A DOA estimation method based on sparse covariance reconstruction and adaptive grid correction

Abstract

The present invention provides a DOA estimation method with sparse covariance reconstruction and adaptive grid correction, which belongs to the field of marine observation technology. The present invention shifts from snapshot-level signal reconstruction to covariance-level sparse modeling, introduces an alternating optimization strategy for energy estimation, integrates the Sherman-Morrison matrix lemma to accurately update the inverse covariance matrix, and introduces an adaptive grid continuous correction mechanism. The present invention constructs a phased optimization framework that integrates sparsity and geometric interpretability, can significantly improve the accuracy of DOA estimation, break through the off-grid error limit, improve robustness under low signal-to-noise ratio and signal correlation, significantly reduce the algorithm computational complexity, improve real-time processing capabilities, and is suitable for complex underwater propagation environments.

Description

Technical Field

[0001] The present invention belongs to the technical field of ocean signal processing, and specifically relates to a Direction-of-Arrival (DOA) estimation method, in particular to a high-precision DOA estimation method combining sparse covariance matrix reconstruction with an adaptive grid correction strategy. Background Art

[0002] Direction-of-arrival (DOA) estimation, a core problem in array signal processing, is widely used in fields such as radar, sonar, wireless communications, and seismic detection. Traditional methods, such as subspace estimation algorithms based on eigendecomposition, perform well under conditions of high signal-to-noise ratios and large snapshots. However, in real-world scenarios, signals often face challenges such as low signal-to-noise ratios, strong correlations between signals, and insufficient snapshots. This makes it difficult to accurately extract subspace structure, thus affecting positioning accuracy.

[0003] In recent years, sparse reconstruction-based DOA estimation methods have made significant progress in improving angular resolution and reducing snapshot requirements. These methods typically construct an overcomplete dictionary on a discrete angular grid, transforming the DOA estimation problem into a sparse signal reconstruction problem. This allows for high-resolution target direction estimation with limited snapshot data. However, these methods still face a number of key limitations in practical applications. First, most methods rely on a fixed angular grid, and the arrival direction of the actual signal often lies between the preset grid points, resulting in significant off-grid errors in the estimation results, especially in scenarios with limited resolution or adjacent angles (such as norm-based regularization methods, sparse iterative covariance estimation (SPICE), etc.). Second, many algorithms require a preset number of signal sources during sparse reconstruction. Typical methods such as the Multiple Signal Classification (MUSIC) algorithm rely significantly on the number of sources. When the actual number of sources is unknown or changes, the estimation stability and accuracy will be significantly reduced, and even false detection or missed detection of targets may occur. In addition, for highly correlated signal sources, the estimation performance of such methods is often not ideal. Subspace methods or covariance fitting methods (such as MUSIC and SPICE) are prone to subspace leakage or covariance deviation in highly correlated signal environments, resulting in significant accuracy degradation. Finally, some current methods that pursue high precision, such as the Maximum Likelihood method and the Covariance Matrix Reconstruction algorithm (Covariance The Matrix Reconstruction Approach (CMRA) or the alternating projections covariance estimation method (AP-Covariance) usually involves high-dimensional nonlinear optimization problems or solving matrix rank constraints, resulting in high overall computational complexity. This makes it difficult to meet the real-time operation requirements of large snapshots, large number of array elements, or embedded platforms.

[0004] Therefore, it is urgent to propose a new DOA estimation method that has the ability to adaptively correct off-grid errors without relying on the prior condition of the number of sources, can adapt to highly correlated signal environments, and has controllable computational complexity, so as to better adapt to the actual application needs in dynamic and complex environments and improve the robustness and practicality of the system. Summary of the Invention

[0005] The purpose of the present invention is to propose a DOA direction estimation method combining sparse covariance reconstruction and adaptive grid correction to overcome the performance degradation problem of existing methods under low signal-to-noise ratio, off-grid error and unknown source number conditions.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A DOA estimation method based on sparse covariance reconstruction and adaptive grid correction includes the following steps:

[0008] S1: Receive array signals and construct covariance matrix: Use a uniform linear array composed of M array elements to receive L snapshots of far-field narrowband signals and construct the received data matrix , and calculate its sample covariance matrix ;

