A broadband sparse spatial spectrum estimation method under underwater strong interference environment

Abstract

A broadband sparse spatial spectrum estimation method in underwater strong interference environment, 1) read in array underwater acoustic target radiation noise data; 2) calculate the average sample covariance matrix at a given frequency point; 3) discretize the azimuth angle space and construct a matrix filter TNNR-MF optimization problem based on the truncated nuclear norm regularization; 4) initialize the external iteration parameters and start the external iteration; 5) initialize the internal iteration variable; 6) start the internal iteration; 7) judge whether to continue the internal iteration; 8) assign the iteration result of step 7) to the first i external iteration result; 9) judge whether to continue the external iteration; 10) estimate the spatial spectrum at the frequency point; 11) return to step 2) to complete the spatial spectrum estimation corresponding to all frequency points in turn; 12) accumulate the spatial spectrum estimation results corresponding to all frequency points to obtain the final broadband spatial spectrum estimation. It guarantees the accuracy of the filtered covariance matrix, thereby ensuring the accuracy of the subsequent spatial spectrum estimation.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic target incident noise signal feature extraction and recognition technology, specifically a broadband sparse spatial spectrum estimation method under strong underwater interference environment. Background Technology

[0002] Underwater target radiated noise refers to the broadband noise radiated into the surrounding waters by surface vessels or underwater vehicles due to mechanical vibrations or propeller rotation during navigation. It can be received by hydrophone arrays at a certain distance. Therefore, underwater target radiated noise is a primary source of information for passive sonar target detection. According to Shannon's formula, the wider the bandwidth of underwater target radiated noise, the more target information it carries, and thus the stronger its anti-interference capability. Currently, direction-of-arrival (DOA) estimation based on broadband target radiated noise is widely used in sonar.

[0003] However, with the rapid development of modern vibration reduction and noise reduction technologies, the source level of radiated noise from underwater targets is constantly decreasing (even becoming "invisible"). Furthermore, in complex underwater environments, the radiated noise of weak targets can be masked by strong interference, all of which make underwater target detection difficult. Commonly used high-resolution DOA estimation algorithms, such as Multi-Signal Classification (MUSIC), Minimum Variance Distortionless Response (MVDR), and Sparse Spectral Fitting (SpSF), become ineffective. Therefore, effective suppression of strong interference is crucial for DOA estimation of weak targets.

[0004] Matrix filters are an effective method for suppressing strong interference, allowing weak target signals in the passband to pass through with minimal distortion while suppressing strong stopband interference. Traditional matrix filters (CMFs) provide a fixed suppression in the stopband. When the interference intensity far exceeds the suppression provided by the CMF, the residual interference will corrupt the covariance matrix after filtering, severely impacting the accuracy of subsequent DOA estimation. Furthermore, the use of interior-point methods to solve its second-order cone programming (SOCP) problem in CMFs leads to long computation times, which are particularly noticeable when processing wideband signals.

[0005] Application No.: 201810677070.9, Patent Title: A Spatial Spectrum Estimation Method for Electromagnetic Targets Based on Sparse Decomposition. This invention patent mainly addresses the problem of estimating the sparse spatial spectrum of broadband acoustic signals under strong underwater interference environments. It primarily comprises two parts: strong interference suppression and broadband sparse spatial spectrum estimation. Strong interference suppression is achieved through the TNNR-MF spatial matrix filter described in this patent. Then, based on the covariance matrix after matrix filtering, a modified sparse spectrum fitting algorithm is used for spatial spectrum estimation.

[0006] The main application area of ​​the comparative patent is electromagnetic target spatial spectrum estimation, but there is no strong interference suppression processing step; and its spatial spectrum estimation method is significantly different from the spatial spectrum estimation method of this patent (step (10) of this patent), as detailed in the following comparison of differences.

[0007] Other differences are as follows:

[0008] 1) The calibration matrix C(θ) in step (2) is used to calibrate the steering matrix, while the matrix filter G(f) in step (10) of this patent is used to calibrate the steering matrix. l Used for spatial filtering. The purposes are different.

