A method and system for off-grid DOA estimation in a polar impulse noise environment

Abstract

This invention discloses an off-grid DOA estimation method and system for polar impulse noise environments, belonging to the field of polar underwater acoustic detection. The method includes: obtaining an array received data matrix based on signals received through a uniform linear array with half-wavelength spacing; initializing the maximum number of iterations, column full-rank random matrices, and row full-rank random matrices; iteratively solving the improved mixed correlation entropy of the residual fitting error matrix as the objective function for subspace decomposition optimization based on the maximum mixed correlation entropy criterion to obtain the optimized array received data matrix; and using an iterative sparse projection algorithm to jointly estimate the sparse signal matrix and grid offset based on a new off-grid model constructed using multi-order Taylor expansion terms, thereby estimating the target's DOA. This invention overcomes the grid mismatch problem to achieve high-precision estimation of target location and exhibits good performance in both Gaussian noise and impulse noise environments.

Description

Technical Field

[0001] This invention relates to the field of polar underwater acoustic detection technology, specifically to a method and system for estimating off-grid DOA under polar impulse noise environment. Background Technology

[0002] The Arctic region is covered by ice and snow year-round. Therefore, natural phenomena such as ice fracturing and compression, driven by ice layers and wind and snow, often result in a large amount of randomly fluctuating impulse noise propagating underwater, severely impacting polar underwater exploration. Most common DOA estimation methods typically assume that background noise follows a Gaussian distribution, which makes them unsuitable for the polar environment, leading to a significant degrade in detection performance. Therefore, there is an urgent need to develop DOA estimation methods suitable for the polar impulse noise environment to provide strong support for polar underwater exploration.

[0003] While some common DOA estimation methods combined with multiple signal classification (MUSIC) algorithms can be used for DOA estimation under impulse noise, they cannot solve the grid mismatch problem, and their ability to resist impulse noise needs to be improved.

[0004] Therefore, a high-resolution DOA estimation method is needed for polar impulse noise environments. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for off-grid DOA estimation in polar impulse noise environments, which solves the grid mismatch problem commonly found in traditional DOA estimation methods, and achieves higher DOA estimation accuracy.

[0006] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0007] Firstly, a method for estimating off-grid DOA under polar impulse noise environment includes the following steps:

[0008] The array received data matrix is ​​obtained based on the target signal received by the receiving array. Initialize the maximum number of iterations T1, and set the maximum tolerance relative error ∈ m Initialize a full-rank random matrix Initialize a full-rank random matrix Initialize the number of iterations for the t-th iteration to t=1, and initialize... Where M represents the number of array elements, N represents the maximum number of snapshots, and Q represents the number of signal sources;

[0009] Based on the initialization of the array received data matrix and related parameters, and according to the maximum mixed correlation entropy criterion, the increase of the mixed correlation entropy of the residual fitting error matrix is ​​selected as the objective function for subspace decomposition optimization and iteratively solved. When t>T1 or Stop the iteration when the optimal full-rank column matrix G and full-rank row matrix Z are obtained, and output the optimal array received data matrix X. ′ v =GZ;

[0010] Based on the optimized array received data matrix, an off-grid model constructed using multi-order Taylor expansion terms is used, and an iterative sparse projection algorithm is employed to jointly estimate the sparse signal matrix and grid offset, thereby estimating the target's DOA.

