Near-field incoherent distribution source positioning method

Abstract

The invention belongs to the technical field of signal processing, and relates to a near-field incoherent distribution source positioning method, which comprises the following steps of: receiving a near-field incoherent distribution source signal by adopting a sensor array, and estimating a covariance estimator of the near-field incoherent distribution source signal; constructing a covariance model of the near-field incoherent distribution source signal according to the covariance estimator; discretizing the angle and distance distribution of the near-field incoherent distribution source to obtain a near-field incoherent distribution source signal covariance model containing a spatial spectrum matrix; constructing a low-rank minimization problem of spatial spectrum estimation according to a near-field incoherent distribution source signal covariance model; solving a low-rank minimization problem to obtain a spatial spectrum estimator; key parameters of angle and distance distribution of a near-field distribution source in the spatial spectrum are extracted according to the spatial spectrum estimator, and the position of a near-field incoherent distribution source is obtained according to the key parameters; according to the method, a parameterized model of near-field incoherent distribution source space distribution does not need to be known, and angle and distance distribution of an estimation source can be directly positioned.

Description

Technical Field

[0001] The invention belongs to the technical field of signal processing, and in particular relates to a near-field incoherent distribution source positioning method. Background Art

[0002] In the fields of sonar, aerial sound source positioning, and mobile car radar positioning, the closer the target source is to the detection sensor array, the more scattered 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 the far-field distributed source, which is mainly related to the wave angle, the array direction vector of the near-field distributed source is not only related to the wave angle but also to the distance. Therefore, the wave angle estimation method of the far-field distributed source cannot be directly used for the positioning of the near-field distributed source. According to the different correlation degrees of signals from different spatial positions, the near-field distributed source can also be divided into near-field coherent distributed sources and incoherent distributed sources. For the same incoherent distributed source, the signals from different spatial positions are incoherent.

[0003] At present, the method of localizing near-field distributed sources mainly extends the far-field distributed source subspace method to the near-field distributed source, and estimates the parameters of the angular 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 angular distribution shapes of all sources are known and the same. However, in actual scenes, the spatial distribution of each source is unknown and different. In order to overcome the shortcomings of the NF-DSPE method, some studies have proposed the Joint Angle, Distance, Spread, Shape Estimator (JADSSE) method (reference: AbouChaaya 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 angular distribution. Both the NF-DISPARE method and the JADSSE method are essentially based on a parameterized angular distribution model, assuming that the angular distribution is of several specific distribution types, and using a matching search algorithm to find the most matching key parameters of spatial distribution angle and distance, namely, distance, central wave angle of arrival, angular spread, and the shape of the angular distribution. However, in actual application scenarios, the exact angular distribution type is often unknown, and the assumed distribution types may not be able to match various complex near-field distribution source scenarios well. In addition, due to the need for multi-dimensional parameter search, the computational complexity is relatively high.

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

[0005] In order to solve the problems existing in the above-mentioned prior art, the present invention proposes a near-field incoherent distributed source positioning method, which includes: using a sensor array to receive near-field incoherent distributed source signals, and estimating the covariance estimator of the near-field incoherent distributed source signals; constructing a covariance model of the near-field incoherent distributed source signals according to the covariance estimator; discretizing the angle and distance distribution of the near-field incoherent distributed source to obtain the covariance model of the near-field incoherent distributed source signal containing a spatial spectrum matrix; constructing a low-rank minimization problem of spatial spectrum estimation according to the covariance model of the near-field incoherent distributed source signal containing the spatial spectrum matrix; solving the low-rank minimization problem to obtain a spatial spectrum estimator; extracting key parameters of the angle and distance distribution of the near-field distributed source in the spatial spectrum according to the spatial spectrum estimator, and obtaining the position of the near-field incoherent distributed source according to the key parameters.

