Assuming that the number of sampling snapshots is B, the estimation of the covariance R of the array output signals can be obtained as:

[0027]

[0028] The eigenvalue decomposition of can be performed, and the estimation of can be set as the minimum eigenvalue of . From formulas (2) and (3), the covariance estimation of the near-field non-coherent distributed source signals can be obtained as:

[0029]

[0030] In the embodiment, the covariance model of the array output signals is derived, the angle and distance distributions of the near-field non-coherent distributed sources are discretized, and the spatial spectrum matrix in the covariance model of the array output signals is obtained. The specific process includes:

[0031] Step 1, according to the near-field non-coherent distributed source signal model formula (1) and the covariance formula (2), the covariance model of the array output signals is derived. s which can be derived as:

[0032]

[0033] where θ' is also the azimuth angle of the direction of arrival, l' is the distance, is the complex number of the signal of the k'th source at the spatial position (θ', l').

[0034] Assuming that the signals of different near-field distributed sources are uncorrelated, and for the same near-field non-coherent signal distributed source, the signals from different positions are uncorrelated, the cross-correlation kernel can be simplified as:

[0035] q kk′ (θ,θ,l,l′)=p k (θ,l)δ kk′ δ(θ-θ′)δ(l-l′) (7)

[0036] where δ kk′Let δ(θ-θ′) be the Dirac delta function, and let δ(θ-θ′) be the Kronecker delta function. Let A represent the power distribution of the k-th near-field incoherent distributed source signal in the angle-range domain. θ,l express Where a θ,l It is a shorthand for a(θ,l). Then R s Formula (5) can be reformulated as:

[0037]

[0038] in, This is called the "spatial spectrum" of a near-field incoherent distribution source.

[0039] Step 2: Discretize the angle and distance distribution of the near-field incoherent distributed sources to obtain the spatial spectrum matrix in the covariance model of the array output signal.

[0040] Discretize the observed angle and distance ranges Θ and Υ to obtain the corresponding uniform discrete points {θ1, θ2, ..., θ m} and {l1,l2,…,l n}, where m and n correspond to the number of discrete points within the angle and distance ranges, respectively. Using p k Discretization of (θ,l) then matrix P k An element can be represented as

[0041] P k (θ g ,l h ) = p k (θ g ,l h ), g=1,2…m, h=1,2…n (9)

[0042] Among them, P k (θ g ,l h ) represents matrix P k The element in row g and column h. Let... For p θ,l The discrete representation can be used to obtain the spatial spectral matrix.

[0043] In order to express R in terms of the estimator P, the matrices R and A in formulas (2) and (8) are transformed. θ,l and Rearrange them all into a vector to obtain

[0044]

[0045] where vec(·) denotes the vectorization operator, i.e., arranging all columns of a matrix into a column vector. and r n are the vectorization of matrix A θ,l and

[0046] Substituting the summation for the integral in (11), r can be approximated as

[0047]

[0048] where and are defined as

[0049]

[0050] In this embodiment, according to the low-rank property of the spatial spectrum matrix, a low-rank minimization problem of spatial spectrum estimation is constructed, and the low-rank minimization problem is solved based on an iterative weighted kernel norm algorithm to obtain the spatial spectrum estimation.

[0051] Specifically, it includes:

[0052] (1) Analyzing the low-rank property of the spatial spectrum matrix.

[0053] When the angle and the distance are independent of each other, the spatial spectrum p k (θ, l) of the kth source can be factorized as p k (θ, l) = p k (θ) p k (l), where p k (θ) and P(l) are the power distribution of the signal of the kth source in the angle domain and the distance domain, respectively. Thus, the spatial spectrum matrix can be expressed as

[0054]

[0055] Since the rank of the vector is 1, it can be obtained that is a matrix with rank 1, so the rank of the spatial spectrum matrix k is not greater than K. Generally, the number of sources K is much less than the number of rows and columns of the matrix k. Therefore, when the angle and the distance are independent of each other, the spatial spectrum matrix k has a low-rank property.

[0056] When the angle and the distance are related, the spatial spectrum matrix P k can be approximated as P k about the central DOA and the central distance, then P k ​The rank of P is at most (M + 1), and the rank of the spatial spectrum matrix P of K sources is no more than K(M + 1). In fact, M is usually 1 or 2, so the spatial spectrum matrix is also approximately low-rank when the angle and distance are related.