[0011] Secondly, an off-grid DOA estimation system for polar impulse noise environments includes:

[0012] The data preparation module obtains the array received data matrix based on the target signal received by the receiving array. Initialize the maximum number of iterations T1, and set the maximum tolerance relative error ∈ m Initialize a full-rank random matrix Initialize a full-rank random matrix Initialize the number of iterations for the t-th iteration to t=1, and initialize... Where M represents the number of array elements, N represents the maximum number of snapshots, and Q represents the number of signal sources;

[0013] The array received data matrix optimization module, based on the initialization of the array received data matrix and related parameters, selects the increase of mixed correlation entropy of the residual fitting error matrix as the objective function for subspace decomposition optimization according to the maximum mixed correlation entropy criterion, and iteratively solves the problem. When t>T1 or Stop the iteration when the optimal full-rank column matrix G and full-rank row matrix Z are obtained, and output the optimal array received data matrix X. ′ v =GZ;

[0014] The off-grid estimation module estimates the target's DOA by using an iterative sparse projection algorithm to jointly estimate the sparse signal matrix and grid offset based on the optimized array received data matrix and an off-grid model constructed using multi-order Taylor expansion terms.

[0015] Thirdly, the present invention also provides a computer device comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, wherein when the programs are executed by the processors, they implement the steps of the off-grid DOA estimation method under polar impulse noise environment as described in the first aspect of the present invention.

[0016] Fourthly, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the off-grid DOA estimation method under polar impulse noise environment as described in the first aspect of the present invention.

[0017] Compared with the prior art, the present invention has the following beneficial effects:

[0018] (1) Improved applicability of the algorithm: Traditional DOA estimation methods assume that background noise follows a Gaussian distribution. However, in reality, background noise does not always follow a Gaussian distribution. In polar environments, due to natural factors such as ice and snow, natural phenomena such as ice breaking and compression often produce random fluctuations in impulse noise. This noise does not follow a Gaussian distribution, and traditional DOA estimation algorithms will experience a decrease in detection performance in such working environments. This invention selects the increase of the mixed correlation entropy of the residual fitting error matrix as the objective function for subspace decomposition optimization based on the maximum mixed correlation entropy criterion (MMCC) to optimize the array received data matrix. An alternating optimization strategy is used to solve this objective function to obtain the array received data matrix with impulse noise filtered out. In addition, the new off-grid model constructed based on multi-level Taylor expansion terms uses an iterative sparse projection algorithm to estimate the sparse signal matrix, thus making this invention statistically optimal in the processing of Gaussian noise. In summary, this invention is applicable and performs well in both Gaussian noise and impulse noise environments.

[0019] (2) Solved the grid mismatch problem: Traditional DOA estimation methods assume that the target falls exactly on a discrete grid. However, in reality, the target is very likely not to fall on the pre-divided discrete grid, which leads to the grid mismatch problem and a decrease in the estimation accuracy of the algorithm. In contrast, this invention proposes a new off-grid model constructed with multi-level Taylor expansion terms, and uses an iterative sparse projection algorithm to jointly estimate the sparse signal matrix and grid offset, thereby overcoming the grid mismatch problem and achieving high-precision estimation of the target's orientation. Attached Figure Description

[0020] Figure 1 This is a flowchart of the new off-grid high-resolution DOA estimation method under polar impulse noise environment of the present invention;

[0021] Figure 2 These are the azimuth spectra of various DOA estimation algorithms under impulse noise, where (a) is the global view and (b) is a magnified local view, where M = 10, N = 500, and GSNR = 0 dB.

[0022] Figure 3 These are the azimuth spectra of various DOA estimation algorithms under impulse noise, where (a) is the global view and (b) is a magnified local view, where M = 10, N = 500, and GSNR = 4dB.

[0023] Figure 4 This is a time-domain waveform of impulse noise collected in the Arctic.

[0024] Figure 5 The root mean square error (RMSE) of various algorithms under different input generalized signal-to-noise ratios in Arctic environmental noise is given, where M = 10 and N = 100. Detailed Implementation

[0025] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to specific embodiments and accompanying drawings.

[0026] Reference Figure 1 The present invention provides a high-resolution DOA estimation method for off-grid environments under polar impulse noise conditions, comprising the following steps:

[0027] Step S1: Obtain the array received data matrix based on the target signal received by the receiving array and initialize the relevant parameters.