[0009] 2) In steps (3) and (4), sparse transform basis is used for signal model construction, while in step (10) of this patent, sparse transform basis is not used.

[0010] 3) Step (6) constructs a quadratic programming (SOCP) problem, while step (10) of this patent constructs a semidefinite programming (SDP) problem using the covariance matrix after matrix filtering. The constructed optimization problems are fundamentally different.

[0011] This invention proposes a broadband sparse spatial spectrum estimation method under strong underwater interference environment. Based on the fast adaptive matrix filter with truncated kernel norm regularization, it can adaptively suppress strong interference while suppressing the error introduced by the matrix filter, ensuring the accuracy of the covariance matrix after filtering, thereby ensuring the accuracy of subsequent spatial spectrum estimation. Summary of the Invention

[0012] To address the DOA estimation problem for weak targets in underwater environments with strong interference, this invention proposes a broadband sparse spatial spectrum estimation method for such environments. This method constructs an adaptive matrix filter optimization problem based on truncated kernel norm regularization. This problem adaptively forms suppressed zeros in the direction of strong interference and suppresses errors introduced by the matrix filter. The constructed matrix filter optimization problem is solved using a fast two-layer APGL algorithm. After solving the APGL algorithm, the accurate covariance matrix and matrix filter operators are obtained simultaneously. Then, a modified SpSF algorithm is presented for spatial spectrum estimation.

[0013] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0014] A broadband sparse spatial spectrum estimation method under strong underwater interference environment includes the following steps:

[0015] (1) Read in the array underwater acoustic target radiated noise data, divide it into segments, and transform each segment of the signal to the frequency domain;

[0016] (2) Calculate the given frequency point fl The average sample covariance matrix at;

[0017] (3) Discretize the azimuth space [-90,90]° into Q candidate directions, use the sample covariance matrix to construct the TNNR-MF optimization problem of matrix filter based on truncated kernel norm regularization under strong underwater interference environment, and initialize its parameters;

[0018] Step (3) specifically includes the following steps:

[0019] (3.1) Discretize the azimuth space [-90, 90]° into Q candidate directions Θ = [θ1, θ2, ..., θ Q ] T ,(·) T Indicates the transpose operator;

[0020] (3.2) The average sample covariance matrix obtained in step (2) At frequency point f l The optimization problem of constructing TNNR-MF under strong underwater interference environment:

[0021]

[0022] in,(·) H The conjugate transpose operator is represented by tr(·) and ||·||. * and ||·|| F Let represent the trace, nuclear norm, and Frobenius norm of the matrix, respectively; ε, δ, and σ are tolerance parameters; and τ and β are regularization parameters. r is the truncation nuclear norm parameter. and These represent the passband and stopband regions, respectively, A(f) l ,Θ P ) and A(fl,Θ S ) are respectively Θ P and Θ S The corresponding steering matrices, Y(fl) and G(fl), represent the frequencies f and f, respectively. l The filtered covariance matrix and matrix filter operators at the specified location. and The first-order derivative operator and the selection matrix are shown below:

[0023]

[0024] (3.3) Moving the optimization problem constraints from step (3.2) to the objective function, we obtain the following optimization problem:

[0025]

[0026] (3.4) Set the regularization parameters τ, β, λ, γ and η for the TNNR-MF optimization problem, set the truncation kernel norm parameter r, and set the internal iteration tolerance ε. in and external iteration tolerance ε out ;

[0027] (4) Initialize the external iteration parameters and perform... Perform singular value decomposition and calculate to obtain The corresponding first r left and right singular vector matrices are then used to begin the outer iteration. In the i-th outer iteration, the... The conjugate transposes of the corresponding first r left and right singular vector matrices are assigned to A respectively. i B i ;

[0028] (5) Initialize the internal iteration variables;

[0029] (6) Begin internal iterations, utilizing the Accelerated Proximal Gradient Method (APGL) at a given point γ(f l At point ), an approximation of the optimization problem is constructed, and then the constructed approximation is used to update Y(f). l ) and matrix filter operator G(f l );

