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

Abstract

The invention provides a sparse covariance reconstruction and adaptive grid correction-based DOA (Direction of Arrival) estimation method, and belongs to the technical field of ocean observation. According to the method, snapshot-level signal reconstruction is changed into covariance-level sparse modeling, an alternating optimization strategy is introduced to carry out energy estimation, a Sherman-Morrison matrix lemma is fused to accurately update a covariance inverse matrix, and an adaptive grid continuous correction mechanism is introduced. According to the method, a staged optimization framework is constructed, sparsity and geometric interpretability are fused, DOA estimation precision can be remarkably improved, off-grid error limitation is broken through, robustness under low signal-to-noise ratio and signal correlation is improved, algorithm calculation complexity is remarkably reduced, real-time processing capacity is improved, and the method is suitable for an underwater complex propagation environment.

Description

Technical Field

[0001] The present invention belongs to the technical field of marine signal processing, and particularly relates to a method for estimating the direction of arrival (DOA), in particular to a high-precision direction-of-arrival estimation method combining sparse covariance matrix reconstruction and an adaptive grid correction strategy. Background Art

[0002] Direction-of-arrival estimation, as a core problem in array signal processing, is widely applied in fields such as radar, sonar, wireless communication, and seismic exploration. Traditional methods, such as subspace estimation algorithms based on eigen decomposition, perform well under conditions of high signal-to-noise ratio and large number of snapshots. However, in practical scenarios, signals often face challenges such as low signal-to-noise ratio, strong correlation between signals, or insufficient number of snapshots, resulting in difficulty in accurately extracting the subspace structure and thus affecting the positioning accuracy.

[0003] In recent years, significant progress has been made in sparse reconstruction-based direction-of-arrival (DOA) estimation methods in terms of improving angular resolution and reducing the requirement for the number of snapshots. Such methods typically transform the DOA estimation problem into a sparse signal reconstruction problem by constructing an overcomplete dictionary on a discrete angular grid, thereby achieving high-resolution estimation of the target direction under the condition of limited snapshot data. However, there are still a series of critical limitations in the practical application of these methods. First, most methods rely on a fixed angular grid, and the actual arrival direction of the signal often lies between the preset grid points, resulting in obvious 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-based estimation (SPICE), etc.). Second, many algorithms need to preset the number of signal sources during the sparse reconstruction process. Typical methods such as the multiple signal classification (MUSIC) algorithm are significantly dependent on the number of sources. When the actual number of sources is unknown or variable, the estimation stability and accuracy will decrease significantly, and there may even be cases of target misdetection or missed detection. In addition, for highly correlated signal sources, the estimation performance of these methods is often not ideal. Subspace-based methods or covariance fitting methods (such as MUSIC and SPICE) are prone to subspace leakage or covariance deviation in a highly correlated signal environment, thereby causing significant accuracy degradation. Finally, some current maximum likelihood-based methods, covariance matrix reconstruction algorithms (Covariance Matrix Reconstruction Approach, CMRA), or alternating projections covariance estimation methods (alternating projections covariance, AP-Covariance) that pursue high precision usually involve high-dimensional non-linear optimization problems or matrix rank constraint solving, resulting in a relatively high overall computational complexity and making it difficult to meet the real-time operation requirements in scenarios with a large number of snapshots, a large number of array elements, or embedded platforms.

[0004] Therefore, there is an urgent need to propose a new DOA estimation method that does not rely on prior conditions of the number of sources, has the ability to adaptively correct off-grid errors, can adapt to a highly correlated signal environment, and has a controllable computational complexity, so as to better meet the actual application requirements in a dynamic and complex environment 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 problem of performance degradation of existing methods under low signal-to-noise ratio, off-grid errors, and unknown number of sources.