[0009] S2: Initialization estimation of signal power and noise power: preset G uniformly distributed grid points in the angle space [-90°, 90°] , construct the initial overcomplete dictionary matrix based on the steering vector of each grid point , and use the least squares method to estimate the signal power matrix and noise power ;

[0010] S3: Alternating Covariance Optimization: Update the signal energy parameters at each grid point based on the negative log-likelihood function minimization criterion. , and filter out The effective grid set ;

[0011] S4: Adaptive grid correction: Based on the gradient descent method and combined with the Armijo criterion, the angle parameters corresponding to the effective grid are optimized and adjusted, and then the dictionary matrix composed of the steering vectors is updated. ;

[0012] S5: Output the estimated value of the direction of arrival: the angle parameter converged by iteration As the result of the direction of arrival estimation, the final azimuth set is output .

[0013] Furthermore, the S2 specifically includes the following steps:

[0014] S21: Initial angle dictionary construction and modeling;

[0015] S211: In Angle Space Internal uniform division grid points, forming a set of direction parameters , to cover the entire range of possible directions of arrival;

[0016] S212: For each angle , generate its corresponding array steering vector:

[0017] ;

[0018] in, is the array element spacing, is the signal wavelength, Represents a transpose operation;

[0019] S213: Arrange all steering vectors in columns to construct the initial dictionary matrix :

[0020] ;

[0021] S214: The received data can be modeled as:

[0022] ;

[0023] in, is the array receiving matrix, is the sparse signal matrix, is the additive white Gaussian noise matrix;

[0024] S215: The expected form of the theoretical covariance matrix is expressed as

[0025] ;

[0026] in, is the diagonal matrix of signal power, is the noise power, for The identity matrix of order, The dimension is The diagonal matrix representing the noise energy, Indicates the dimension The augmented complete dictionary matrix of Represented by the signal energy diagonal matrix and noise energy matrix The augmented energy matrix, , Express expectations, Represents the conjugate transpose operation.

[0027] S22: Based on received data and the augmented complete dictionary matrix , estimated signal amplitude matrix, signal power matrix , and noise power , including the following sub-steps:

[0028] S221: Calculate the signal amplitude matrix by the least squares method :

[0029] ;

[0030] S222: Signal and Noise Power Matrix It can be estimated as:

[0031] ;

[0032] in, It means taking diagonal elements to form a diagonal matrix;

[0033] S223: Initial signal energy matrix and noise energy :

[0034] ;

[0035] in, Indicates 1 to Elements, Indicates the The energy corresponding to the grid, Represents a sum operation.

[0036] Furthermore, the S3 includes the following steps:

[0037] S31: Assuming that the received signal is a zero-mean complex Gaussian distribution, its joint probability density function can be expressed as:

[0038] ;

[0039] in, Represents a continuous multiplication operation, represents the exponential function, represents the trace of the matrix. Taking the logarithm and omitting the constant term, we get the negative log-likelihood function expression:

[0040] ;

[0041] S32: Adopting an alternating optimization framework to decompose the global signal energy estimation problem into a grid-point-by-grid parameter update problem:

[0042] S321: Under the condition of fixing other parameters, its negative log-likelihood function is

[0043] ;

[0044] in, Indicates that it does not contain The covariance matrix of atoms, Denotes the determinant of the matrix. In order to make Get the minimum value, right Taking the derivative and setting it to zero, we get:

[0045] ;

[0046] in represents the inverse of the covariance matrix.

[0047] S322: The covariance matrix represents the sum of two parts, namely:

[0048] ;

[0049] in, Indicates removal of The covariance term of atoms, ; To simplify the solution of the inverse covariance matrix, the Sherman-Morrison formula is used to Simplify:

[0050] ;

[0051] The formula is Reversible holds true, where ;

[0052] S323: Negative log-likelihood function about The target term is substituted into the above formula and expanded into

[0053] ;

[0054] in, , ;

[0055] S324: Formula The second term in can be simplified to:

[0056] ;

[0057] in, ;

[0058] S325: and Substitute into Available The update expression is:

[0059] ;

[0060] S33: Repeat the alternating optimization process in S32 and update the signal energy matrix to Iteration formation

[0061] ;

[0062] S34: If satisfied (in represents the Frobenius norm, is the preset convergence threshold), then update the covariance matrix:

[0063] ;

[0064] S35: Passed Filter the active atom set:

[0065] ;

[0066] This set is used to guide subsequent adaptive mesh fine-tuning.