[0030] Step (6) specifically includes the following steps:

[0031] (6.1) Set Z(f) l :=(Y(f l ),G(f l )),make:

[0032] g(Z(f l ))=||Y(f l )|| *

[0033] as well as:

[0034]

[0035] Using g(Z(f) l )) and h i (Z(f l The optimization problem in step (3.3) is transformed into the following optimization problem:

[0036]

[0037] (6.2) Solve using the APGL algorithm at a given point γ(f) l )=(H 1 (f l ),H 2 (fl Construct a function F(Z(f) at the position )) l The approximation of )), that is:

[0038]

[0039] The above expression can be converted into the following form:

[0040]

[0041] (6.3) Update Z(f) iteratively l ), γ(f l ) and t can complete the solution of the optimization problem in step (6.1). In the k-th inner iteration, Using Q(Z(f) l ),γ(f l Update using the unique minimum value of ))

[0042]

[0043] in:

[0044]

[0045]

[0046] In the formula, H 1 (f l ) and H 2 (f l The initial values ​​of ) are set as follows: It includes the following components:

[0047]

[0048]

[0049] In the above formula:

[0050]

[0051] T1=A(f l ,Θ S A H (f l ,Θ S )

[0052] T2=A(f l ,Θ P A H (f l ,Θ P )

[0053]

[0054] (6.4) Based on the optimization problem in step (6.3), and Update using the following method:

[0055]

[0056]

[0057] In the above optimization problem, The solution is obtained using the Singular Value Thresholding (SVT) method, as shown below:

[0058]

[0059] In the formula, σ m m=1,...,M,U and V are respectively The singular value, left and right singular value vector matrices;

[0060] (7) If the rate of decrease of the optimization problem function is less than the set threshold or the number of internal iterations is greater than the set maximum value, then exit the internal iteration; otherwise, return to step (6) to continue the iteration.

[0061] (8) Assign the iteration result of step (7) to the result of the i-th external iteration;

[0062] (9) If regarding Y(f) l ) and G(f l If the Frobenius norm of the change value is less than the set threshold or the number of external iterations is greater than the set maximum value, then exit the external iteration; otherwise, return to step (4) to continue the iteration.

[0063] (10) Based on Y(f) l ) and G(f l The frequency point f is estimated using the external iteration results of the modified sparse spectrum fitting algorithm SpSF. l Spatial spectrum at the location;

[0064] Step (10) specifically includes the following steps: Based on the results obtained in step (9) at frequency f l The filtered covariance matrix Y(f) at the point l ) and matrix filter operator G(f l The semidefinite programming problem (SDP) at frequency f is obtained by solving the following problem. l Spatial spectrum at location:

[0065]

[0066] Where vec(·) is the matrix perpendicularization operator, ||·||1 and ||·||2 represent the 1-norm and 2-norm of the vector, respectively, and * and Representing the conjugate operation and the Kronecker product, respectively, μ is the regularization parameter, and the matrix... The qth column is In the formula l(f l ,θ q ) is a matrix The q-th column, q = 1,...,Q, where A(f l ,Θ) is the guiding matrix corresponding to Θ, To estimate the spatial power spectrum, The estimated Gaussian white noise power;

[0067] (11) Return to step (2) and complete the spatial spectrum estimation corresponding to all frequency points in sequence;

[0068] Step (11) specifically includes the following steps: repeat steps (2) to (10) to complete the spatial spectrum estimation corresponding to all frequency points in sequence;

[0069] (12) Sum the spatial spectrum estimation results corresponding to all frequency points to obtain the final broadband spatial spectrum estimate;

[0070] Step (12) specifically includes the following steps: sum up the spatial spectrum estimation results corresponding to all frequency points to obtain the final broadband spatial spectrum estimate:

[0071]

[0072] As a further improvement of the present invention, step (1) specifically includes the following steps:

[0073] (1.1) Read in the time-domain data of underwater acoustic target radiation noise from the M-element array and divide it into segments B;

[0074] (1.2) Set the number of Discrete Fourier Transform (DFT) points L, transform the B-segment time-domain signal to the frequency domain, and obtain the array at frequency point f. l The output of the signal at point b is x. l (b), b=1,...,B, l=1,...,L.