[0006] To achieve the above object, the present invention adopts the following technical solutions: A DOA estimation method for sparse covariance reconstruction and adaptive grid correction, the method comprising the following steps: S1: Receive array signals and construct a covariance matrix: Use a uniform linear array composed of M array elements to receive far-field narrowband signals of L snapshots, and construct a received data matrix and calculate its sample covariance matrix ; S2: Initial estimation of signal power and noise power: Preset G uniformly distributed grid points in the angular space [-90°, 90°] Based on the steering vectors of each grid point, construct an initial over-complete dictionary matrix and use the least squares method to estimate the signal power matrix and the noise power ; S3: Alternating covariance optimization: According to the negative log-likelihood function minimization criterion, update the signal energy parameter by grid points, and screen out the effective grid set that satisfies ; ; S4: Adaptive grid correction: Optimize and adjust the angle parameters corresponding to the effective grids based on the gradient descent method and combined with the Armijo criterion, and then update the dictionary matrix composed of steering vectors ; S5: Output the estimated DOA value: Use the angle parameter after iterative convergence as the estimated DOA result, and output the final azimuth angle set .

[0007] Furthermore, the S2 specifically includes the following steps: S21: Construction and modeling of the initial angle dictionary; S211: Uniformly divide in the angular space into grid points to form a direction parameter set to cover the entire possible DOA range; S212: For each angle , generate its corresponding array steering vector: ; where is the element spacing, is the signal wavelength, represents the transpose operation; S213: Arrange all the steering vectors in columns to construct the initial dictionary matrix : ; S214: The received data can be 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 unit matrix, The dimension is The diagonal matrix representing the noise energy, The dimension is The augmented complete dictionary matrix of Represented by the signal energy diagonal matrix and the noise energy matrix The augmented energy matrix, , Express expectations, Represents the conjugate transpose operation.

[0008] 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: 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 : ; Among them, represents the elements from 1 to . represents the th grid-corresponding energy, represents the summation operation.

[0009] Furthermore, the S3 includes the following steps: S31: On the premise that the received signal is assumed to be a zero-mean complex Gaussian distribution, its joint probability density function can be expressed as: ; Among them, represents the product operation, represents the exponential function, represents the trace of the matrix. Taking the logarithm of and omitting the constant term, the negative log-likelihood function expression is obtained: ; S32: Adopt an alternating optimization framework to decompose the global signal energy estimation problem into parameter update problems for each grid point: S321: Under the condition of fixing other parameters, its negative log-likelihood function is ; Among them, represents the covariance matrix without the th atom, represents the determinant of the matrix. In order to make achieve the minimum value, take the derivative of with respect to and set the derivative value to zero, and we can get: ; Among them represents the inverse matrix of the covariance matrix.

[0010] S322: The covariance matrix represents the sum of two parts, that is: ; Among them, represents removing the covariance term of the th atom, ; To simplify the solution of the inverse of the covariance matrix, use the Sherman-Morrison formula to simplify : ; This equation holds when is reversible, where ; S323: Substitute the target term of the negative log-likelihood function with respect to into the above equation and expand it to ; where , ; S324: The second term in the formula can be simplified to: ; where ; S325: Substitute and into to obtain the updated expression of as: ; S33: Repeat the alternating optimization process in S32, update the signal energy matrix to the th iteration to form ; S34: If (where represents the Frobenius norm and is a preset convergence threshold) is satisfied, then update the covariance matrix: ; S35: Screen the active atom set through : ; This set is used to guide the subsequent adaptive grid fine-tuning.

[0011] Furthermore, the said S4 includes the following steps: S41: According to the active atom set screened in S35, extract the corresponding steering vectors from the original dictionary and construct a sub-dictionary matrix: ; where represents the number of atoms in the active atom set, and correspondingly construct a signal energy diagonal matrix: ; For subsequent angular fine-tuning and optimization, the specific process is as follows: S42: Construct an optimization objective function that minimizes the data reconstruction error: ; Wherein, Can be estimated by regularized least squares as ; Wherein, the regularization parameter .