[0057] (2) Construct a low-rank minimization problem for spatial spectrum estimation. The specific implementation is as follows

[0058] Since mn is usually much larger than N 2 , formula (12) can be regarded as an underdetermined equation group about the variable , and P has an infinite number of solutions. However, P has a low-rank characteristic, so the traditional linear equation solving problem (11) can be converted into a low-rank minimization problem for solving as follows

[0059]

[0060] Among them, the estimator can be obtained from the signal covariance estimator in step 1

[0061] In fact, the rank minimization problem is an NP-hard problem, and the nuclear norm is the tightest convex relaxation of the rank function, and the rank function can be replaced by the nuclear norm. Considering the estimation error caused by additive noise, the rank minimization problem of formula (13) can be formulated into the following convex relaxation form

[0062]

[0063] Among them, the nuclear norm of the matrix Here σ i (P) represents the i-th singular value of P, and σ i (P) > σ i+1 (P). ε>0 reflects the noise level. ‖·‖2 represents the 2-norm of the vector.

[0064] (3) Solve the spatial spectrum of the low-rank minimization problem based on the iterative weighted nuclear norm algorithm.

[0065] Formula (13) can be regularized as

[0066]

[0067] Among them, 0<λ≤1 is a regularization parameter. In fact, the nuclear norm cannot obtain the optimal solution of the rank function, fortunately, there are some better non-convex rank replacement functions and put forward, such as the iterative weighted nuclear norm, the truncated nuclear norm, the Sp norm, etc. To simplify the process, this method uses the iterative weighted nuclear norm to show the effectiveness of the low-rank matrix recovery framework for spatial spectrum estimation of near-field incoherent distributed sources.

[0068] Let According to the iterative weighted kernel norm method, the formula can be written as

[0069]

[0070] Set g δ (x) = 1 - e -x / δ can better approximate the rank function, can be solved by an iterative process

[0071]

[0072] Here s represents the s-th iteration, is the derivative of g δ (x), where g δ (x) = 1 - e -x / δ According to the iterative weighting strategy, formula (17) is updated to the iterative weighted kernel norm minimization form:

[0073]

[0074] where λ is a regularization parameter, s represents the s-th iteration, is an intermediate parameter, σ i (P) is the i-th singular value of P, P is a low-rank matrix, μ is a convergence parameter, P s is the value of P in the s-th iteration; f(P s ) is reflects the noise variance level; is the derivative of f(P s ) with respect to P s ;‖·‖ F denotes the matrix F norm, and ‖·‖2 denotes the vector 2 norm.

[0075] Here μ > L(f) ensures convergence, where is the Lipschitz constant of f; ‖·‖ F denotes the matrix F norm. is the derivative of f(P s ) with respect to P s ; according to the weighted singular value threshold operator, there is a global optimal solution for obtaining a low-rank matrix P as:

[0076]

[0077] where is the singular value decomposition of matrix Y, where ∑, U and V are the singular value diagonal matrix, left singular matrix and right singular matrix of the singular value decomposition of Y, respectively; the i-th row and i-th column element of matrix is where ∑ii Let represent the element in the i-th row and i-th column of the matrix ∑.

[0078] During the iteration process, an initial value P is roughly obtained according to the nuclear norm minimization formula (15). 0 The initial value of δ is set to 8σ1(P). 0 ), and in each iteration, δ s+1 =δ s / ρ, ρ>1, to ensure faster iteration convergence. Set μ = 1.5L(f) to ensure convergence, set λ, iteration threshold ∈ 0, and let the iteration stopping rule be |P s+1 -P s | F / |P s | F <∈0. An estimate of P can be obtained when the iteration converges.

[0079] In this embodiment, the first and second moments are used to extract key parameters related to the angle and distance distribution of near-field sources in the spatial spectrum. These key parameters include the central angle, central distance, angle spread, and distance spread.

[0080] Based on the estimated spatial spectrum Key parameters of the angular and distance distributions of near-field incoherent sources are estimated using first and second-order moments: central angle, angular spread, central distance, and distance spread. The central angle can be estimated using the first-order raw moment. and center distance for

[0081]

[0082] The angle extension is estimated based on the second-order central moment. and distance expansion for:

[0083]

[0084] Where, Θ k and Υ k These represent the distribution ranges of the angle and distance of the k-th NFID source signal, respectively. η is the estimator of the spatial spectral matrix of the source; η is the distribution parameter, η = 1 when the distribution is Gaussian or Laplace, and η = 3 when the distribution is uniform.

[0085] In this embodiment, the beneficial effects of the present invention can be further illustrated by simulation results. The simulation experimental conditions are as follows:

[0086] 1. The method of this invention provides spatial spectrum estimation for near-field incoherent distributed sources.

[0087] Assuming the angle and distance distributions are uncorrelated, set the spatial spectrum of two near-field incoherent distributed source signals with different distribution types, one Gaussian distribution and the other uniform distribution. Thus the probability density functions of the spatial spectrum of the two sources can be obtained as

[0088]

[0089] Set the angle and distance parameters of the two sources as The observation range is set as [20°, 50°]x[30λ, 60λ], and the corresponding discrete resolutions are 1° and λ, respectively. The number of array sensors is N=60, the number of snapshots B is 5x10 4 , and SNR=20dB. The iteration parameter is set as λ=0.4, and the iteration stop threshold is set as ε0=10 -5 .