[0067] Furthermore, the S4 includes the following steps:

[0068] S41: Based on the active atom set selected in S35, the corresponding steering vector is extracted from the original dictionary to construct a sub-dictionary matrix:

[0069] ;

[0070] in, Represents the number of atoms in the active atomic set and constructs the corresponding signal energy diagonal matrix:

[0071] ;

[0072] It is used for subsequent angle fine-tuning optimization. The specific process is as follows:

[0073] S42: Construct an optimization objective function to minimize data reconstruction error:

[0074] ;

[0075] in, It can be estimated by regularized least squares method as

[0076] ;

[0077] Among them, the regularization parameter .

[0078] S43: For each active direction parameter , calculate the objective function Regarding its partial derivatives, it is used for subsequent gradient descent optimization:

[0079] ;

[0080] in, Represents the real part operation, which guides the vector function to the angle parameter The first-order derivative of is:

[0081] ;

[0082] This derivative is used to update the direction of each angle component in the gradient descent method.

[0083] S44: Use the Armijo condition for step size control to ensure that each angle update can effectively reduce the objective function value:

[0084] ;

[0085] in, is the step size control parameter, For the The adaptive step size of the iteration, , in step length Under the premise of satisfying the Armijo condition, the direction parameter is updated as follows:

[0086] ;

[0087] S45: Using the updated angle parameters Construct a new steering vector and update the dictionary matrix:

[0088] ;

[0089] And serve as the input for the next round of iteration until convergence.

[0090] Furthermore, the step S5 includes: when the angle update fails to reach the convergence condition, , then continue to iterate, where is the preset angle convergence threshold, Represents the Euclidean norm, the specific process is:

[0091] S51: In each iteration, first calculate the gradient based on the current angle parameter ;

[0092] S52: Update parameters in each direction according to the gradient descent formula , and reconstruct the dictionary matrix from the new angle ;

[0093] S53: Using the updated dictionary matrix , the signal coefficient matrix is estimated by regularized least squares method ;

[0094] S54: When the iteration meets the convergence condition, the final estimated direction of arrival set is output

[0095] .

[0096] Compared with the prior art, the advantages and beneficial effects of the present invention are:

[0097] 1. The technical advantages of the present invention are as follows:

[0098] 1. Shift from snapshot-level signal reconstruction to covariance-level sparse modeling (reducing computational complexity)

[0099] The present invention models the covariance matrix, constructs a minimization objective function between the structured covariance and the sample covariance, and uses the sparsity assumption to perform energy estimation, which greatly reduces the data dimension and algorithm complexity.

[0100] 2. Introducing an alternating optimization strategy for energy estimation (improving iterative convergence stability)

[0101] The present invention adopts an alternating optimization mechanism based on the negative log-likelihood function to update the signal energy parameters atom by atom, which can effectively control the gradual convergence of the estimation error in each round of optimization and improve the robustness to noise inconsistency and interference components.

[0102] 3. Integrate the Sherman-Morrison matrix lemma to accurately update the inverse covariance matrix (enhanced derivation efficiency)

[0103] The present invention uses the Sherman-Morrison matrix inversion lemma to quickly update the analytical expression of the inverse covariance matrix during the atomic update process, ensuring convergence stability and improving computational efficiency.

[0104] 4. Introducing an adaptive grid continuous correction mechanism (eliminating off-grid errors)

[0105] Based on the coarse screening of signal energy, the present invention introduces a gradient descent optimization strategy for the active atom set, and fine-tunes the angle parameters in a continuous domain using the reconstruction error minimization criterion, effectively overcoming the structural limitation of traditional sparse algorithms that cannot exceed the grid resolution.

[0106] Second, the beneficial effects of the present invention are as follows:

[0107] By introducing alternating sparse covariance modeling and adaptive grid correction mechanisms, this paper significantly improves the accuracy, robustness, and computational efficiency of the direction of arrival estimation method in complex underwater acoustic environments. This is mainly reflected in the following aspects:

[0108] 1. Significantly improve DOA estimation accuracy and break through off-grid error limits

[0109] Traditional sparse reconstruction methods rely on a fixed discrete angle grid, which is susceptible to "off-grid errors" and limits the estimated resolution. Based on the initial sparse energy estimate, this method uses a gradient descent algorithm to continuously fine-tune the active direction parameters, effectively overcoming the discretization limitations and achieving high-precision estimation that far exceeds the angular step resolution, improving the ability to resolve weak signals and near-angle targets.