[0012] S43: For each active direction parameter , calculate the partial derivative of the objective function with respect to it, for subsequent gradient descent optimization: ; Wherein, Represents the real part extraction operation, and the first-order derivative of the steering vector function with respect to the angle parameter is: ; This derivative is used to update the direction of each angle component in the gradient descent method.

[0013] S44: Adopt the Armijo condition for step size control to ensure that each angle update can effectively reduce the objective function value: ; Wherein, Is the step size control parameter, Is the adaptive step size of the -th iteration, , on the premise that the step size satisfies the Armijo condition, the direction parameter is updated as: ; S45: Use the updated angle parameter to construct a new steering vector and update the dictionary matrix: ; And use it as the input for the next round of iteration until convergence.

[0014] Furthermore, the said S5 includes: when the angle update does not meet the convergence condition, that is , then continue the iteration, wherein is a preset angle convergence threshold, represents the Euclidean norm, and the specific process is as follows: S51: In each iteration, first calculate the gradient based on the current angle parameter ; S52: Update each direction parameter according to the gradient descent formula , and reconstruct the dictionary matrix from the new angles ; S53: Use the updated dictionary matrix , and estimate the signal coefficient matrix through regularized least squares ; S54: When the iteration meets the convergence condition, output the finally estimated set of directions of arrival .

[0015] Compared with the prior art, the advantages and beneficial effects of the present invention are as follows: First, the technical advantages of the present invention are as follows: 1. From snapshot-level signal reconstruction to covariance-level sparse modeling (reducing computational complexity) The present invention models the covariance matrix. By constructing a minimization objective function between the structured covariance and the sample covariance, and using the sparsity assumption for energy estimation, it greatly reduces the data dimension and the algorithm complexity.

[0016] 2. Introducing an alternating optimization strategy for energy estimation (enhancing the stability of iterative convergence) The present invention adopts an alternating optimization mechanism based on the negative log-likelihood function, and updates the signal energy parameters atom by atom, which can effectively control the estimation error to gradually converge within each round of optimization, and enhance the robustness to noise inconsistency and interference components.

[0017] 3. Incorporating the Sherman-Morrison matrix lemma to accurately update the covariance inverse matrix (enhancing the derivation efficiency) The present invention uses the matrix inversion lemma (Sherman-Morrison) during the atom update process to achieve fast analytical update of the covariance inverse matrix, ensuring convergence stability and improving the operation efficiency.

[0018] 4. Introducing an adaptive grid continuous correction mechanism (eliminating off-grid errors) Based on the rough screening of the signal energy, the present invention introduces a gradient descent optimization strategy for the active atom set, and finely tunes the angle parameters in the continuous domain with the minimum reconstruction error criterion, effectively overcoming the structural limitation that the traditional sparse algorithm cannot exceed the grid resolution.

[0019] Second, the beneficial effects of the present invention are as follows: The present invention significantly improves the accuracy, robustness, and computational efficiency of the direction-of-arrival (DOA) estimation method in complex underwater acoustic environments by introducing an alternating sparse covariance modeling and adaptive grid correction mechanism, which is mainly reflected in the following aspects: 1. Significantly improve the DOA estimation accuracy and break through the off-grid error limit Traditional sparse reconstruction methods rely on fixed discrete angle grids and are easily affected by "off-grid errors", resulting in limited estimation resolution. Based on the initial sparse energy estimation, the present invention uses the gradient descent algorithm to continuously fine-tune the active direction parameters, effectively overcoming the discretization limitation and achieving high-precision estimation far beyond the angle step resolution, thereby enhancing the resolution ability for weak signals and near-angle targets.

[0020] 2. Enhance the robustness under low signal-to-noise ratio and signal correlation The present invention adopts a covariance-level signal modeling method, avoiding direct dependence on snapshot data, reducing the noise amplification effect, and enhancing the robustness of the algorithm under conditions of inconsistent signal power and non-uniform noise levels through an alternating update strategy, which is especially suitable for complex underwater propagation environments.