[0075] As a further improvement of the present invention, step (2) specifically includes the following steps: the array at frequency point f l The average sample covariance matrix output at point is:

[0076]

[0077] As a further improvement of the present invention, step (4) specifically includes the following steps:

[0078] (4.1) Initialize the matrix filter operator G0(f l ) = J M Filtered covariance matrix With the external iteration count i = 1, set the maximum external iteration count I. in and maximum number of internal iterations I out J M It is an M×M matrix of all 1s;

[0079] (4.2) For the covariance matrix Performing singular value decomposition, we can obtain In the i-th outer iteration, let A i =(u1,…,u r ) H B i =(v1,…,v r ) H Let U and V be the conjugate transposes of the first r singular vector matrices of U and V, respectively.

[0080] As a further improvement of the present invention, step (5) specifically includes the following steps: initializing the internal iteration count k = 1 and the parameter t1 = 1, setting...

[0081] As a further improvement of the present invention, step (7) specifically includes the following steps:

[0082] (7.1) Calculation

[0083] (7.2) Let k = k + 1, calculate If Δ k <ε in Or the number of internal iterations is greater than the set maximum value I. in If the condition is met, exit the internal iteration; otherwise, return to step (6) to update sequentially. and t k+1 γ k+1 (f l This allows for continued iteration.

[0084] As a further improvement of the present invention, step (8) specifically includes the following steps: assigning the iteration result of step (7) to the result of the i-th external iteration, that is...

[0085] As a further improvement of the present invention, step (9) specifically includes the following steps:

[0086] (9.1) Calculation

[0087] (9.2) Let i=i+1, if Δ i-1<ε out Or the number of external iterations is greater than the set maximum value I. out Then exit the outer iteration and output Y(f) l ) = Y i-1 (f l ) and G(f l ) = G i-1 (f l Otherwise, return to step (4.2) to continue the iteration.

[0088] Compared with existing technologies, the method disclosed in this invention has the following advantages: the matrix filter constructed based on the truncated nuclear norm can suppress strong interference while also suppressing the error introduced by the matrix filter, thereby obtaining an accurate filtered covariance matrix; the fast two-layer APGL iterative solution algorithm simultaneously outputs the accurate filtered covariance matrix and matrix filter operators, ensuring the accuracy of subsequent SpSF algorithm spatial spectrum estimation. The entire algorithm has a short computation time and high resolution, making it suitable for fast and accurate broadband spatial spectrum estimation. Attached Figure Description

[0089] Figure 1 This is a flowchart illustrating the implementation of the method of the present invention.

[0090] Figure 2 The trajectory diagrams for two strong interferences (beam energy diagrams estimated using the SpSF method).

[0091] Figure 3 This is the broadband spatial spectrum estimation result at 69s in the example.

[0092] Figure 4 The image shows the beam energy diagram corresponding to the 5-minute sea trial data in the example. Detailed Implementation

[0093] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0094] This invention estimates the broadband sparse spatial spectrum under strong underwater interference. It uses TNNR-MF to perform matrix filtering on the covariance matrix corresponding to each frequency point within the bandwidth and uses a modified SpSF method to estimate the spatial spectrum. Broadband spatial spectrum estimation can be achieved by adding the spatial spectra corresponding to all frequency points.

[0095] Example 1:

[0096] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments.