[0090] As Figures 3-4 shown in the figure, the real spatial spectrum and the spatial spectrum estimated by the method of the application are consistent. This shows that the method of the application can effectively estimate the spatial spectrum of near-field incoherent distributed sources with different distribution types.

[0091] 2. Estimation of key parameters of near-field incoherent distributed sources by the method of the application

[0092] In order to compare the performance of the method of the application and the traditional subspace NF-DISPARE and JADSSE methods in estimating key parameters under complex distribution, consider that the signals of two near-field incoherent distributed sources have asymmetric distribution in space. The angle and distance distributions are still uncorrelated, wherein the angle distribution is the superposition of two Gaussian distributions, and the distance distribution is the superposition of Gaussian distribution and uniform distribution. Represent the Gaussian distribution and the uniform distribution by ρ G (μ0,Δ) and ρ U (μ0,Δ), respectively, wherein μ0 and Δ are the center parameter and the spread parameter, respectively. Set the edge distribution of the angle and distance as

[0093] p1(θ)=0.7ρ G (28°,2°)+0.3ρ G (30°,2°)

[0094] p1(l)=0.7ρ U (53λ,2λ)+0.3ρ G (55λ,2λ)

[0095] p2(θ)=0.6ρ G (41°,1°)+0.4ρ G (38°,1°)

[0096] p2(l)=0.8ρ U (38λ,3λ)+0.2ρ G (40 in, 3λ).

[0097] Therefore, the spatial spectrum of the k-th source is p. k (θ,l)=p k (θ)p k (l), the shape of the spectral distribution is as follows Figure 5 As shown. The number of sensors was set to N = 50, and the number of snapshots to B = 5000. The search ranges for the center angle and distance of the NF-DISPARE and JADSSE methods were set to the observation range of this invention, and the search ranges for angle and distance extensions were set to [1°, 10°] × [λ, 10λ], with corresponding resolutions of 1° and λ. Furthermore, the NF-DISPARE method assumes that both the angle and distance distributions are Gaussian. The search range for the angle distribution shape parameter of the JADSSE method was set to [0, 10], with a resolution of 2. The experiments were based on 150 Monte Carlo experiments, and RMSE was used to evaluate the performance of each method in estimating key parameters. In the formula, M = 150 is the number of Monte Carlo experiments, α k It is the true value of the key parameter of the k-th source. It is the estimated value of the key parameter of the k-th source in the i-th Monte Carlo experiment.

[0098] Figures 6-9 The results show the RMSE (Recovery Mean Squared) of the estimation of key parameters (center angle θ0, center distance l0, angle spread Δθ, and distance spread Δl) by various methods as a function of signal-to-noise ratio (SNR) when the signal has an asymmetric spatial distribution. Since the JADSSE-based method does not estimate the spread parameters, therefore... Figures 8-9 The RMSE results for the JADSSE method's estimation of Δθ and Δl are not shown. As can be seen from the figure, the method of this invention has higher parameter estimation accuracy compared to the NF-DISPARE and JADSSE methods. This is because the specific distributions assumed by the NF-DISPARE and JADSSE methods do not match asymmetric distributions well. In contrast, the method of this invention directly estimates the spatial spectrum without requiring knowledge of the type of spectral distribution, thus making it more suitable for general spatial distributions.

[0099] 2. The operational efficiency of the method of this invention for estimating parameters of near-field incoherent distributed sources.

[0100] To evaluate the computational complexity of each estimation method for spatial distribution parameter estimation, the average CPU runtime of the Monte Carlo experiment was statistically analyzed as the number of sensors N increased. The number of sensors N was increased from 20 to 60, and the SNR was set to 10 dB, while the source distribution parameters and system parameters remained the same as in the previous example. Figure 10It is shown that the method of the present application runs much faster than the NF-DISPARE and JADSSE methods, which require a multi-dimensional search, and thus has lower computational complexity.