[0021] 3. Significantly reduce the computational complexity of the algorithm and improve the real-time processing ability 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. Combining with the Sherman-Morrison formula to accurately and quickly update the covariance inverse matrix, high-resolution estimation with a low computational burden is achieved, having strong engineering deployment value and adaptability to embedded platforms.

[0022] 4. Do not require prior determination of the number of signal sources, enhancing application flexibility The present invention automatically discriminates the active direction set through a sparse energy screening mechanism, avoiding the model deviation caused by the dependence or misjudgment of the number of signal sources in traditional methods, and is applicable to practical underwater application scenarios such as uncertain number of sources, intermittent appearance of targets, or non-uniform distribution.

[0023] 5. Construct a phased optimization framework, integrating sparsity and geometric interpretability The present invention combines sparse estimation and geometric optimization, possessing both the high-resolution characteristics of sparse methods and the interpretability based on continuous optimization of the steering vector, which is helpful for subsequent array structure adaptation, adaptive adjustment, and error analysis, providing a technical basis for constructing an expandable underwater acoustic positioning / sensing system. Brief Description of the Drawings

[0024] Figure 1 It is a schematic diagram of the uniform linear array structure used in the method of the present invention.

[0025] Figure 2Comparison of the root mean square error (RMSE) of DOA estimation for each method under different signal-to-noise ratio conditions.

[0026] Figure 3 Comparison of the root mean square error (RMSE) of DOA estimation for each method under different numbers of snapshots.

[0027] Figure 4 Comparison of the convergence performance of the proposed algorithm under different signal-to-noise ratio conditions.

[0028] Figure 5 Comparison of the running time complexity of each algorithm under different numbers of snapshots.

[0029] Figure 6 Variation of the root mean square error (RMSE) of DOA estimation under different initial grid numbers.

[0030] Figure 7 Comparison of the root mean square error of DOA estimation for each method under different signal correlation coefficient conditions. Specific implementation manner

[0031] To make the purpose, technical solutions and advantages of the present disclosure more clear and understandable, the following further details the present disclosure in conjunction with specific embodiments and with reference to the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present disclosure, rather than all of them. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present disclosure without creative efforts fall within the scope of protection of the present disclosure.

[0032] To more clearly illustrate the "DOA estimation method based on sparse covariance and grid correction" proposed by the present invention, the following gives two complete implementation examples in combination with the implementation process, mathematical model and application scenario: Embodiment 1 A flow of a DOA estimation method based on sparse covariance and grid correction, applicable to the task of estimating the direction of arrival of far-field narrowband signals received by a uniform linear array, and details the implementation steps: Step 1: Receive the array signal and construct the covariance matrix: Use a uniform linear array composed of array elements to receive snapshots of far-field narrowband signals, construct the received data matrix , and calculate its sample covariance matrix ; Uniformly divide grid points within the angular space to form the direction parameter set to cover the entire possible range of direction of arrival; For each angle , generate its corresponding array steering vector: (1) Arrange all steering vectors in columns to construct an initial dictionary matrix : (2) The received data can be modeled as: (3) Step 2: The expected form of the theoretical covariance matrix of the array received data can be expressed as: (4) Based on the received data and the augmented complete dictionary matrix , estimate the signal amplitude matrix, and calculate the signal amplitude matrix by the least squares method: (5) The signal and noise power matrix can be estimated as: (6) The initial signal energy matrix and the noise energy : (7) Step 3: On the premise of assuming that the received signal is a zero-mean complex Gaussian distribution, its joint probability density function can be expressed as: (8) Take the logarithm of and omit the constant term to obtain the expression of the negative log-likelihood function: (9) Adopt an alternating optimization framework to decompose the global signal energy estimation problem into parameter update problems for each grid point. That is, under the condition of fixing other parameters, its negative log-likelihood function is: (10) To make achieve the minimum value, take the derivative of with respect to and set the derivative value to zero, and we can get: (11) The covariance matrix represents the sum of two parts, that is: (12) Use the Sherman-Morrison formula to simplify : (13) Substituting the target term of the negative log-likelihood function with respect to into the above equation, it can be expanded as: (14) The second term in the formula can be simplified to: (15) Substituting and into gives the update expression of as: Repeating the above alternating optimization process, update the signal energy matrix to the th iteration to form (17) If is satisfied (where represents the Frobenius norm and is a preset convergence threshold), then update the covariance matrix: (18) Filter the active atom set through : (19) This set is used to guide the subsequent adaptive grid fine-tuning.