[0097] A broadband sparse spatial spectrum estimation method for underwater environments with strong interference, such as Figure 1 As shown, it includes the following steps:

[0098] Step 1 is as follows:

[0099] (1.1) Read in 20s of time-domain data of underwater acoustic target radiated noise from an M=32 element array, with element spacing d=3.2m and sampling rate f. s =4000Hz, divided into 39 segments with a 50% overlap, this data contains 6 weak targets and 2 strong interferences. The 6 weak targets are located near -20°, -14°, -5°, 0°, 3°, and 8° respectively. Strong interference 1 is towed ship noise, located near -68°, and strong interference 2 moves from near 13° to near 23°. The trajectory diagrams of the two strong interferences (beam energy diagrams estimated using the SpSF method) are as follows. Figure 2 As shown;

[0100] (1.2) Set the DFT point number L = 4000 and the frequency range to [120, 230] Hz. Transform each time-domain signal to the frequency domain to obtain the array at frequency point f. l The output of the b-th segment of the signal at ∈ [120, 230] Hz is x. l (b), b=1,...,B, l=1,...,L.

[0101] Step 2 is as follows:

[0102] Array at frequency point f l The average sample covariance matrix output at point is:

[0103]

[0104] Step 3 specifically involves:

[0105] (3.1) Discretize the azimuth space [-90, 90]° into Q = 181 candidate directions Θ = [θ1, θ2, ..., θ Q ] T , where θ q The corresponding steering vector is λ l For frequency f l For the corresponding wavelengths, the passband and stopband ranges of TNNR-MF are set to [-20,3]° and [-90,30]°∪[13,90]°, respectively;

[0106] (3.2) The average sample covariance matrix obtained in step (2) At frequency point f l Construct a TNNR-MF optimization problem;

[0107] (3.4) Set the regularization parameter τ = 3 × 10 for the matrix filter optimization problem. -6 β = 4 × 10-2 λ = 7 × 10 -6 γ = 7 × 10 -7 and η = 3 × 10 -3 Set the truncation kernel norm parameter r = 6, and set the internal iteration tolerance ε. in =2×10 -9 and external iteration tolerance ε out =3×10 -5 .

[0108] Step 4 is as follows:

[0109] (4.1) Initialize the matrix filter operator G0(f l ) = J M Filtered covariance matrix With the external iteration count i = 1, set the maximum external iteration count I. in =300 and maximum internal iteration count I out =300;

[0110] (4.2) For the covariance matrix Performing singular value decomposition, we can obtain In the i-th outer iteration, let A i =(u1,…,u r ) H B i =(v1,…,v r ) H Let U and V be the conjugate transposes of the first r singular vector matrices of U and V, respectively.

[0111] Step 5 specifically involves:

[0112] Initialize the internal iteration count k = 1 and the parameter t1 = 1, and set...

[0113] Step 6 specifically involves:

[0114] (6.1) Begin internal iteration, H 1 (f l ) and H 2 (f l The initial values ​​of ) are set as follows:

[0115] (6.4) Update sequentially t k+1 and γ k+1 (f l ).

[0116] Step 7 specifically includes:

[0117] (7.1) Calculation

[0118] (7.2) Let k = k + 1, calculate If Δ k <ε in Or the number of internal iterations is greater than the set maximum value I. in If the condition is met, exit the internal iteration; otherwise, return to step (6) to update sequentially. t k+1 and γ k+1 (f l This allows for continued iteration.

[0119] Step 8 specifically includes:

[0120] Assign the iteration result of step (7) to the result of the i-th external iteration, i.e.

[0121] Step 9 specifically includes:

[0122] (9.1) Calculation

[0123] (9.2) Let i=i+1, if Δ i-1 <ε out Or the number of external iterations is greater than the set maximum value I. out Then exit the outer iteration and output Y(f) l ) = Y i-1 (f l ) and G(f l ) = G i-1 (f l Otherwise, return to step (4.2) to continue the iteration.

[0124] Step 10 specifically involves:

[0125] Based on the result obtained in step (9) at frequency f l The filtered covariance matrix Y(f) at the point l ) and matrix filter operator G(f l The modified SpSF method for solving the SDP problem was solved using the CVX toolbox, yielding results at frequency f. l Spatial spectrum at the location

[0126] Step 11 is as follows:

[0127] Repeat steps (2) to (10) to complete the spatial spectrum estimation for all frequency points in sequence.

