Subspace smooth sparse reconstruction passive direction of arrival estimation method under strong interference

Abstract

The invention provides a subspace smooth sparse reconstruction passive direction of arrival estimation method under strong interference. The method comprises the following steps: firstly, constructing a far-field airspace sparse signal model received by an array; and obtaining a signal subspace covariance matrix through subspace projection and enhanced space smoothing. And estimating the distribution of the signal power in the spatial domain by using a covariance fitting criterion. And a far-field grid point evolution criterion is formulated, so that the grid points are gradually split along with iteration according to the rule. And outputting the signal power hyper-parameter as a spatial spectrum estimation result, and performing peak searching on the spatial spectrum to obtain a direction-of-arrival estimation result. The method has the advantages that the subspace projection technology is introduced, and the adverse effect of strong interference signals on weak target detection is greatly weakened; by enhancing the spatial smoothing technology, the robustness of coherent signals is improved, and meanwhile, the spatial spectrum reconstruction precision is improved. A grid evolution method is utilized, so that grid points non-uniformly cover an interested airspace with emphasis, and the calculation efficiency of the method is remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the field of underwater acoustic detection, and in particular relates to a subspace smoothing and sparse reconstruction passive direction of arrival estimation method under strong interference. Background Art

[0002] Common methods for estimating direction of arrival (DOA) in strong interference environments include the minimum variance distortionless response (MVDR) method and the forward subspace projection method (FSPM). The former effectively suppresses strong interference by adaptively forming a beam null in the direction of strong interference, while the latter normalizes the power of each sound source signal through subspace projection and then further reduces the impact of strong interference through matrix filtering techniques. However, these methods typically involve matrix inversion or eigendecomposition steps, which significantly degrades DOA estimation performance when faced with strongly correlated (coherent) signals. Furthermore, the resolution of these algorithms is significantly lower than that of existing super-resolution sparse reconstruction methods.

[0003] Common sparse reconstruction passive DOA estimation methods include sparse Bayesian learning (SBL), off-grid sparse Bayesian inference (OGSBI), sparse iterative covariance estimation (SPICE), and sparse parameter method (SPA). These methods exploit the sparse spatial distribution of sound source signals and discretize the spatial domain of interest into a series of grid points. These methods estimate the signal power at each grid point, thereby obtaining DOA estimates. These methods achieve high resolution while being robust to low signal-to-noise ratios, small snapshots, and correlated signals. However, sparse reconstruction methods require reconstructing signal power to achieve DOA estimation. When a strong interfering sound source is located in close proximity to a weak target source, the strong interference will inevitably mask the weak target. The efficient SPICE (ESPICE) method, which uses the signal subspace as the input to the covariance fitting criterion, significantly improves azimuth resolution while maintaining strong interference rejection. However, because subspace projection requires an eigendecomposition step, the ESPICE method, like subspace-based methods, suffers from a significant degradation in DOA estimation performance when faced with strongly correlated or coherent signals. Furthermore, because sparse algorithms require repeated iterations or the use of convex optimization tools, they are computationally intensive and hinder engineering implementation. Summary of the Invention

[0004] In order to solve the problem of the above-mentioned DOA estimation method in a strong interference environment, the present invention provides a subspace smoothing and sparse reconstruction passive direction of arrival estimation method under strong interference.

[0005] The objective of the present invention is achieved through the following technical solutions. This method of passive direction of arrival estimation under strong interference by subspace smoothing and sparse reconstruction constructs a far-field sparse model, uses subspace projection technology and enhanced spatial smoothing (ESS) technology to achieve power normalization of interference and target signals, and then obtains high-resolution spatial spectrum estimation results through a sparse iterative covariance estimation process. At the same time, grid evolution technology is used to achieve autonomous splitting and learning of grid points near the target position, which can improve the direction finding accuracy while improving the method's computational efficiency. The method specifically includes the following steps:

[0006] Step 1: Construct the far-field spatial sparse signal covariance model R received by the array;

[0007] Step 2: By sampling the covariance matrix Eigen decomposition obtains the signal subspace matrix U S , and then the subspace projection matrix R is obtained by spatial projection technology U =U S U S H ;