[0033] Step 4: According to the active atom indices screened in Step 3, extract the corresponding steering vectors from the original dictionary to construct a sub-dictionary matrix: (20) And correspondingly construct a signal energy diagonal matrix: (21) For subsequent angular fine-tuning optimization, construct an optimization objective function that minimizes the data reconstruction error: (22) where can be estimated by the least squares method with the regularization parameter : (23) For each active direction parameter , calculate the partial derivative of the objective function with respect to it for subsequent gradient descent optimization: (24) Among them, the first-order derivative of the steering vector function with respect to the angle parameter is: (25) This derivative is used to update the direction of each angle component in the gradient descent method. The Armijo condition is adopted for step size control to ensure that each angle update can effectively reduce the objective function value: (26) On the premise that the step size satisfies the Armijo condition, the direction parameter is updated as: (27) Using the updated angle parameter to construct a new steering vector and update the dictionary matrix: (28) And use it as the input for the next round of iteration until convergence.

[0034] Step 5. When the angle update does not meet the convergence condition, that is, , continue the iteration. In each iteration, first calculate the gradient based on the current angle parameter; update each direction parameter according to the gradient descent formula, and reconstruct the dictionary matrix from the new angles; use the updated dictionary matrix to estimate the signal coefficient matrix through the regularized least squares method; when the iteration meets the convergence condition, output the finally estimated set of directions of arrival: (29) Example 2: To verify the effectiveness of the method proposed in Example 1, a set of simulation experiments are constructed to compare with the current mainstream DOA estimation methods, and performance evaluations are carried out under various typical simulation conditions. The experimental dataset is generated in the following way: Set the number of array elements as , the number of targets as , the number of snapshots is adjustable from 1 to 1000, and the array element spacing is equal to half wavelength. The target incident angles are randomly and uniformly distributed in and , the signals are independent complex Gaussian processes, and the noise follows a zero-mean white noise model. The total number of simulation times is set to 500 Monte Carlo repeated trials.

[0035] The comparison algorithms include: • The traditional subspace method MUSIC; • The sparse covariance estimation method SPICE; • Covariance Reconstruction Method Based on Nuclear Norm Optimization (CMRA); • Sparse Covariance and Adaptive Grid Calibration Estimation Method proposed by the present invention.

[0036] 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 implementations to ensure fairness.

[0037] Figure 1 is a schematic diagram of the uniform linear array structure used in this embodiment. The array consists of array elements with a spacing of . Signals arrive from different angles, and the array is used to receive target echoes.

[0038] Figure 2 shows the comparison of the root mean square error (RMSE) of DOA estimation for each method under different signal-to-noise ratio conditions. In the experiment, the number of targets is set to , the signal incident angles are uniformly distributed within the range of and , the number of snapshots is , the signal-to-noise ratio is set at intervals of 5 dB within the range of dB, and Monte Carlo trials are conducted at each signal-to-noise ratio. The performance index of the trials is measured by the root mean square error (RMSE). (30) where is the th true incident angle, and is the rd estimated incident angle in the th trial. The method of the present invention still maintains a low RMSE at medium and low signal-to-noise ratios, and has stronger anti-noise ability compared with MUSIC, SPICE, and CMRA when SNR < 5 dB.

[0039] Figure 3 reflects the change trend of the RMSE of DOA estimation for each method under different numbers of snapshots. Fixing dB, as the number of snapshots decreases, the estimation error of the traditional methods increases significantly, while the method of the present invention still maintains high accuracy under the condition of single snapshot due to adopting covariance reconstruction and grid calibration.