[0110] 2. Improve robustness under low signal-to-noise ratio and signal correlation

[0111] The present invention adopts a covariance-level signal modeling method to avoid direct dependence on snapshot data, reduce the noise amplification effect, and enhance the robustness of the algorithm under conditions of inconsistent signal power and non-uniform noise level through an alternating update strategy. It is particularly suitable for complex underwater propagation environments.

[0112] 3. Significantly reduce algorithm computational complexity and improve real-time processing capabilities

[0113] Compared with the method based on snapshot-level sparse solution, the present invention performs energy reconstruction in the covariance dimension, which can effectively reduce the matrix dimension and iteration overhead. Combined with the Sherman-Morrison formula, the inverse covariance matrix can be accurately and quickly updated, achieving high-resolution estimation with a low computational burden. It has strong engineering deployment value and adaptability to embedded platforms.

[0114] 4. No need to predetermine the number of signal sources, enhancing application flexibility

[0115] The present invention automatically identifies the active direction set through a sparse energy screening mechanism, avoiding the model bias caused by dependence on the number of signal sources or misjudgment in traditional methods. It is suitable for actual underwater application scenarios such as uncertain source number, intermittent target appearance or non-uniform distribution.

[0116] 5. Build a staged optimization framework that combines sparsity and geometric interpretability

[0117] The present invention combines sparse estimation with geometric optimization, combining the high-resolution characteristics of sparse methods with the interpretability based on continuous optimization of steering vectors, which helps in subsequent array structure adaptation, adaptive adjustment and error analysis, and provides a technical basis for building a scalable underwater acoustic positioning / perception system. BRIEF DESCRIPTION OF THE DRAWINGS

[0118] Figure 1 Schematic diagram of the uniform linear array structure used in the method of the present invention.

[0119] Figure 2 Comparison of the root mean square error (RMSE) of DOA estimation of various methods under different signal-to-noise ratio conditions.

[0120] Figure 3 Comparison of the root mean square error (RMSE) of DOA estimation of various methods under different snapshot numbers.

[0121] Figure 4 Comparison of the convergence performance of the proposed algorithm under different signal-to-noise ratio conditions.

[0122] Figure 5 Comparison of the running time complexity of each algorithm under different snapshot numbers.

[0123] Figure 6 The changes of the root mean square error (RMSE) of DOA estimation under different initial grid numbers are shown in Figure 2.

[0124] Figure 7 Comparison of the root mean square error of DOA estimation of various methods under different signal correlation coefficients. DETAILED DESCRIPTION

[0125] To make the objectives, technical solutions, and advantages of the present invention more clearly understood, the present invention is further described below in detail with reference to specific embodiments and the accompanying drawings. It is apparent that the embodiments described are only a portion of the embodiments of the present invention, not all of them. All other embodiments derived by persons of ordinary skill in the art based on the embodiments disclosed herein without inventive effort are intended to fall within the scope of protection of the present invention.

[0126] In order to more clearly illustrate the "DOA estimation method with sparse covariance and grid correction" proposed in the present invention, two complete implementation examples are given below in combination with the implementation process, mathematical model and application scenarios:

[0127] Example 1

[0128] A sparse covariance and grid-corrected DOA estimation method is presented. It is suitable for DOA estimation of far-field narrowband signals received by a uniform linear array. The implementation steps are detailed in detail:

[0129] Step 1: Receive array signals and construct covariance matrix: uniform linear array receiver consisting of array elements Sub-snapshot far-field narrowband signal to build the receiving data matrix , and calculate its sample covariance matrix ; In angle space Internal uniform division grid points, forming a set of direction parameters , to cover the entire range of possible directions of arrival;

[0130] For each angle , generate its corresponding array steering vector:

[0131] (1)

[0132] Arrange all steering vectors in columns to construct the initial dictionary matrix :

[0133] (2)

[0134] Receiving data can be modeled as:

[0135] (3)

[0136] Step 2: The expected form of the theoretical covariance matrix of the array received data can be expressed as:

[0137] (4)

[0138] Based on received data and the augmented complete dictionary matrix , estimate the signal amplitude matrix, calculate the signal amplitude matrix by the least squares method :