[0128] Step 12 specifically involves:

[0129] The spatial spectrum estimation results corresponding to all frequency points are summed to obtain the final broadband spatial spectrum estimate:

[0130]

[0131] The broadband spatial spectrum estimation results at 69s are as follows: Figure 3 As shown, the power of the strongest interference is about 40 dB stronger than that of the weakest target signal.

[0132] Step 13 specifically involves:

[0133] (12.1) Return to step (1), step 3s, continue reading 20s of data, repeat step (1) to step (12) until the spatial spectrum estimation of 5min of data is completed;

[0134] (12.2) Draw the beam energy diagram corresponding to the 5-minute sea trial data, such as... Figure 4 As shown, the broadband sparse spatial spectrum estimation method under strong underwater interference environment successfully resolved five weak targets in the directions of -20°, -14°, -5°, 0°, and 3°. The target in the 8° direction located in the transition zone (3,13)° was also successfully resolved.

[0135] The above embodiments demonstrate that the broadband spatial spectrum estimated using the above method under strong underwater interference conditions has good discriminative power for multiple weak targets, and can effectively achieve fast and accurate DOA estimation for multiple weak targets under strong underwater interference conditions.

[0136] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any modifications or equivalent changes made based on the technical essence of the present invention shall still fall within the scope of protection claimed by the present invention.

Claims

1. A wideband sparse spatial spectrum estimation method in a strong underwater interference environment, characterized in that, Includes the following steps: (1) Read in the array underwater acoustic target radiated noise data, divide it into segments, and transform each segment of the signal to the frequency domain; (2) calculating the average sample covariance matrix at a given frequency point ​ (3) The azimuth angle space is discretized into candidate directions, and a matrix filter TNNR-MF optimization problem based on the truncated nuclear norm regularization in the underwater strong interference environment is constructed using the sample covariance matrix, and the parameters thereof are initialized; Step (3) specifically includes the following steps: (3.1) Azimuth space Discretization Candidate directions , Indicates the transpose operator; (3.2) The average sample covariance matrix obtained from step (2) At frequency The optimization problem of constructing TNNR-MF under strong underwater interference environment: ； in, This represents the conjugate transpose operator. , and Let these represent the trace, nuclear norm, and Frobenius norm of the matrix, respectively. , and For tolerance parameters, and For regularization parameters, r is the truncation nuclear norm parameter. and These are the passband and stopband regions, respectively. and They are respectively and The corresponding guidance matrix, and Frequency The filtered covariance matrix and matrix filter operators at the specified location. and The first-order derivative operator and the selection matrix are shown below: ； (3.3) Moving the optimization problem constraints from step (3.2) to the objective function, we obtain the following optimization problem: ； (3.4) Setting regularization parameters for the TNNR-MF optimization problem , , , and Set the truncation kernel norm parameter r, and set the internal iteration tolerance. and external iteration tolerance ; (4) Initialize the external iteration parameters and perform... Perform singular value decomposition and calculate to obtain The corresponding first r left and right singular vector matrices are then used to begin the outer iteration. In the i-th outer iteration, the... The conjugate transposes of the corresponding first r left and right singular vector matrices are respectively assigned to , ; (5) Initialize the internal iteration variables; (6) Begin internal iterations, using the Accelerated Proximal Gradient (APGL) method at a given point. We construct an approximation of the optimization problem, and then use this approximation to update... and matrix filter operators ; Step (6) specifically includes the following steps: (6.1) Setting ,make: ； as well as: ； use and The optimization problem in step (3.3) is transformed into the following optimization problem: ； (6.2) Solve using the APGL algorithm, at a given point Construct about functions An approximation of, i.e.: ； The above expression can be converted into the following form: ； (6.3) Through iterative updates , and This completes the solution to the optimization problem in step (6.1), at the... In the next internal iteration use Update using the unique minimum value: ； in: ； ； In the formula, , and The initial values ​​are set as follows: , , It includes the following components: ； ； In the above formula: ； (6.4) Based on the optimization problem in step (6.3), and Update using the following method: ； ； In the above optimization problem, The solution is obtained using the Singular Value Thresholding (SVT) method, as shown below: ； In the formula, , and They are The singular value, left and right singular value vector matrices; (7) If the rate of decrease of the optimization problem function is less than the set threshold or the number of internal iterations is greater than the set maximum value, then exit the internal iteration; otherwise, return to step (6) to continue the iteration. (8) Assign the iteration result of step (7) to the result of the i-th external iteration; (9) If regarding and If the Frobenius norm of the change value is less than the set threshold or the number of external iterations is greater than the set maximum value, then exit the external iteration; otherwise, return to step (4) to continue the iteration. (10) Based on and The frequency points are estimated using the external iteration results and the modified sparse spectrum fitting algorithm SpSF. Spatial spectrum at the location; Step (10) specifically includes the following steps: based on the frequency obtained in step (9) The filtered covariance matrix at the point and matrix filter operators The frequency can be obtained by solving the following semidefinite programming SDP problem. Spatial spectrum at location: ； in, This is the matrix verticalization operator. and Let these represent the 1-norm and 2-norm of the vector, respectively. and These represent the conjugate operation and the Kronecker product, respectively. For regularization parameters, the matrix The qth column is In the formula For matrix The qth column, ,in for The corresponding guidance matrix, To estimate the spatial power spectrum, The estimated Gaussian white noise power; (11) Return to step (2) and complete the spatial spectrum estimation for all frequency points in sequence; Step (11) specifically includes the following steps: repeat steps (2) to (10) to complete the spatial spectrum estimation corresponding to all frequency points in sequence; (12) Sum the spatial spectrum estimation results corresponding to all frequency points to obtain the final broadband spatial spectrum estimate; Step (12) specifically includes the following steps: sum up the spatial spectrum estimation results corresponding to all frequency points to obtain the final broadband spatial spectrum estimate: 。 2. The broadband sparse spatial spectrum estimation method under strong underwater interference environment according to claim 1, characterized in that, Step (1) specifically includes the following steps: (1.1) Read in the time-domain data of underwater acoustic target radiation noise from the M-element array and divide it into segments B; (1.2) Set the number of Discrete Fourier Transform (DFT) points L, transform the B-segment time-domain signal to the frequency domain, and obtain the array at the frequency points. The output of the signal at point b is , , .