[0028] Considering a far-field narrowband signal model, in a polar impulse noise environment, a uniform linear array with half-wavelength spacing is used to receive the target signal. The nth snapshot signal received by the array is represented as:

[0029]

[0030] in This represents the nth snapshot signal received by the array, where uppercase M indicates the number of array elements, and s q (n) represents the complex envelope of the signal, and N represents the maximum number of snapshots. This is the background noise signal, where Q is the number of signal sources, and the steering vector of the q-th signal is represented as...

[0031] Obtain the array received data matrix Initialize the maximum number of iterations T1, and set the maximum tolerance relative error ∈ m =10 -5 Initialize a full-rank random matrix Initialize a full-rank random matrix Initialize the number of iterations for the t-th iteration to t=1, and initialize...

[0032] Step S2: Based on the initialization of the array received data matrix and related parameters, according to the maximum mixed correlation entropy criterion (MMCC), the improved mixed correlation entropy of the residual fitting error matrix is ​​selected as the objective function for subspace decomposition optimization and iteratively solved to obtain the optimized array received data matrix.

[0033] Let t = t + 1, if t > T1 or Then output the optimized new array receive data matrix; otherwise, repeat the iterative operation. The detailed process is as follows:

[0034] Array receiving data matrix X v It can be decomposed into low-rank components:

[0035] X v =GZ

[0036] The mathematical relationship between the adaptive kernel bandwidth value and the residual value is as follows:

[0037] δ j =δ0tan -1 (|e mn |)

[0038] δ0 represents the initial kernel bandwidth of the Gaussian kernel function with correlation entropy, δ j To adaptively update the kernel bandwidth of the true Gaussian kernel function using the residual values, the specific Gaussian kernel function is as follows:

[0039]

[0040] Among them, e mn =X vmn -(GZ) mn X vmn Representing matrix X v The (m,n)th element, (GZ) mn This represents the (m,n)th element of matrix (GZ);

[0041] The definition of increasing the mixed correlation entropy is:

[0042]

[0043] Improving the residual fitting error matrix by using the mixed correlation entropy as the objective function for subspace decomposition optimization:

[0044]

[0045] Where, r j Let r1 represent the j-th mixing coefficient, and r1 + r2 = 1.

[0046] Hybrid correlation entropy is robust to outliers, making it particularly suitable for handling data containing impulse noise. However, the kernel bandwidth of traditional hybrid correlation entropy is fixed and cannot adaptively update with the magnitude of the residual signal, providing an opportunity for improvement. Therefore, this invention proposes an improved hybrid correlation entropy whose kernel bandwidth can adaptively update with changes in the magnitude of the residual signal.

[0047] The objective function is solved using an alternating optimization strategy:

[0048]

[0049]

[0050] For solving It can be broken down into N subproblems for solving:

[0051]

[0052] in Representing matrix X v The nth column, z n Represents the nth column of matrix Z.

[0053]

[0054] For solving It can be decomposed into M subproblems for solving:

[0055]

[0056] in, Representing matrix X v The m-th line, g [m] T This represents the m-th row of matrix G;

[0057] The two problems above have the same solution; the following section will detail how to obtain g. [m] (t+1) The solution process:

[0058] definition let right Differentiating yields the following equation:

[0059]

[0060] Where Φ represents a diagonal matrix, and its nth element on the diagonal can be represented as:

[0061]

[0062] Here express The nth element, Representative matrix The element in the nth row;

[0063] In this invention, the stochastic gradient method is used for searching. The maximum value, It can be obtained in the (t+1)th iteration:

[0064]

[0065] To make the formulas more concise, subscripts and superscripts will be omitted unless necessary, as shown below: Right now G represents [m] (t+1) The transpose of [m] is omitted.

[0066] Here This represents the result of the previous iteration, with a step size of μ. (t) This is how it's calculated:

[0067]

[0068] The optimized column full-rank matrix G and row full-rank matrix Z are obtained through iteration, and the optimized array received data matrix X′ is output. v =GZ.