[0008] Step 3: By U Perform enhanced spatial smoothing to obtain its rank-recovered covariance matrix R ESS-R ;

[0009] Step 4: R ESS-SS As input matrix Using the covariance fitting criterion The estimated value of the signal power vector is obtained by iterative convergence, where the estimated value of the signal power vector in the qth iteration is expressed as

[0010] Step 5: Perform grid evolution; in the qth iteration, Input the roulette model and get the q+1th iteration using the grid Θ (q+1) , and use this grid to rebuild R;

[0011] Step 6: Determine whether the iteration is terminated by the iteration termination threshold, otherwise return to step 4; after the iteration is terminated, the spatial spectrum result of the final output is Perform peak search to obtain target direction of arrival estimate

[0012] The beneficial effects of the present invention are:

[0013] This paper proposes a method for passive direction of arrival estimation using subspace smoothing and sparse reconstruction under strong interference. This study addresses the problem of weak target detection under strong interference. By combining subspace projection technology, enhanced spatial smoothing technology, covariance fitting criteria, and grid evolution technology, a method for passive direction of arrival estimation using subspace smoothing and sparse reconstruction under strong interference is proposed. This method provides an effective solution to the problem of passive direction estimation of weak targets in scenarios where strong interference and weak targets are adjacent. The advantages of this method over traditional sparse reconstruction passive direction of arrival estimation methods are:

[0014] (1) The subspace projection technology is introduced to normalize the power of the sound source signals, which greatly reduces the adverse effects of strong interference signals on weak target detection.

[0015] (2) By strengthening the spatial smoothing technology, the signal subspace is directly smoothed, which improves the robustness to coherent signals and the accuracy of spatial spectrum reconstruction.

[0016] (3) By using the far-field and near-field grid evolution method, the grid points are made to cover the airspace of interest non-uniformly and with emphasis, avoiding the contradiction between positioning accuracy and computational complexity and significantly improving the computational efficiency of the method. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art or ordinary technicians, other drawings can be obtained based on these drawings without paying any creative work.

[0018] Figure 1 is a schematic diagram of overlapping sub-arrays;

[0019] Figure 2 For the roulette model;

[0020] Figure 3 is the grid evolution process;

[0021] Figure 4 Far-field spatial spectra of each algorithm under signal independence conditions: (a) θ1 = 103.8°, θ2 = 138.5°; (b) θ1 = 103.8°, θ2 = 108.5°.

[0022] Figure 5 Far-field spatial spectra of each algorithm under signal coherence conditions: (a) θ1 = 103.8°, θ2 = 138.5°; (b) θ1 = 103.8°, θ2 = 108.5°.

[0023] Figure 6Figure 3. DOA estimation performance under signal independence conditions as a function of angular separation: (a) Successful resolution probability as a function of angular separation; (b) azimuth estimation root mean square error as a function of angular separation.

[0024] Figure 7 Figure 3. DOA estimation performance under signal coherence conditions as a function of angular separation: (a) Successful resolution probability as a function of angular separation; (b) RMS error of azimuth estimation as a function of angular separation. DETAILED DESCRIPTION

[0025] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without creative work are within the scope of protection of the present invention.

[0026] As shown in the figure, the present invention provides a passive DOA estimation method using subspace smoothing and sparse reconstruction under strong interference. This method addresses the problem of weak target detection under strong interference. The method involves the following steps: First, a sparse signal model of the far-field spatial domain received by the array is constructed. Then, the signal subspace covariance matrix is obtained through subspace projection and enhanced spatial smoothing. Next, the spatial distribution of signal power is estimated using a covariance fitting criterion. Subsequently, a far-field grid point evolution criterion is formulated to encourage the grid points to gradually split according to the rule over iterations. Finally, the signal power hyperparameter is output as the spatial spectrum estimation result, and the DOA estimation result is obtained by searching for peaks in the spatial spectrum.

[0027] The method specifically comprises the following steps:

[0028] Step 1: Construct a covariance model of the far-field spatial sparse signal received by the array.