[0006] Beneficial effects of the present invention:

[0007] The present invention does not require a parameterized model of the spatial distribution of a near-field incoherent distribution source, can directly locate and estimate the angle and distance distribution of the source, and can flexibly extract key parameters of the distribution as needed, and the algorithm complexity of the present invention is low. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 A signal model diagram of a near-field incoherent distribution source of the present invention;

[0009] Figure 2 It is an overall flow chart of the near-field incoherent distribution source positioning method of the present invention;

[0010] Figure 3 Simulate the actual spatial spectrum under the symmetrical distribution of the present invention;

[0011] Figure 4 A spatial spectrum diagram estimated by simulation of the present invention;

[0012] Figure 5 Simulate the actual spatial spectrum in the asymmetric distribution case of the present invention;

[0013] Figure 6 This is a graph showing the change of RMSE of the central angle estimation according to the present invention with the signal-to-noise ratio;

[0014] Figure 7 This is a graph showing the change of RMSE of center distance estimation with signal-to-noise ratio in the present invention;

[0015] Figure 8 This is a graph showing the change of RMSE of angle expansion estimation with signal-to-noise ratio according to the present invention;

[0016] Fig. 9 This is a graph showing the variation of RMSE of distance expansion estimation with signal-to-noise ratio according to the present invention;

[0017] Fig.10 This is a graph showing how the running time of the present invention changes with the number of sensors. DETAILED DESCRIPTION

[0018] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

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

[0020] In this embodiment, the signal model of the near-field incoherent distribution source is as follows: Figure 1 As shown, it specifically includes: in two-dimensional space, consider K near-field spatially distributed narrow-band source signals incident on a uniform linear array containing N sensors, and the spacing d between adjacent sensors is half the wavelength of the source signal λ is the wavelength of the narrowband source signal. Assuming that the near-field incoherently distributed source signal has both angular expansion and distance expansion, the array output signal at time t is It can be expressed as:

[0021]

[0022] in, is a set of complex numbers; θ and Θ represent the azimuth and angular range of the wave arrival direction respectively; l and Υ represent the distance and distance range respectively. k (θ,l,t) represents the signal of the kth source at the spatial position (θ,l). The array direction vector where j is an imaginary unit, (·) T is the 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 signal is independent of the noise, the covariance of the array output signal can be expressed as:

[0024]

[0025] Among them, E(·) represents expectation; (·) H Represents the matrix conjugate transpose; R s and are the covariances of the source signal and Gaussian white noise respectively; is the noise variance, and I is the identity matrix.

[0026] Assuming the number of sampling snapshots is B, the estimated value of the array output signal covariance R is:

[0027]

[0028] right By performing eigenvalue decomposition, we can The estimator is set to The minimum eigenvalue of , from formulas (2) and (3), the covariance estimator of the near-field incoherent distribution source signal can be obtained as:

[0029]

[0030] In this embodiment, the covariance model of the array output signal is derived, the angle and distance distribution of the near-field incoherent distribution source are discretized, and the spatial spectrum matrix in the covariance model of the array output signal is obtained. The specific process includes:

[0031] Step 1: According to the near-field incoherent distributed source signal model formula (1) and the covariance formula (2), derive the covariance model of the array output signal. s It can be deduced as:

[0032]

[0033] Among them, θ′ is also the azimuth of the wave arrival direction, 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 from different near-field distribution sources are uncorrelated, and for the same near-field incoherent signal distribution source, the signals from different positions are uncorrelated, the cross-correlation kernel can be simplified to:

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

[0036] Among them, δ kk′is the Dirac delta function, and δ(θ-θ′) is the Kronecker delta function; is the power distribution of the kth near-field incoherent distribution source signal in the angle-distance domain. θ,l express where a θ,l is the abbreviation of a(θ,l). Then R s Formula (5) can be reformulated as:

[0037]

[0038] in, It is called the "spatial spectrum" of a near-field incoherently distributed source.

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

[0040] The observed angle and distance ranges Θ and Υ are discretized 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 in the angle and distance ranges, respectively. Indicates p k The discretization of (θ, l) is as follows: k The elements 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 the matrix P k The element at row g and column h. For p θ,l The discrete representation of the spatial spectrum matrix can be obtained

[0043] In order to express R with the estimated quantity P, the matrices R and A in formulas (2) and (8) are θ,l and Rearrange them into a vector, and we get

[0044]

[0045] Among them, vec(·) represents the vectorization operator, which links all the columns of the matrix into a column vector. and r n The matrix A θ,l and Vectorization of .