[0069] Step S3: Based on the optimized array received data matrix, and the off-grid model constructed based on the multi-order Taylor expansion, the iterative sparse projection algorithm is used to jointly estimate the sparse signal matrix and grid offset.

[0070] Input the optimized array receive data matrix X′ v array manifold dictionary set The first derivative matrix of the array manifold dictionary set Second derivative matrix in It is a guide vector The array of manifold dictionaries It is composed of vectors The first derivative matrix formed It is by The second derivative matrix is ​​formed, the maximum number of iterations in the inner loop is H=5, and the maximum number of iterations in the outer loop is H. max =5, number of signal sources Q, compression factor c = 0.9, relative error of grid offset τ1 = 10 -4 Multi-order Taylor expansion terms are used to construct the off-grid model:

[0071]

[0072] Where, a(θ) q ) represents the steering vector of the target signal. The steering vector representing the grid point closest to the target signal. express about The first derivative, express about The second derivative, β q The grid offset parameter, specifically the true orientation of the signal, is: Where the grid offset parameter β q These are the parameters to be estimated.

[0073] The DOA estimation method of this invention employs a novel off-mesh model and utilizes a differentiable function to approximate the l0 norm to jointly estimate the sparse signal and mesh offset parameters. The sparse signal is recovered using an iterative sparse projection (ISP) method, which includes a sparsification step and a projection step. First, the sparse signal matrix is ​​initialized as follows: Initialize the parameter ξ Initialize sparse step size μ ξ =0.5, initialize the number of iterations i=0.

[0074] Then, the process proceeds to iteration, employing an iterative sparse projection algorithm to jointly estimate the sparse signal matrix. The specific steps of the algorithm for mesh offset β are as follows:

[0075] While i≤H max do

[0076] i = i + 1

[0077] While ξ>ξ f do

[0078] Fork1 = 1, ..., H

[0079]

[0080]

[0081] Endfor

[0082] ξ=cξ

[0083] End while

[0084]

[0085]

[0086]

[0087] Exit

[0088] Endif

[0089] End while

[0090] Output sparse signal matrix Grid offset β.

[0091] The algorithm process described above is further explained below:

[0092] First, there exists a large outer loop, which iterates 5 times, i.e., H. max =5. Within the large outer loop, there are two smaller loops. The first smaller loop (called loop 1) updates the sparse signal matrix. This includes a sparsification step and a projection step. The termination condition for loop 1 is: ξ≤ξ f Or its iteration count is greater than H = 200. In loop 1, ξ f =5×10 -4 ξ is a parameter of the differentiable function in the sparsification step, which is a function approximately in the 0-norm:

[0093]

[0094] Where ΔH ξ Representation function H ξ Differentiation operation.

[0095] In the second small loop (called loop 2), after loop 1, the sparse signal matrix... Once obtained, the location of the grid point containing the signal can be found. In loop 2, it is only necessary to update the grid offset b corresponding to the location of the grid point containing the signal. β (This vector is a grid offset vector composed of the offsets β of each grid point). Loop 2 also contains two steps: a sparsification step and a projection step. These two steps are similar to the two steps in loop 1, where the function ΔH... Q With ΔH ξ The definition is similar, for It has the following definition:

[0096]

[0097] in, Where β q d represents the grid offset of the q-th signal, and d represents the grid spacing. For example, if the grid spacing is set to 1 degree between 0 degrees and 180 degrees, then the angle of the grid points is divided into: 0 degrees, 1 degree, ..., 180 degrees.

[0098] Step S4, after obtaining the sparse signal matrix After the grid offset β, according to the formula The target's DOAs can be estimated.