[0029] Consider K independent narrowband far-field plane wave signals s k (t), k=1,…,K, from different angles θ k The incident light is incident on a uniform linear array (ULA) with M elements, and the element spacing is half a wavelength. Where λ is the signal wavelength. At this time, the signal received by the array at time t is ( represents the complex field) can be expressed as

[0030] y(t)=As(t)+n(t)

[0031] where s(t)=[s1(t),…,s K (t)] T ((·) T represents transpose), The isotropic additive Gaussian white noise received by the array has a mean of 0 and a variance of σ 2 I M and I M represents the M×M identity matrix. A = [a(θ1),…,a(θ K )] is the array manifold, and a(θ k ) is the steering vector corresponding to the k-th far-field target signal, which is defined as

[0032]

[0033] Assuming that the source signals and the noise are independent, the data covariance matrix can be expressed as

[0034]

[0035] where (·) H denotes the conjugate transpose, and represents the source signal power matrix. It should be noted that if the source signals are independent of each other, then P = diag(p), where diag(p) represents a diagonal matrix with p as the diagonal elements, and p = [p1,…,p K , where p k represents the signal power of the k-th source. When the source signals are correlated, P is no longer a diagonal matrix, and the non-diagonal elements gradually increase as the correlation between the signals increases. When the signals are completely correlated (coherent), rank(P) < K (rank(·) represents the rank of the matrix), that is, the rank deficiency phenomenon occurs. For the convenience of description in this invention, the independent signal model is still used in the subsequent formula derivation, and the coherent signals will be noted additionally when involved.

[0036] The far-field spatial range [0°~360°] is uniformly discretized into a set of grid points Θ = [Θ1,…,Θ I , where I represents the number of grid points and satisfies the condition K << I, and α = Θ i+1 -Θ i is defined as the grid spacing. At this time, the data covariance matrix under the sparse model can be expressed as

[0037]

[0038] where Φ = [a(Θ1),…,a(Θ I )] is an overcomplete dictionary set, and its columns are called basis functions. is obtained by padding p with zeros. Assuming is the grid point closest to θ k , at this time satisfies the property

[0039]

[0040] Step 2: Perform subspace projection on the data covariance matrix.

[0041] Data covariance matrix Can be decomposed into

[0042]

[0043] in Y=[y(1),…,y(T)], where T represents the number of signal snapshots. S and U N denote the signal subspace matrix and the noise subspace matrix respectively, ∑ S =diag(δ1,…,δ K ) and ∑ N =diag(δ K+1 ,…,δ M ) represent U S and U N The corresponding eigenvalue matrix, δ m is a matrix The mth eigenvalue is arranged in descending order. On this basis, Projection R on the signal subspace U It can be expressed as

[0044]

[0045] P U =[A(θ) H A(θ)] -1

[0046] Step 3: Perform enhanced spatial smoothing on the subspace projection covariance matrix.

[0047] Based on the M-element ULA of the present invention, the array is divided into X overlapping sub-arrays (see the attached Figure 1 ), each sub-array contains N array elements, where M, X and N satisfy the relationship: M=X+N-1. Under this condition, the array output y of the xth (x∈{1,…,X})th sub-array at time t x (t) can be expressed as:

[0048] y x (t) = A x s(t)+n x (t)

[0049] where n x (t) = [n(t)] x:x+N-1 ([·] x:x+N-1 The xth to x+N-1th elements of the vector are the noise received by the xth sub-matrix. xRepresents the array manifold of the sub-array, defining the matrix Then A x =A1D x-1 Based on this, the cross-covariance matrix R of the x-th sub-matrix and the z-th sub-matrix under noise-free conditions is xz for:

[0050]

[0051] E{·} represents the expectation, the backward covariance matrix of the x-th submatrix and the z-th submatrix It can be expressed as

[0052]

[0053] in(·) * represents conjugate, J is the anti-diagonal unit matrix (also known as the commutative matrix), Represents the backward operation of the matrix, as shown above. In the subspace projection matrix R U Based on the space, when the ESS method is used directly on the subspace, the output rank recovery covariance matrix is

[0054]

[0055] where Λ xz The subspace matrix corresponding to the x-th sub-matrix and the z-th sub-matrix is shown. Specifically, assuming that the array elements of the x-th sub-matrix correspond to the x-th to x+N-1-th array elements of the original M-element ULA, and the array elements of the z-th sub-matrix correspond to the z-th to z+N-1-th array elements, then Λ xz =(R U ) (x:x+N-1),(z:z+N-1) , that is, Λ xz R U A matrix consisting of elements from row x to row x+N-1 and from column z to column z+N-1.