[0139] (5)

[0140] Signal and noise power matrices It can be estimated as:

[0141] (6)

[0142] Initial signal energy matrix and noise energy :

[0143] (7)

[0144] Step 3: Assuming that the received signal is a zero-mean complex Gaussian distribution, its joint probability density function can be expressed as:

[0145] (8)

[0146] right Taking the logarithm and omitting the constant term, we get the negative log-likelihood function expression:

[0147] (9)

[0148] The alternating optimization framework is used to decompose the global signal energy estimation problem into a parameter update problem for each grid point. That is, under the condition that other parameters are fixed, its negative log-likelihood function is:

[0149] (10)

[0150] In order to make Get the minimum value, right Taking the derivative and setting it to zero, we get:

[0151] (11)

[0152] The covariance matrix represents the sum of two parts, namely:

[0153] (12)

[0154] The Sherman-Morrison formula was used to Simplify:

[0155] (13)

[0156] The negative log-likelihood function is about The target term of is substituted into the above formula and can be expanded as follows:

[0157] (14)

[0158] formula The second term in can be simplified to:

[0159] (15)

[0160] Will and Substitute into Available The update expression is:

[0161] (16)

[0162] Repeat the above alternating optimization process and update the signal energy matrix to Iteration formation

[0163] (17)

[0164] If satisfied (in represents the Frobenius norm, is the preset convergence threshold), then update the covariance matrix:

[0165] (18)

[0166] pass Filter the active atom set:

[0167] (19)

[0168] This set is used to guide subsequent adaptive mesh fine-tuning.

[0169] Step 4: Based on the active atom index selected in step 3, extract the corresponding steering vector from the original dictionary and construct the sub-dictionary matrix:

[0170] (20)

[0171] And construct the signal energy diagonal matrix accordingly:

[0172] (twenty one)

[0173] Used for subsequent angle fine-tuning optimization to construct the optimization objective function that minimizes the data reconstruction error:

[0174] (twenty two)

[0175] in, The regularization parameter The least squares estimate of

[0176] (twenty three)

[0177] For each active direction parameter , calculate the objective function Regarding its partial derivatives, it is used for subsequent gradient descent optimization:

[0178] (twenty four)

[0179] Among them, the steering vector function is the angle parameter The first-order derivative of is:

[0180] (25)

[0181] This derivative is used to update the direction of each angle component in the gradient descent method. The Armijo condition is used for step size control to ensure that each angle update can effectively reduce the objective function value:

[0182] (26)

[0183] In step length Under the premise of satisfying the Armijo condition, the direction parameter is updated as follows:

[0184] (27)

[0185] Using the updated angle parameters Construct a new steering vector and update the dictionary matrix:

[0186] (28)

[0187] And serve as the input for the next round of iteration until convergence.

[0188] Step 5: When the angle update fails to meet the convergence condition, In each iteration, the gradient is first calculated based on the current angle parameter. ; Update the parameters in each direction according to the gradient descent formula , and reconstruct the dictionary matrix from the new angle ; Using the updated dictionary matrix , the signal coefficient matrix is estimated by regularized least squares method ; When the iteration meets the convergence condition, the final estimated direction of arrival set is output:

[0189] (29)

[0190] Example 2:

[0191] In order to verify the effectiveness of the method proposed in Example 1, a set of simulation experiments was constructed to compare the current mainstream DOA estimation methods and to evaluate their performance under a variety of typical simulation conditions. The experimental data set was generated in the following way: the number of array elements was set to , the target number is , snapshot number Adjustable from 1 to 1000, the array element spacing is equal to half wavelength. The target incident angle is randomly and evenly distributed in and , the signal is an independent complex Gaussian process, the noise obeys the zero-mean white noise model, and the total number of simulations is set to 500 Monte Carlo repeated experiments.

[0192] The comparison algorithms include:

[0193] • Traditional subspace method MUSIC;

[0194] • Sparse covariance estimation method SPICE;

[0195] • Covariance reconstruction method CMRA based on nuclear norm optimization;

[0196] • The sparse covariance and adaptive grid correction estimation method proposed in this invention.

[0197] The above methods uniformly adopt the same steering vector construction and array structure, and the parameter configurations of all methods are set according to the original literature or public implementation to ensure fairness.