[0040] Figure 4 shows the method of the present invention with the number of snapshots being Convergence performance under different signal-to-noise ratios. With the maximum number of iterations set at 500, the relationship between the reconstruction error and the number of iteration rounds under different SNRs was recorded. The results show that the proposed method can achieve the convergence accuracy within fewer iteration steps and has high computational efficiency.

[0041] Figure 5 The running times of each algorithm under different numbers of snapshots under dB conditions were compared. Since the proposed invention introduces a closed-form solution and an efficient matrix update strategy in the alternating update structure, the computational burden is significantly reduced while maintaining the accuracy.

[0042] Figure 6 The variation of the DOA estimation RMSE under different initial grid numbers was presented. As the grid density increases, the performance of the traditional method is limited by the off-grid error and the improvement is limited; while the method of the proposed invention significantly breaks through the initial resolution limit through continuous domain fine-tuning, achieving higher estimation accuracy and being insensitive to the initial grid setting.

[0043] Figure 7 RMSE comparison under different signal correlation coefficients conditions. The algorithm of the proposed invention still maintains good estimation ability in the (strong correlation) scenario, showing excellent anti-coherence and being applicable to the actual complex signal environment.

[0044] This embodiment systematically demonstrates the robustness and superior performance of the method of the proposed invention in difficult scenarios such as low SNR, small samples, high correlation, and near angles, providing a feasible technical basis for actual engineering deployment.

[0045] The specific embodiments described above further elaborate on the purpose, technical solutions, and beneficial effects of the disclosure of the present invention. It should be understood that the above description is only the specific embodiments of the disclosure of the present invention and is not used to limit the disclosure of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the disclosure of the present invention shall be included within the protection scope of the disclosure of the present invention.

Claims

1. A DOA estimation method based on sparse covariance reconstruction and adaptive grid correction, characterized in that The method includes the following steps: S1: Receive the array signal and construct the covariance matrix: Use a uniform linear array composed of M array elements to receive the far-field narrowband signal of L snapshots, and construct the received data matrix , and calculate its sample covariance matrix ; S2: Initial estimation of signal power and noise power: In the angular space preset uniformly distributed grid points , construct an initial overcomplete dictionary matrix based on the steering vectors of each grid point , and use the least squares method to estimate the signal power matrix and the noise power ; S3: Alternating covariance optimization: According to the negative log-likelihood function minimization criterion, update the signal energy parameter at grid points and screen out the effective grid set that satisfies , and ; ; S4: Adaptive grid correction: Based on the gradient descent method and combined with the Armijo criterion, optimize and adjust the angle parameters corresponding to the effective grid, and then update the dictionary matrix composed of steering vectors. ; S5: Output the estimated value of the direction of arrival: Use the angle parameter after iterative convergence as the estimated result of the direction of arrival, and output the final set of azimuth angles.

2. The DOA estimation method according to claim 1, characterized in that S2 includes the following steps: S21: Construction and modeling of the initial angle dictionary; S22: Based on the received data and the augmented complete dictionary matrix , estimate the signal amplitude matrix, the signal power matrix , and the noise power .

3. The DOA estimation method according to claim 2, wherein, Specifically, S21 includes: S211: Uniformly divide in the angular space into grid points to form a direction parameter set ; S212: For each angle , generate its corresponding array steering vector: ； Among them, is the element spacing, is the signal wavelength, represents the transpose operation; S213: Arrange the steering vectors column by column to construct an initial dictionary matrix : ； S214: The received data is modeled as: ； Among them, is the array reception matrix, is the sparse signal matrix, is the additive white Gaussian noise matrix; The expected form of the theoretical covariance matrix is expressed as ； Among them, is the diagonal matrix of signal power, is the noise power, is the identity matrix of order is the diagonal matrix representing the noise energy with dimension ; represents the augmented complete dictionary matrix with dimension ; represents the augmented energy matrix composed of the signal energy diagonal matrix and the noise energy matrix ; , represents the expectation, represents the conjugate transpose operation.