[0056] Step 4: Use the covariance fitting criterion to iteratively converge to obtain the estimated value of the signal power vector.

[0057] In the sparse iterative covariance matrix estimation process, the overcomplete covariance model can be expressed as

[0058]

[0059] in At this point, the covariance model R can be seen as Therefore, the completion The estimation of can realize the estimation of the signal power distribution at each grid point, and then obtain the far-field spatial spectrum and DOA estimation results. The objective function of sparse iterative covariance matrix estimation is

[0060]

[0061] in is called the covariance fitting criterion, Represents R -1 The positive definite square root of As the input of the objective function, in the present invention By solving the objective function, we can obtain The update formula is as follows

[0062]

[0063] in Indicates the last iteration The estimated result, weight ω i Defined as

[0064]

[0065] Before iterative update, the periodogram method is usually used to set The initial value of the iteration is

[0066]

[0067] When no mesh evolution is performed, iterate repeatedly and The update formula can be realized In the iterative calculation, the definition (q) Represents the variable in the qth iteration, take Middle front I (q) (I (q) is the number of grid points in the qth iteration) element is the signal power vector estimate, that is, the spatial spectrum estimate Step 5: Perform grid evolution.

[0068] Before the grid evolution, a smaller grid spacing, such as α = 1°, is used to perform a few (e.g., 5) sparse iterative covariance estimation iterations to obtain a certain degree of confidence. The estimated results are used as a basis for the formal iterative calculation (the number of iterations starts at q = 1). Based on this, the grid evolution process is briefly described as follows:

[0069] 1) Split grid point selection

[0070] By estimating the signal power vector in the qth iteration Perform peak search to obtain the peak value μ of each spectrum peak (q) =[μ1 (q) ,…,μ K′ (q)], where K′ represents the number of peaks, which usually satisfies K′≥K. μ (q) The corresponding grid set can be expressed as The elements are arranged in ascending order. According to the spatial spectrum properties, the higher the peak value, the higher the probability of the target appearing at the grid point. Based on this characteristic, the weight v of each peak value corresponding to the grid point is defined as (q) =[v1 (q) ,…,v K′ (q) ]for

[0071]

[0072] where v i (q) Indicates peak value μ k (q) Then, through the roulette model (see the attached Figure 2 ) to resample the grid points. In the roulette model, first construct (q) =[v1 (q) ,…,v K′ (q) ] proportional to the sector of the wheel, then Generate K′ random numbers uniformly distributed within the range, when a random number ξ satisfies the condition When the peak value μ k (q) Corresponding grid points After repeating the random number generation steps L times (K′ random numbers are generated each time), if If the number of times selected is ≥ L, then Can be split.

[0073] 2) Grid point splitting

[0074] Assuming grid points is the grid to be split, and its corresponding splitting space is

[0075]

[0076] where r (q) Represents the splitting radius. When q=1, r (q) Can be defined as

[0077]

[0078] Then, the airspace to be split is evenly divided into J grid points, which belong to the grid set Θ of the q+1th iteration (q+1)If K″ grid points are selected as the grid points to be split in the q+1th iteration, the number of grid points in the q+1th iteration is I (q+1) =JK″.

[0079] In the qth (q≥2)th iteration, if Θ k (q) No new peak appears in the grid to be refined, and the splitting radius is halved, that is, If a new peak appears in the grid to be refined, the splitting radius r (q) The splitting radius will be recalculated according to the calculation method of q=1.

[0080] In summary, taking the qth and q+1th iterations as examples, the grid evolution process is as follows: Figure 3 In the figure, the white squares represent grid points, the black horizontal lines represent the airspace range, and the vertical dotted lines represent the directions corresponding to the grid points. Figure 3 As shown, consider K = 2 sound source signals incident from the directions of θ1 and θ2, which are represented by red vertical solid lines. (q) , the spatial spectrum estimation result is obtained through the sparse iterative covariance estimation process The spatial spectrum estimation result is shown in blue in the figure. Subsequently, the weights corresponding to each grid point are calculated through the splitting grid point selection step (represented by blue circles in the figure; the larger the circle, the higher the weight). The roulette wheel model is then used to select the grid points to be split. The grid point splitting step then uniformly discretizes the split space corresponding to the grid point to be split into multiple grid points, thus obtaining the grid set Θ for the q+1th iteration. (q+1) , and then perform spatial spectrum estimation based on and so on.