[0099] The superscript H indicates transpose. Ps is the power spectrum of the signal. For example, a grid is set at 1-degree intervals within the angular range of 0 to 180 degrees, i.e., 0 degrees, 1 degree, ..., 180 degrees. However, when the target azimuth is (10.3 degrees, 20.4 degrees), there will be a grid deviation (obviously, this grid deviation is 0.3 degrees, 0.4 degrees). According to the formula... The grid angles (10 degrees and 20 degrees) closest to the target DOAs can be found based on the locations of the two points with the highest power spectra (consistent with the number of targets). Then, the grid offset β of the angle deviation between these two grid points is updated (0.3 degrees and 0.4 degrees in this example) to obtain a new grid model, i.e., 0 degrees, 1 degree, ... 10.3 degrees, ..., 20.4 degrees, ... 180 degrees.

[0100] The advantages of this invention will be further explained below in conjunction with simulation studies and experimental data processing results. Obviously, the described experimental results are only some embodiments of this invention, not all embodiments, and are used only for illustration and explanation, not to limit the application of this invention. All other embodiments obtained by those skilled in the art based on the experimental data processing results of this invention without inventive effort should fall within the scope of protection of this invention.

[0101] The simulation and experimental studies of this invention are as follows:

[0102] Simulation conditions: In the simulation experiment, the symmetric α-stable distribution (SαS) model was used to simulate the generation of impulse noise in the polar environment, and two narrowband signals were used as signal sources incident on the array.

[0103] The generalized signal-to-noise ratio is defined as:

[0104]

[0105] Where N represents the maximum number of snapshots, and q1 represents the deviation of the impulse noise, similar to the variance in Gaussian noise.

[0106] Here, simulation experiments are conducted to verify the performance of the proposed novel off-grid DOA estimation method based on maximum improved hybrid correlation entropy iterative sparse projection (MMCC-ISP), and its performance is compared with some other state-of-the-art methods, such as p-norm multiple signal classification (L). p The algorithms include: -MUSIC (Maximize Correlation Entropy Multiple Signal Classification) algorithm, Maximize Correlation Entropy Multiple Signal Classification (MCC-MUSIC) algorithm, Fractional Low-Order Phase Moment Multiple Signal Classification (PFLOM-MUSIC) algorithm, and Fractional Low-Order Correlation Multiple Signal Classification (FLOM-MUSIC) algorithm.

[0107] Figure 2The diagram shows the azimuth spectrum of each DOA estimation algorithm under impulse noise when GSNR = 0dB. It can be seen that when there is grid mismatch, other algorithms cannot overcome this problem and there is always a certain grid mismatch error. However, the algorithm proposed in this invention can solve the grid mismatch error and has higher estimation accuracy. In addition, the azimuth spectrum power of the algorithm proposed in this invention is mainly concentrated at the target azimuth, and it has the best azimuth spectrum performance.

[0108] Figure 3 The diagram shows the azimuth spectrum of each DOA estimation algorithm under impulse noise when GSNR = 4dB. It can be seen that when there is grid mismatch, other algorithms cannot overcome this problem and there is always a certain grid mismatch error. However, the algorithm proposed in this invention can solve the grid mismatch error and has higher estimation accuracy. In addition, the azimuth spectrum power of the algorithm proposed in this invention is mainly concentrated at the target azimuth, and it has the best azimuth spectrum performance.

[0109] Experimental conditions: Using collected Arctic environmental noise, the root mean square error of various algorithms under different input generalized signal-to-noise ratios was studied, where M=10 and N=100.

[0110] Figure 4 The collected Arctic noise data shows that at certain times, the noise amplitude increases sharply, exhibiting impulse noise characteristics. Therefore, the method of this invention is designed to address this actual situation.

[0111] Figure 5 The table shows the root mean square error (RMSE) of various algorithms under different input generalized signal-to-noise ratios in Arctic environmental noise, where M = 10 and N = 100. It can be seen that the algorithm proposed in this invention has the lowest RMSE compared to other algorithms, therefore the method proposed in this invention has better DOA estimation performance in polar impulse noise environments.