[0198] Figure 1 This is a schematic diagram of the uniform linear array structure used in this embodiment. The array consists of The array elements are composed of ,The signals are incident from different angles and the array is used to receive the target ,echoes.

[0199] Figure 2 The comparison of the root mean square error (RMSE) of DOA estimation of each method under different signal-to-noise ratio conditions is shown. The number of targets in the experiment is set to , the signal incident angle is and Evenly distributed within the range, the number of snapshots is , the signal-to-noise ratio is The interval within dB is set to 5dB, and the signal-to-noise ratio is set to Monte Carlo experiments, where the performance of the experiment is measured by the root mean square error (RMSE)

[0200] (30)

[0201] in, For the The true angle of incidence, For the In the first test The proposed method maintains a low RMSE at low and medium signal-to-noise ratios and has stronger noise immunity than MUSIC, SPICE, and CMRA when SNR < 5 dB.

[0202] Figure 3 It reflects the changing trend of RMSE of DOA estimation of each method under different snapshot numbers. dB. As the number of snapshots decreases, the estimation error of the traditional method increases significantly. However, the method of the present invention maintains high accuracy under the condition of a single snapshot due to the use of covariance reconstruction and grid correction.

[0203] Figure 4 The method of the present invention is shown in the snapshot number Convergence performance under different signal-to-noise ratio conditions. With a maximum number of iterations of 500 as the upper limit, the relationship between reconstruction error and iteration number at different SNRs is recorded. The results show that this method can achieve convergence accuracy within a relatively small number of iterations, resulting in high computational efficiency.

[0204] Figure 5 Comparison The running time of each algorithm under different snapshot numbers under dB conditions. Due to the introduction of closed-form solutions and efficient matrix update strategies in the alternating update structure, the present invention significantly reduces the computational burden while maintaining accuracy.

[0205] Figure 6 The changes of RMSE of DOA estimation under different initial grid numbers are presented. As the grid density increases, the performance of the traditional method is limited by the off-grid error and the improvement is limited; however, the method of the present invention significantly breaks through the initial resolution limitation through continuous domain fine-tuning, achieves higher estimation accuracy, and has a better effect on the initial grid setting. Insensitive.

[0206] Figure 7 For different signal correlation coefficients The RMSE comparison under the conditions of the present invention. It still maintains good estimation capabilities in (strongly correlated) scenarios, exhibits excellent anti-coherence, and is suitable for actual complex signal environments.

[0207] This embodiment systematically demonstrates the robustness and superior performance of the method of the present invention in difficult scenarios such as low SNR, small sample, high correlation, and close angle, providing a feasible technical basis for actual engineering deployment.

[0208] The specific embodiments described above further illustrate the purpose, technical solutions and beneficial effects disclosed in the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A DOA estimation method based on sparse covariance reconstruction and adaptive grid correction, characterized in that: The method comprises the following steps: S1: Receive array signals and construct covariance matrix: Use a uniform linear array composed of M array elements to receive L snapshots of far-field narrowband signals and construct the received data matrix , and calculate its sample covariance matrix ; S2: Initial estimation of signal power and noise power: in angle space Built-in presets Evenly distributed grid points , construct the initial overcomplete dictionary matrix based on the steering vector of each grid point , and use the least squares method to estimate the signal power matrix and noise power ; S3: Alternating Covariance Optimization: Update the signal energy parameters at each grid point based on the negative log-likelihood function minimization criterion. , and filter out The effective grid set ; S3 comprises the following steps: S31: Assuming that the received signal is a zero-mean complex Gaussian distribution, its joint probability density function is expressed as: ； in, Represents a continuous multiplication operation, represents the exponential function, represents the trace of the matrix; taking the logarithm of formula (8) and omitting the constant term, we get the negative log-likelihood function expression: ； S32: Adopting an alternating optimization framework to decompose the global signal energy estimation problem into a grid-point-by-grid parameter update problem: S33: Repeat the alternating optimization process in S32 and update the signal energy matrix to The iterations are: ； S34: If satisfied (in represents the Frobenius norm, is the preset convergence threshold), then update the covariance matrix: ； S35: Passed Filter the active atom set: ； This set is used to guide subsequent adaptive grid fine-tuning; S4: Adaptive grid correction: Based on the gradient descent method and combined with the Armijo criterion, the angle parameters corresponding to the effective grid are optimized and adjusted, and then the dictionary matrix composed of the steering vectors is updated. ; S5: Output the estimated value of the direction of arrival: the angle parameter converged by iteration As the result of the direction of arrival estimation, the final azimuth set is output .