[0081] Getting new grid points Then, according to the definition of the steering vector in step 2, the dictionary set Φ is reconstructed (q+1) , and then update R by the periodogram method (q+1) ,Right now

[0082]

[0083] The R (q+1) Will be updated input.

[0084] 3) Termination of division

[0085] In order to avoid unlimited splitting of grid points, a grid spacing threshold G is set. α , when G α ≥α min When , the grid splitting process is stopped, where α min is the minimum grid spacing, and the minimum grid spacing in the qth iteration is defined as

[0086]

[0087] The mesh evolution process is carried out synchronously with the iterative convergence process (see step 4). If the mesh splitting process stops first, mesh evolution will no longer be performed in the subsequent iterative convergence process.

[0088] Step 6: After terminating the iteration, obtain the target direction of arrival estimate.

[0089] The sparse iterative covariance matrix estimation process gradually converges by repeatedly iterating the hyperparameters and then outputs The first I elements in the far-field spatial spectrum are used to obtain the DOA estimation result through the spatial spectrum peak search. In order to avoid the algorithm of the present invention from iterating infinitely, the iteration number threshold G is set. q and tolerance threshold Tolerance Defined as

[0090]

[0091] When the number of iterations q ≥ G q or tolerance When , the iteration is terminated.

[0092] Assume that the number of iterations at the termination of the iteration is z, take Middle front I (z) The elements are the estimated values of the signal power vector right Perform peak search operation and take the grid point angle corresponding to the first K maximum peaks as the DOA estimation result

[0093] The subspace smoothing and sparse reconstruction passive direction of arrival estimation method under strong interference designed by the present invention is verified by simulation, and the results are explained.

[0094] The simulation results provide a performance comparison between the present invention's subspace smoothed sparse reconstruction passive direction of arrival estimation method under strong interference (ESS-ESPICE), the subspace projection method (FSPM), the multiple signal classification method (MUSIC), the sparse Bayesian learning method (SBL), and the sparse iterative covariance estimation method (SPICE).

[0095] Simulation 1 is used to verify the improvement of spatial spectrum estimation performance and computational efficiency of the present invention in a strong interference environment. The simulation parameters are as follows: a 15-element uniform linear array (ULA) with equal element spacing is deployed underwater, and the elements are distributed on the ULA with half-wave spacing. Assume that the interference signal is incident from θ1=103.8°, the interference-to-noise ratio (INR) is 20dB, the target signal is incident from θ2, and the signal-to-noise ratio (SNR) is -10dB. The number of snapshots T=200, the far-field grid spacing α=1°, and the termination condition of the sparse reconstruction method is G ε =200. In the ESS-ESPICE algorithm of the present invention, the number of array elements of the subarray is N=10, the number of refined grid points J=20, and the grid spacing threshold G in the grid evolution is α =0.5°. In this simulation, we consider the cases where θ2=108.5° and θ2=138.5°, the interference and the target signal are independent and coherent. The spatial spectrum comparison results of the signal independence condition are in Figure 4 The comparison results under signal coherence conditions are given as follows: Figure 5 To verify the degree of reduction in computational complexity of the proposed method, this simulation uses the computational time on the same computer as the measurement standard, and the computational time of each sparse reconstruction algorithm is statistically shown in Table 1.