[0112] In summary, this invention proposes a novel off-grid high-resolution (MMCC-ISP) DOA estimation method based on polar impulse noise environment. According to the maximum mixed correlation entropy criterion (MMCC), the improved mixed correlation entropy of the residual fitting error matrix is ​​selected as the objective function for subspace decomposition optimization to optimize the array received data matrix. An alternating optimization strategy is used to solve this objective function to obtain the array received data matrix after filtering out impulse noise. After obtaining the optimized array received data matrix, a novel off-grid model based on multi-level Taylor expansion terms is constructed, and an iterative sparse projection algorithm is used to jointly estimate the sparse signal matrix and grid offset, thereby overcoming the grid mismatch problem and achieving high-precision estimation of the target's azimuth.

[0113] In another embodiment, the present invention also provides an off-grid DOA estimation system for polar impulse noise environments, comprising:

[0114] The data preparation module obtains the array received data matrix based on the target signal received by the receiving array. Initialize the maximum number of iterations T1, and set the maximum tolerance relative error ∈ m Initialize a full-rank random matrix Initialize a full-rank random matrix Initialize the number of iterations for the t-th iteration to t=1, and initialize... Where M represents the number of array elements, N represents the maximum number of snapshots, and Q represents the number of signal sources;

[0115] The array received data matrix optimization module, based on the initialization of the array received data matrix and related parameters, selects the increase of mixed correlation entropy of the residual fitting error matrix as the objective function for subspace decomposition optimization according to the maximum mixed correlation entropy criterion, and iteratively solves the problem. When t>T1 or Stop the iteration when the optimal full-rank column matrix G and full-rank row matrix Z are obtained, and output the optimal array received data matrix X. ′ v =GZ;

[0116] The off-grid estimation module estimates the target's DOA by using an iterative sparse projection algorithm to jointly estimate the sparse signal matrix and grid offset based on the optimized array received data matrix and an off-grid model constructed using multi-order Taylor expansion terms.

[0117] It should be understood that the off-grid DOA estimation system in the polar impulse noise environment of the present invention can implement all the technical solutions in the above method embodiments. The functions of each functional module can be specifically implemented according to the methods in the above method embodiments. The specific implementation process can be referred to the relevant descriptions in the above embodiments, which will not be repeated here.

[0118] The present invention also provides a computer device, comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, wherein when the programs are executed by the processors, they implement the steps of the encrypted traffic identification method based on quaternion convolutional neural networks as described above.

[0119] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the encrypted traffic identification method based on a quaternion convolutional neural network as described above.

[0120] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, apparatus, computer devices, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0121] This invention is described with reference to a flowchart of a method according to embodiments of the invention. It should be understood that each step in the flowchart and combinations thereof can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing device, generate instructions for implementing the process. Figure 1 A device for a function specified in one or more processes.

[0122] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 The function specified in one or more processes.

[0123] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 Steps of a specified function in one or more processes.

Claims

1. A method for estimating off-grid DOA under polar impulse noise environment, characterized in that, Includes the following steps: The array received data matrix is ​​obtained based on the target signal received by the receiving array. Initialize the maximum number of iterations Set the maximum tolerance relative error. Initialize a full-rank random matrix Initialize a full-rank random matrix Initialize the first The number of iterations is ,initialization Where M represents the number of array elements, Represents the maximum number of snapshots. The number of signal sources; Based on the initialization of the array received data matrix and related parameters, and according to the maximum mixed correlation entropy criterion, the increase of the mixed correlation entropy of the residual fitting error matrix is ​​selected as the objective function for subspace decomposition optimization and iteratively solved. or Stop iterating when the optimal full-rank column matrix is ​​obtained. and full-rank matrix Output the optimized array receive data matrix ; Based on the optimized array received data matrix, an off-grid model constructed using multi-order Taylor expansion terms is used, and an iterative sparse projection algorithm is employed to jointly estimate the sparse signal matrix and grid offset, thereby estimating the target's DOA.