[0046] By replacing the integral formula in formula (11) with the summation formula, r can be approximately expressed as:

[0047]

[0048] in, and is defined as:

[0049]

[0050] In this embodiment, according to the low-rank characteristic 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 nuclear norm algorithm to obtain the spatial spectrum estimation.

[0051] Specifically include:

[0052] (1) Analyze the low-rank characteristics of the spatial spectrum matrix.

[0053] When the angle and distance are independent, the spatial spectrum p of the kth source k (θ,l) can be factorized into 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 distance domain respectively. Therefore, the spatial spectrum matrix can be expressed as

[0054]

[0055] Since the rank of the vector is 1, we can get is a matrix of rank 1, so the rank of the spatial spectrum matrix k is no greater than K. Generally speaking, the number of sources K is much smaller than the number of rows and columns of the matrix k. Therefore, when the angle and distance are independent of each other, the spatial spectrum matrix k has a low rank property.

[0056] When angle and distance are related, the spatial spectrum matrix P k It can be approximated as P k The M-order Taylor series expansion of the center DOA and the center distance, then P kThe rank of is at most (M+1), and the rank of the spatial spectrum matrix P of K sources is no greater than K(M+1). In practice, M is usually 1 or 2, so when the angle and distance are related, the spatial spectrum matrix is ​​also approximately low-rank.

[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 , so formula (12) can be regarded as a variable The underdetermined system of equations, P has infinite solutions. However, P has a low-rank property, so according to the constraints, the traditional linear equation solving problem (11) can be transformed into the following low-rank minimization problem solution:

[0059]

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

[0061] In fact, the rank minimization problem is an NP-hard problem. 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 as 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 vector 2-norm.

[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 into

[0066]

[0067] Where 0<λ≤1 is the regularization parameter. In fact, the nuclear norm cannot obtain the optimal solution of the rank function. Fortunately, some better non-convex rank substitute functions have been proposed, such as iterative weighted nuclear norm, truncated nuclear norm, Sp norm, etc. To simplify the process, this method uses iterative weighted nuclear norm to show the effectiveness of the low-rank matrix recovery framework for the spatial spectrum estimation of near-field incoherent distribution sources.

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

[0069]

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

[0071]

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

[0073]

[0074] Among them, λ is the regularization parameter, s represents the sth iteration, is the intermediate parameter, σ i (P) is the i-th singular value of P, P is a low-rank matrix, μ is the convergence parameter, P s is the value of P in the sth iteration; f(P s )for Reflects the noise variance level; f(P s ) s The derivative of ; ‖·‖ F represents the matrix F-norm, and ‖·‖2 represents the vector 2-norm.

[0075] Here μ>L(f) ensures convergence, where yes Lipschitz constant; ‖·‖ F Represents the norm of the matrix F. f(P s ) s The derivative of ; According to the weighted singular value threshold operator, the low-rank matrix P has a global optimal solution:

[0076]

[0077] in is the singular value decomposition of the 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 matrix The element in the i-th row and i-th column of is where ∑ii Represents the element in the i-th row and i-th column of the matrix ∑.

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

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

[0080] According to the estimated spatial spectrum The first and second order moments are used to estimate the key parameters of the angle and distance distribution of the near-field incoherent distribution source, namely the center angle, angle spread, center distance and distance spread. The center angle can be estimated based on the first order origin moment. Distance from center for

[0081]

[0082] Estimate the angular spread based on the second-order central moment and distance extension for:

[0083]

[0084] Among them, Θ k and k are the distribution ranges of the angle and distance of the kth NFID source signal, is the estimate of the spatial spectrum matrix of the source; η is the distribution parameter, when the distribution is Gaussian distribution or Laplace distribution, η = 1, when it is uniform distribution, η = 3.