3. The broadband sparse spatial spectrum estimation method under strong underwater interference environment according to claim 2, characterized in that, Step (2) specifically includes the following steps: the array at the frequency point The average sample covariance matrix output at point is: 。 4. The broadband sparse spatial spectrum estimation method under strong underwater interference environment according to claim 1, characterized in that, Step (4) specifically includes the following steps: (4.1) Initialize matrix filter operators Filtered covariance matrix and number of external iterations Set the maximum number of external iterations. and maximum number of internal iterations ,in It is a size of A matrix of all ones; (4.2) For the covariance matrix Performing singular value decomposition, we can obtain In the i-th outer iteration, set , They are respectively and The conjugate transpose of the first r singular vector matrices.

5. The broadband sparse spatial spectrum estimation method under strong underwater interference environment according to claim 1, characterized in that, Step (5) specifically includes the following steps: Initialize the number of internal iterations. ,parameter ,set up , .

6. The broadband sparse spatial spectrum estimation method under strong underwater interference environment according to claim 1, characterized in that, Step (7) specifically includes the following steps: (7.1) Calculation ; (7.2) Let ,calculate ,like Or the number of internal iterations exceeds the set maximum value. If the condition is met, exit the internal iteration; otherwise, return to step (6) to update sequentially. , and , Thus, the iteration continues.

7. The broadband sparse spatial spectrum estimation method under strong underwater interference environment according to claim 1, characterized in that, Step (8) specifically includes the following steps: assigning the iteration result of step (7) to the result of the i-th external iteration, i.e. , .

8. The broadband sparse spatial spectrum estimation method under strong underwater interference environment according to claim 1, characterized in that, Step (9) specifically includes the following steps: (9.1) Calculation ; (9.2) Order ,like Or the number of external iterations is greater than the set maximum value. Then exit the outer iteration and output. and Otherwise, return to step (4.2) and continue iterating.

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