2. The method according to claim 1, characterized in that, The target signal is received via a uniform linear array with half-wavelength spacing. The array receives the first... A snapshot signal is represented as: , ； in The number received by the array A quick snapshot signal, Represents the complex envelope of the signal. Represents the maximum number of snapshots. It is a background noise signal. It is the number of signal sources, the first The steering vector of each signal is represented as , Indicates the first The true location of the signal.

3. The method according to claim 1, characterized in that, The objective function for subspace decomposition optimization is: ； Among these, increasing the mixed correlation entropy: ； This represents the initial kernel bandwidth of the Gaussian kernel function, indicating the correlation entropy. To adaptively update the kernel bandwidth of the true Gaussian kernel function using the residual values, ; , Representative matrix No. One element, Representative matrix No. One element, Representing the A mixing coefficient, and ; The objective function is solved using an alternating optimization strategy: ； 。 4. The method according to claim 1, characterized in that, The off-grid model of multi-order Taylor expansion is: ； in, The steering vector representing the target signal. The steering vector representing the grid point closest to the target signal. express about The first derivative, express about The second derivative, Representing the grid offset parameter, the true orientation of the signal is: , where the grid offset parameter These are the parameters to be estimated.

5. The method according to claim 4, characterized in that, The use of iterative sparse projection algorithms to jointly estimate the sparse signal matrix and grid offset includes: Initialize the sparse signal matrix as follows Initialization parameters initial value ,parameter It is a differentiable function in the sparsification step of the sparse signal matrix. The parameters, the initialization step size of the sparse step. Initialize the number of iterations ; For sparse signal matrices, according to Perform sparsification processing. Representation function The differentiation operation, according to Projection continues until the set number of cycles or Less than or equal to the set threshold ; For grid offset, according to Perform sparsification processing. This represents the grid offset vector composed of the offsets β of each grid point. For the differentiable function in the sparsification step of the grid offset, Representation function The differentiation operation, according to Project until ,in This represents the relative error of the grid offset. , , d represents the grid offset of the q-th signal, and d represents the grid spacing; Output sparse signal matrix Grid offset .

6. The method according to claim 1, characterized in that, The estimated DOA of the target includes: according to the formula The power spectrum Ps of the signal is obtained. The matrix is ​​a sparse signal matrix, and the superscript H indicates transpose. The grid angle closest to the target DOAs is determined based on the location of the point with the highest power spectrum that matches the number of targets. The grid offset β of the found grid angle is updated to obtain a new grid model.

7. An off-grid DOA estimation system for polar impulse noise environments, characterized in that, include: The data preparation module obtains the array received data matrix based on the target signal received by the receiving array. Initialize the maximum number of iterations Set the maximum tolerance relative error. Initialize a full-rank random matrix Initialize a full-rank random matrix Initialize the first The number of iterations is ,initialization Where M represents the number of array elements, Represents the maximum number of snapshots. The number of signal sources; The array received data matrix optimization module, based on the initialization of the array received data matrix and related parameters, selects the increase of the mixed correlation entropy of the residual fitting error matrix as the objective function for subspace decomposition optimization according to the maximum mixed correlation entropy criterion, and iteratively solves the problem. or Stop iterating when the optimal full-rank column matrix is ​​obtained. and full-rank matrix Output the optimized array receive data matrix ; The off-grid estimation module estimates the target's DOA by using an iterative sparse projection algorithm to jointly estimate the sparse signal matrix and grid offset based on the optimized array received data matrix and an off-grid model constructed using multi-order Taylor expansion terms.

8. A computer device, characterized in that, include: One or more processors; Memory; And one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, wherein when the programs are executed by the processors, they implement the steps of the off-grid DOA estimation method under polar impulse noise environment as claimed in any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the off-grid DOA estimation method under polar impulse noise environment as described in any one of claims 1-6.

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