[0096] Table 1 Calculation time of each algorithm (unit: seconds)

[0097]

[0098] Depend on Figure 4 (a) It can be seen that under the conditions that the sound source signals are independent and the interference is far away from the target, FSPM, MUSIC, SBL, SPICE and ESS-ESPICE methods can all achieve effective DOA estimation of the target. When the interference is close to the target, such as Figure 4 As shown in (b), only the ESS-ESPICE method can effectively detect the target DOA, which shows that the ESS-ESPICE method has the ability to detect high resolution and weak targets in a strong interference environment. Figure 5 The spatial spectrum comparison results under the coherence condition of the sound source signal are given. Figure 5 (a) It can be seen that when the sound sources are far apart, SBL and the ESS-ESPICE method of the present invention can achieve accurate target DOA estimation. Among them, the spectrum peak of ESS-ESPICE is the sharpest. However, the FSPM, MUSIC, and SPICE methods are affected by the coherent signal and cannot effectively estimate the target direction. This result further verifies the decorrelation performance of ESS-type methods. Figure 5 (b) shows the spatial spectrum results in the scenario where strong interference and weak targets are close to each other. Due to the influence of resolution, only the ESS-ESPICE of the present invention can accurately estimate the DOA of the weak target. Figure 4 and Figure 5 The results show that, among all the compared methods, only the ESS-ESPICE method of the present invention can achieve effective weak target DOA estimation in both independent and coherent signal scenarios. Simulation results demonstrate that ESS-ESPICE has greater versatility and is more suitable for passive DOA estimation scenarios where the sound source signal is unknown. As shown in Table 1, the ESS-ESPICE method effectively reduces computational complexity and significantly improves computational efficiency through grid evolution technology.

[0099] Simulation 2 uses 200 Monte Carlo tests to statistically analyze the impact of the present invention on resolution and direction-finding accuracy. Considering that the interference signal is incident from θ1, the INR is 20dB, and the target signal is incident from θ2 = θ1 + △θ, the SNR is -10dB, and △θ represents the angle interval, which gradually changes from 1° to 10°. In each Monte Carlo test, θ1 is randomly generated in the range of [70° to 100°]. The rest of the conditions are the same as those in Simulation 1. This simulation also considers two scenarios: signal independence and coherence. Figure 6 The DOA estimation performance under signal independence conditions is given, including the probability of successful resolution and the root mean square error (RMSE) of the azimuth estimation, as well as the variation of the angular separation. Figure 7 The results under coherent conditions are given.

[0100] The minimum angle at which the probability of successful resolution reaches 90% is defined as the "minimum resolvable angle". The smaller the angle, the higher the resolution of the algorithm. Figure 6 (a) shows that in the signal-independent scenario, the minimum resolvable angle of ESS-ESPICE in this paper is 4°, which is significantly smaller than that of other algorithms. Figure 6 (b) It can be seen that due to the use of grid evolution technology, the ESS-ESPICE algorithm breaks through the limitation of the initial grid spacing α = 1°, and the RMSE is always smaller than other methods. Figure 7 In the coherent signal results shown in (a), the minimum resolvable angle of ESS-ESPICE is 4°. Under the condition of angle interval △θ < 4°, the resolution probability is significantly higher than that of other comparison algorithms. Figure 7 (b) It can be seen that ESS-ESPICE benefits from the grid evolution technology and has better DOA estimation accuracy than other compared methods. In summary, the improvement of resolution and direction finding accuracy of the ESS-ESPICE method in strong interference environment is verified.