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

[0086] 1. Spatial spectrum estimation of near-field incoherent distribution sources by the method of the present invention

[0087] Assuming that the distribution of angle and distance is unrelated, the spatial spectra of two near-field incoherent distribution source signals are set to have different distribution types, one is Gaussian distribution and the other is uniform distribution. Thus, the probability density functions of the two source spatial spectra can be obtained as

[0088]

[0089] Set the angle and distance parameters of the two sources to The observation range is set to [20°, 50°] × [30λ, 60λ], and the corresponding discrete resolutions are 1° and λ, respectively. The number of array sensors is N = 60, and the number of snapshots B is 5 × 10 4 , SNR = 20dB. Iteration parameter setting λ = 0.4, iteration stop threshold setting ∈0 = 10 -5 .

[0090] like Figure 3-Figure 4 The real spatial spectrum and the spatial spectrum estimated by the method of the present invention are shown. It can be seen that the estimated spatial spectrum has good consistency with the real spatial spectrum. This shows that the method of the present invention can effectively estimate the spatial spectrum of different distribution types of near-field incoherent distribution sources.

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

[0092] In order to compare the performance of the proposed method with the traditional subspace NF-DISPARE and JADSSE methods for key parameter estimation under complex distribution. Consider that the signals of two near-field incoherent distribution sources have asymmetric distribution in space. The distribution of angle and distance is still unrelated, where the angle distribution is the superposition of two Gaussian distributions. The distance distribution is the superposition of Gaussian distribution and uniform distribution. Use ρ G (μ0,Δ) and ρ U (μ0,Δ) represents Gaussian distribution and uniform distribution, where μ0 and Δ are the center parameter and spread parameter, respectively. The marginal distribution of angle and distance is set to

[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 input, 3λ).

[0097] Thus, the spatial spectrum of the kth 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. In addition, the number of sensors is set to N=50, and the number of snapshots is set to B=5000. The search range of the central angle and distance of the NF-DISPARE and JADSSE methods is set to the observation range of the present invention, and the search range of the angle and distance extension is set to [1°, 10°]×[λ, 10λ], and the corresponding resolutions are 1° and λ. In addition, the NF-DISPARE method assumes that both the angle distribution and the distance distribution are Gaussian distributions. The search range of the angle distribution shape parameter of the JADSSE method is set to [0,10], with a resolution of 2. The experiment is based on 150 Monte Carlo experiments, and RMSE is used to evaluate the performance of each method for key parameter estimation, where Where, M = 150 is the number of Monte Carlo experiments, α k is the true value of the key parameter of the kth source, is the estimated value of the key parameter of the kth source in the i-th Monte Carlo experiment.

[0098] Figure 6-Figure 9 The figure shows the variation of RMSE of the key parameters center angle θ0, center distance l0, angle spread Δθ and distance spread Δl estimated by each method with the signal-to-noise ratio SNR when the signal has an asymmetric distribution in space. Since the JADSSE method does not estimate the expansion parameters, Figure 8-Figure 9 The RMSE results of the JADSSE method for Δθ and Δl estimation are not shown. According to the legend results, it can be seen that compared with the NF-DISPARE and JADSSE methods, the method of the present invention has a higher parameter estimation accuracy. This is because the specific distribution assumed by the NF-DISPARE and JADSSE methods cannot match the asymmetric distribution well. The method of the present invention directly estimates the spatial spectrum and does not require the type of known spectral distribution, so it is more suitable for general spatial distribution.

[0099] 2. The operating efficiency of the method of the present invention for near-field incoherent distributed source parameter estimation

[0100] In order to evaluate the computational complexity of each estimation method for spatial distribution parameter estimation, the average CPU running time of the Monte Carlo experiment is statistically analyzed as the number of sensors N changes. The number of sensors N is set to increase from 20 to 60, the SNR is 10dB, and the source distribution parameters and system parameters are set the same as the previous example. Fig.10It is shown that the method of the present invention runs much faster than the NF-DISPARE and JADSSE methods which require multi-dimensional search, and therefore has a lower computational complexity.