4. The DOA estimation method according to claim 2, wherein, Specifically, S22 includes: S221: Calculate the signal amplitude matrix by the least squares method : ； S222: Signal and noise power matrix Can be estimated as: ； Among them, means taking diagonal elements to form a diagonal matrix; S223: Initial signal energy matrix and noise energy : ； Among them, represents elements from 1 to . represents the energy corresponding to the th grid, represents a summation operation.

5. The DOA estimation method according to claim 1, wherein S3 includes the following steps: S31: On the premise that the received signal is assumed to be a zero-mean complex Gaussian distribution, its joint probability density function is expressed as: ； Among them, represents the product operation, represents the exponential function, represents the trace of a matrix; taking the logarithm of formula (8) and omitting the constant term, the negative log-likelihood function expression is obtained: ； S32: The global signal energy estimation problem is decomposed into parameter update problems for each grid point by using an alternating optimization framework: S33: Repeat the alternating optimization process in S32, update the signal energy matrix until the th iteration to form ； S34: If the following condition is satisfied (where represents the Frobenius norm, and is a preset convergence threshold), then update the covariance matrix: ； S35: By screening the active atom set: ； This set is used to guide subsequent adaptive grid fine-tuning.

6. The DOA estimation method according to claim 5, wherein Specifically, S32 includes the following steps: S321: Under the condition of fixing other parameters, its negative log-likelihood function is ； Among them, represents the covariance matrix that does not include the th atom, represents the determinant of the matrix; in order to make achieve the minimum value, is derived, and the derivative value is set to zero, resulting in: ； wherein represents the inverse matrix of the covariance matrix; The covariance matrix can be written in the form of the sum of two parts, that is: ； Among them, represents removing the covariance term of the th atom, ; the Sherman-Morrison formula is used to simplify : ； This formula holds when is reversible, where ; S323: Substitute the target term of the negative log-likelihood function with respect to into the above formula and expand it to ； Among them, , ; S324: Formula The second term in: is simplified to: ； Among them, ; S325: Substitute and into to obtain The update expression for: 。 7. The DOA estimation method according to claim 1, wherein S4 includes the following steps: S41: According to the active atom set selected in S35, the corresponding steering vectors are extracted from the original dictionary to construct a sub-dictionary matrix: ； Among them, represents the number of atoms in the active atom set and correspondingly constructs the signal energy diagonal matrix: ； For subsequent angle fine-tuning optimization; S42: Construct an optimization objective function that minimizes the data reconstruction error: ； Among them, can be estimated by the regularized least squares method as: ； Among them, the regularization parameter ; S43: For each active direction parameter , calculate the partial derivative of the objective function with respect to it: ； Among them, represents the operation of taking the real part. The first-order derivative of the steering vector function with respect to the angular parameter is: ； This derivative is used for updating the direction of each angle component in the gradient descent method; S44: The Armijo condition is used for step size control: ； Among them, is the step size control parameter, is the adaptive step size of the -th iteration. When the step size satisfies the Armijo condition, the direction parameter is updated as follows: ； S45: Utilize the updated angle parameters Construct a new steering vector and update the dictionary matrix: ； And used as the input for the next round of iteration until convergence.

8. The DOA estimation method according to claim 1, characterized in that, The S5 includes: when the angle update does not meet the convergence condition, that is then continue to iterate, where is a preset angle convergence threshold, represents the Euclidean norm, and the specific process is as follows: S51: In each iteration, first calculate the gradient based on the current angular parameter ; S52: Update the parameters in each direction according to the gradient descent formula , and reconstruct the dictionary matrix with the new angles ; S53: Estimate the signal coefficient matrix by using the updated dictionary matrix , through the regularized least squares method ; S54: When the iteration satisfies the convergence condition, output the finally estimated set of directions of arrival: 。

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