2. The DOA estimation method according to claim 1, wherein: The S2 comprises the following steps: S21: Initial angle dictionary construction and modeling; S22: Based on received data and the augmented complete dictionary matrix , estimated signal amplitude matrix, signal power matrix , and noise power .

3. The DOA estimation method according to claim 2, wherein: The S21 specifically includes: S211: In Angle Space Internal uniform division grid points, forming a set of direction parameters ; S212: For each angle , generate its corresponding array steering vector: ； in, is the array element spacing, is the signal wavelength, Represents a transpose operation; S213: Arrange the steering vectors in columns to construct the initial dictionary matrix : ； S214: Received data is modeled as: ； in, is the array receiving matrix, is the sparse signal matrix, is the additive white Gaussian noise matrix; S215: The expected form of the theoretical covariance matrix is expressed as ； in, is the diagonal matrix of signal power, is the noise power, for The identity matrix of order, The dimension is The diagonal matrix representing the noise energy, Indicates the dimension The augmented complete dictionary matrix of Represented by the signal energy diagonal matrix and noise energy matrix The augmented energy matrix, , Express expectations, Represents the conjugate transpose operation.

4. The DOA estimation method according to claim 2, wherein: The S22 specifically includes: S221: Calculate the signal amplitude matrix by the least squares method : ； S222: Signal and Noise Power Matrix It can be estimated as: ； in, It means taking diagonal elements to form a diagonal matrix; S223: Initial signal energy matrix and noise energy : ； in, Indicates 1 to Elements, Indicates the The energy corresponding to the grid, Represents a sum operation.

5. The DOA estimation method according to claim 1, wherein: The S32 specifically includes the following steps: S321: When other parameters are fixed, the negative log-likelihood function is: ； in, Indicates that it does not contain The covariance matrix of atoms, Denotes the determinant of the matrix; in order to make Get the minimum value, right Taking the derivative and setting it to zero, we get: ； in represents the inverse matrix of the covariance matrix; S322: The covariance matrix can be written as the sum of two parts, namely: ； in, Indicates removal of The covariance term of atoms, ; Using Sherman-Morrison formula Simplify: ； The formula is Reversible holds true, where ; S323: Negative log-likelihood function about The target term is substituted into the above formula and expanded into ； in, , ; S324: Formula The second term in simplifies to: ； in, ; S325: and Substitute into have to The update expression is: 。 6. The DOA estimation method according to claim 1, wherein: The S4 comprises the following steps: S41: Based on the active atom set selected in S35, the corresponding steering vector is extracted from the original dictionary to construct a sub-dictionary matrix: ； in, Represents the number of atoms in the active atomic set and constructs the corresponding signal energy diagonal matrix: ； Used for subsequent angle fine-tuning and optimization; S42: Construct an optimization objective function to minimize data reconstruction error: ； in, It can be estimated by regularized least squares method as: ； Among them, the regularization parameter ; S43: For each active direction parameter , calculate the objective function About its partial derivatives: ； in, Represents the real part operation, which guides the vector function to the angle parameter The first-order derivative of is: ； This derivative is used to update the direction of each angle component in the gradient descent method; S44: Step size control using Armijo conditions: ； in, is the step size control parameter, For the The adaptive step size of the iteration, , in step length Under the premise of satisfying the Armijo condition, the direction parameter is updated as follows: ； S45: Using the updated angle parameters Construct a new steering vector and update the dictionary matrix: ； And serve as the input for the next round of iteration until convergence.

7. The DOA estimation method according to claim 1, wherein: The S5 includes: when the angle update does not meet the convergence condition, that is, , then continue to iterate, where is the preset angle convergence threshold, Represents the Euclidean norm, the specific process is: S51: In each iteration, first calculate the gradient based on the current angle parameter ; S52: Update parameters in each direction according to the gradient descent formula , and reconstruct the dictionary matrix from the new angle ; S53: Using the updated dictionary matrix , the signal coefficient matrix is estimated by regularized least squares method ; S54: When the iteration meets the convergence condition, the final estimated direction of arrival set is output: 。

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