[0101] The above examples further illustrate the objects, technical solutions and advantages of the present application. It should be understood that the above examples are merely preferred embodiments of the present application and are not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made to the present application within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for locating a near-field incoherent distributed source, the method comprising: The application comprises the following steps: Receiving near-field non-coherent distributed source signals by using a sensor array, and estimating a covariance estimation of the near-field non-coherent distributed source signals; Constructing a covariance model of the near-field non-coherent distributed source signals according to the covariance estimation; Discretizing the angle and distance distribution of the near-field non-coherent distributed source to obtain a near-field non-coherent distributed source signal covariance model containing a spatial spectrum matrix; constructing a low-rank minimization problem of spatial spectrum estimation according to the near-field non-coherent distributed source signal covariance model containing the spatial spectrum matrix; solving the low-rank minimization problem to obtain a spatial spectrum estimation; Extracting key parameters of the angle and distance distribution of the near-field distributed source in the spatial spectrum according to the spatial spectrum estimation, and obtaining the position of the near-field non-coherent distributed source according to the key parameters; The covariance model of the near-field non-coherent distributed source signals comprises the following steps: Since the signals of different near-field distributed sources are not correlated, and the signals from different positions are not coherent for the same near-field non-coherent signal distributed source, the cross-correlation kernel can be simplified as: q kk′ (θ,θ,l,l′)=p k (θ,l)δ kk′ δ(θ-θ′)δ(l-l′) where δ kk′ is the Dirac delta function, δ(θ - θ') is the Kronecker delta function; is the power distribution of the k-th near-field non-coherent distributed source in the angle-range domain, p θ,l is the "spatial spectrum" of the near-field non-coherent distributed source; The covariance estimation of the sensor array output signal comprises the following steps: obtaining the signal x(t) output by the sensor array at time t; calculating the covariance of the signal x(t), and estimating the estimation of the output signal covariance; estimating the covariance estimation of the near-field non-coherent distributed source signals according to the covariance estimation of the output signal; the array output signal at time t is: where θ and Θ represent the azimuth angle and angular range of the direction of arrival, respectively; l and Y represent the distance and distance range, respectively; s k (θ, l, t) represents the signal of the kth source at the spatial position (θ, l), a(θ, l) is the array direction vector, j is the imaginary unit, (·) T is the matrix transpose, w is the component of the signal along the direction of arrival, φ is the phase difference; n(t) is additive white Gaussian noise; The angle and distance distribution of the discretized near-field incoherent distributed source includes: discretizing the angle range Θ and the distance range γ to obtain uniform discrete points {θ1, θ2, …, θN} and {l1, l2, …, lM} in the ranges; and optimizing the array output signal expression according to the uniform discrete points to obtain a near-field incoherent distributed source signal covariance model containing a spatial spectrum matrix. m} and {l1, l2, …, l n}; the discretization of p k (θ, l) is represented by a matrix P k when the angle range is discretized, and the element of P k is represented as: P k (θ g ,l h )=p k (θ g ,l h ),g=1,2…m,h=1,2…n Among them, P k (θ g ,l h ) represents matrix P k The element in row g and column h; take P as p θ,l The discrete representation is used to obtain the spatial spectral matrix P; According to the spatial spectrum matrix, the covariance of the source signal received by the array is calculated: where vec(·) denotes the vectorization operator, and r n are the vectorization of the matrices A θ,l and respectively. The covariance of the source signal received by the array is simplified, that is: Solving the low-rank minimization problem comprises: converting the low-rank minimization problem into an iterative weighted kernel norm minimization problem by using an iterative weighted kernel norm algorithm; solving the iterative weighted kernel norm minimization problem by using a weighted singular value threshold operator, and obtaining a global optimal solution of the low-rank matrix P when an iteration stopping condition is met in the calculation process, the optimal solution being a spatial spectrum estimator; obtaining a rough initial value P of P in the iteration process 0 , setting an initial value of δ as 8σ1(P 0 ), and making δ s+1 = δ s / ρ in each iteration; setting μ = 1.5L(f), setting λ, an iteration threshold value ∈0, and setting an iteration stopping rule as |P s+1 -P s | F / |P s | F < ∈0; and obtaining an estimator of P when the iteration converges 2. The method of claim 1, wherein, The sensor array includes N sensors uniformly distributed on a straight line, and the distance d between two adjacent sensors is half of the wavelength of the source signal where λ is the wavelength of the source signal.

3. The method of claim 1, wherein, The covariance estimation of the near-field non-coherent distributed source signals is estimated as: wherein is a covariance estimate of the near-field incoherent distributed source signal, is an estimate of the array output signal covariance R, is the noise variance, I is the identity matrix, L is the maximum time, x(t) is the output signal at time t, (·) H denotes the matrix conjugate transpose, B is the number of sample snapshots.

4. The method of claim 1, wherein, The low-rank minimization problem of spatial spectrum estimation is: where rank(·) is the matrix rank function, is the estimator, vec(·) denotes the vectorization operator, and r is the covariance of the source signals received by the array.

5. The method of claim 1, wherein, The iterative weighted kernel norm minimization problem is: where λ is a regularization parameter, s denotes the s-th iteration, is an intermediate parameter, σ i (P) is the i-th singular value of P, P is a low-rank matrix, μ is a convergence parameter; P s is the value of P in the s-th iteration, f(P s ) is a function reflecting the noise variance level, is the derivative of f(P s ) with respect to P s ;‖·‖ F denotes the matrix F-norm, and ‖·‖2 denotes the vector 2-norm.

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