[0101] The above embodiments further illustrate the purpose, technical solutions and advantages of the present invention in detail. It should be understood that the above embodiments are only preferred implementation modes of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made to the present invention within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A near-field incoherent distribution source positioning method, characterized in that: include: A sensor array is used to receive a near-field incoherent distribution source signal, and a covariance estimate of the near-field incoherent distribution source signal is estimated; Constructing the covariance model of near-field incoherent distribution source signal based on the covariance estimator; Discretize the angle and distance distribution of the near-field incoherent distribution source to obtain the near-field incoherent distribution source signal covariance model containing the spatial spectrum matrix; construct a low-rank minimization problem for spatial spectrum estimation based on the near-field incoherent distribution source signal covariance model containing the spatial spectrum matrix; solve the low-rank minimization problem to obtain the spatial spectrum estimate; The key parameters of the angle and distance distribution of the near-field distribution source in the spatial spectrum are extracted according to the spatial spectrum estimation, and the position of the near-field incoherent distribution source is obtained according to the key parameters.

2. A near-field incoherent distribution source positioning method according to claim 1, characterized in that: The sensor array includes N sensors evenly distributed in a straight line, and the distance d between two adjacent sensors is half the wavelength of the source signal. Where λ is the wavelength of the source signal.

3. A near-field incoherent distribution source positioning method according to claim 1, characterized in that: Estimating the covariance of the sensor array output signal includes: obtaining the signal x(t) output by the sensor array at time t; calculating the covariance of the signal x(t) and estimating the estimator of the covariance of the output signal; estimating the covariance estimator of the near-field incoherent distribution source signal according to the covariance estimator of the output signal.

4. A near-field incoherent distribution source positioning method according to claim 3, characterized in that: The covariance estimator of the near-field incoherently distributed source signal is: in, is the covariance estimator of the near-field incoherently distributed source signal, is the estimator of the array output signal covariance R, is the noise variance, I is the unit matrix, L is the maximum time, x(t) is the output signal at time t, (·) H represents the conjugate transpose of the matrix, and B is the number of sampling snapshots.

5. A near-field incoherent distribution source positioning method according to claim 1, characterized in that: The covariance model of the near-field incoherently distributed source signal is: R s =∫ Θ ∫ Υ A θ，l p θ,l dldθ Among them, A θ，l is the array direction vector a θ，l The matrix, p θ，l is the spatial spectrum, Θ is the angle range, Y is the distance range, θ is the angle of the signal, and l is the distance of the signal.

6. A near-field incoherent distribution source positioning method according to claim 1, characterized in that: Discretizing the angle and distance distribution of the near-field incoherent distribution source includes: discretizing the angle range θ and the distance range Y to obtain uniform discrete points {θ1, θ2, ..., θ m } and {l1,l2,...,l n }; The array output signal expression is optimized according to uniform discrete points, and the near-field incoherent distribution source signal covariance model containing the spatial spectrum matrix is ​​obtained.

7. A near-field incoherent distribution source positioning method according to claim 1, characterized in that: The low-rank minimization problem for spatial spectrum estimation is: Among them, rank(·) is the matrix rank function, is the estimator, vec(·) represents the vectorization operator, and r is the covariance of the source signal received by the array.

8. A near-field incoherent distribution source positioning method according to claim 1, characterized in that: Solving the low-rank minimization problem includes: using an iterative weighted nuclear norm algorithm to convert the low-rank minimization problem into an iterative weighted nuclear norm minimization problem; using a weighted singular value threshold operator to solve the iterative weighted nuclear norm minimization problem, and when the iterative stopping condition is met during the calculation process, the low-rank matrix P is obtained to have a global optimal solution, which is a spatial spectrum estimator.

9. A near-field incoherent distribution source positioning method according to claim 8, characterized in that: The iterative weighted nuclear norm minimization problem is: Among them, λ is the regularization parameter, s represents the sth iteration, is the intermediate parameter, σ i (P) is the i-th singular value of P, P is a low-rank matrix, μ is the convergence parameter; P s is the value of P in the sth iteration, f(P s ) reflects the noise variance level, f(P s ) s The derivative of ||·|| F represents the matrix F-norm, and ||·||2 represents the vector 2-norm.

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