[0101] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the scope of the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A method for passive direction of arrival estimation using subspace smoothing and sparse reconstruction under strong interference, characterized by: The steps are as follows: Step 1: Construct the far-field spatial sparse signal covariance model R received by the array; Step 2: By sampling the covariance matrix Eigen decomposition obtains the signal subspace matrix U S , and then the subspace projection matrix R is obtained by spatial projection technology U =U S U S H ; Step 3: By U Perform enhanced spatial smoothing to obtain its rank-recovered covariance matrix R ESS-SS ; Step 4: R ESS-SS As input matrix Using the covariance fitting criterion, the estimated value of the signal power vector is obtained through iterative convergence, where the estimated value of the signal power vector in the qth iteration is expressed as Step 5: Perform grid evolution; in the qth iteration, Input the roulette model and get the q+1th iteration using the grid Θ (q+1) , and use this grid to rebuild R; Step 6: Determine whether the iteration is terminated by the iteration termination threshold, otherwise return to step 4; After the iteration is terminated, the final output spatial spectrum result is Perform peak search to obtain target direction of arrival estimate 2. The method for passive direction of arrival estimation using subspace smoothing and sparse reconstruction under strong interference according to claim 1, characterized in that: In step 1, the far field spatial range [0°~360°] is uniformly discretized into a set of grid points Θ=[Θ1,…,Θ I ], where I represents the number of grid points, and satisfies the conditions K<<I, α=Θ i+1 -Θ i Defined as the grid spacing, the data covariance matrix under the sparse model can be expressed as where Φ=[a(Θ1),…,a(Θ I )] is an overcomplete dictionary set, and its columns are called basis functions; Obtained by filling p with zero values, assuming is the distance θ k The nearest grid point, at this time Satisfaction properties 3. The method for passive direction of arrival estimation using subspace smoothing and sparse reconstruction under strong interference according to claim 2, characterized in that: In step 2, the sampling covariance matrix Can be decomposed into in T represents the number of signal snapshots, U S and U N denote the signal subspace matrix and the noise subspace matrix respectively, Σ S =diag(δ1, ..., δ K ) and Σ N =diag(δ K+1 ,...,δ M ) represent U S and U N The corresponding eigenvalue matrix, δ m is a matrix The mth eigenvalue is arranged in descending order; on this basis, Projection R on the signal subspace U It can be expressed as 4. The method for passive direction of arrival estimation using subspace smoothing and sparse reconstruction under strong interference according to claim 3, characterized in that: In step 3, based on the M-element ULA, the array is divided into X overlapping sub-arrays, each of which contains N elements, where M, X, and N satisfy the relationship: M = X + N - 1. Under this condition, the array output y of the x-th (x∈{1,…,X}) sub-array at time t is x (t) can be expressed as: y x (t)=A x s(t)+n x (t) where n x (t) = [n(t)] x:x+N-1 is the noise received by the x-th sub-array, [·] x:x+N-1 Represents the xth to x+N-1th elements of a vector; A x Represents the array manifold of the sub-array, defining the matrix Then A x =A1D x-1 ; Based on this, the cross-covariance matrix R of the x-th sub-matrix and the z-th sub-matrix under noise-free conditions is xz for: R xz =E{y x (t)y z (t) H } =A1D x-1 E{s(t)s(t) H }(A1D z-1 ) H =A1D x-1 P(A1D z-1 ) H E{·} represents the expectation, the backward covariance matrix of the x-th submatrix and the z-th submatrix It can be expressed as in(·) * represents conjugate, J is the anti-diagonal unit matrix, Represents the backward operation of the matrix, projecting the matrix R in the subspace U Based on the space, when the ESS method is used directly on the subspace, the output rank recovery covariance matrix is: where Λ xz The table represents the subspace matrix corresponding to the x-th sub-matrix and the z-th sub-matrix. Specifically, assuming that the array elements of the x-th sub-matrix correspond to the x-th to x+N-1-th array elements of the original M-element ULA, and the array elements of the z-th sub-matrix correspond to the z-th to z+N-1-th array elements, then Λ xz =(R U ) (x:x+N-1),(z:z+N-1) , that is, Λ xz R U A matrix consisting of elements from row x to row x+N-1 and from column z to column z+N-1.

5. The method for passive direction of arrival estimation using subspace smoothing and sparse reconstruction under strong interference according to claim 4, characterized in that: In step 4, during the sparse iterative covariance matrix estimation process, the overcomplete covariance model can be expressed as in At this point, the covariance model R can be seen as Function; Complete The estimation of can realize the estimation of signal power distribution at each grid point, and then obtain the far-field spatial spectrum and DOA estimation results. The objective function of sparse iterative covariance matrix estimation is in is called the covariance fitting criterion, Represents R -1 The positive definite square root of As the input of the objective function, By solving the objective function, we can obtain The update formula is as follows in Indicates the last iteration The estimated result, weight ω i Defined as Before iterative update, use the periodogram method to set The initial value of the iteration is When no mesh evolution is performed, iterate repeatedly and The update formula can be realized The gradual convergence of; in the iterative calculation, the definition (q) Represents the variable in the qth iteration, take Middle front I (q) The elements are the estimated values of the signal power vector, i.e. the estimated values of the spatial spectrum Among them I (q) is the number of grid points in the qth iteration.

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