DOA estimation method and device based on spatial smoothing weighted sparse bayes algorithm

Abstract

This invention discloses a method and apparatus for DOA estimation based on a spatially smoothed weighted sparse Bayesian algorithm. The method includes: reconstructing and normalizing the covariance matrix of the received signal from the array and the theoretical covariance matrix, and considering off-network error to construct a sparse reconstruction DOA estimation model under off-network conditions; obtaining a weight vector based on the spatially smoothed Capon algorithm and the theoretical covariance matrix; updating the parameters of the sparse Bayesian learning in the sparse reconstruction DOA estimation model according to the weight vector to obtain the first parameter; performing adaptive grid refinement based on the first parameter and the bipartite grid interpolation method, and iteratively updating the parameters of the sparse Bayesian learning; ending the iteration when a preset convergence condition is met, and outputting the DOA estimate.

Description

Technical Field

[0001] This invention relates to the field of underwater array signal processing and direction of arrival (DOA) estimation technology, and in particular to a DOA estimation method and apparatus based on a spatially smooth weighted sparse Bayesian algorithm. Background Technology

[0002] Direction of Arrival (DOA) estimation is a core topic in underwater acoustic array signal processing and is widely used in underwater target detection, localization, and tracking. In practical engineering applications, although increasing the linear array aperture can significantly improve the spatial resolution and accuracy of direction of arrival estimation, the deployment cost and engineering maintenance difficulty of large-aperture arrays are extremely high.

[0003] Traditional DOA estimation methods mainly include traditional beamforming methods and subspace algorithms. Traditional beamforming methods are limited by the Rayleigh limit and have low resolution in multi-target scenarios. Subspace algorithms, represented by multiple signal classification and rotation-invariant subspaces, have higher resolution, but their performance is highly dependent on the prediction of the number of signal sources. Furthermore, in environments with low signal-to-noise ratios, few snapshots, or coherent signals, their estimation accuracy is significantly reduced due to noise subspace perturbations. In recent years, sparse reconstruction methods based on compressed sensing theory have provided a new paradigm for DOA estimation. By transforming orientation estimation into a sparse signal recovery problem, these methods can overcome the limitations of traditional sampling theorems. Among them, sparse Bayesian learning, with its ability to model sparse priors of signals within a probabilistic framework, exhibits better convergence accuracy and tolerance to array manifold correlations compared to Lp norm regularization methods. However, existing sparse Bayesian learning algorithms still face the following challenges when dealing with multi-target estimation in small-aperture arrays: On the one hand, while off-grid sparse Bayesian learning methods and those based on bipartite mesh refinement can improve estimation accuracy and resolution to some extent through off-grid error compensation and mesh refinement strategies, the true off-grid error information is easily overwhelmed by noise at low signal-to-noise ratios. Mesh refinement struggles to fundamentally distinguish signal components from noise disturbances, and inaccurate mesh refinement leads to decreased DOA estimation accuracy in multi-target scenarios. Furthermore, its multi-target resolution is limited by the physical array aperture. On the other hand, to improve the sparsity of signal recovery and suppress interference from non-target directions, existing research often employs multi-signal classification spatial spectra for weighting, but the limitation of the number of signal sources must be anticipated. Furthermore, while sparse Bayesian learning methods based on the covariance matrix can expand the array aperture, with a small number of snapshots, the second-order statistics of the sample covariance matrix are difficult to guarantee convergence to the theoretical value. In practical applications, especially in complex marine acoustic environments, noise distribution often deviates from the ideal Gaussian assumption. This modeling bias caused by noise distribution mismatch and a limited number of snapshots leads to a mismatch in the sparse reconstruction DOA estimation model built based on asymptotic second-order statistical properties, reducing the algorithm's reconstruction accuracy and robustness. In summary, the existing technology mainly suffers from the following drawbacks: (a) The traditional strategies of off-grid error compensation and mesh refinement are susceptible to noise interference in estimation performance, and the DOA estimation performance is low under low signal-to-noise ratio.

[0004] (ii) Existing weighted sparse Bayesian algorithms rely heavily on the number of known sources, making them difficult to adapt to non-cooperative underwater exploration scenarios where the number of targets is unknown.

[0005] (iii) Sparse Bayesian learning methods based on covariance matrix are susceptible to model mismatch. Under the background of limited snapshot number and non-ideal ocean noise, there is a lack of effective mechanism for sparse reconstruction DOA estimation model correction to suppress the performance drop caused by model mismatch, resulting in insufficient robustness.

[0006] Therefore, a new technical solution is urgently needed to solve the technical problem of how to achieve high-precision resolution DOA estimation for multiple targets under the condition of limited array aperture. Summary of the Invention

[0007] This invention provides a DOA estimation method and apparatus based on a spatially smooth weighted sparse Bayesian algorithm, which solves the technical problem of how to achieve high-precision DOA estimation of multiple targets under the condition of finite array aperture.

[0008] To achieve the above objectives, this invention provides a DOA estimation method based on a spatially smooth weighted sparse Bayesian algorithm, comprising: Based on the sample covariance matrix and theoretical covariance matrix of the array received signal, covariance reconstruction and normalization are performed, and off-network error is considered to construct a sparse reconstruction DOA estimation model under off-network conditions. The weight vector is obtained based on the spatial smoothing Capon algorithm and the theoretical covariance matrix; the parameters of the sparse Bayesian learning in the sparse reconstruction DOA estimation model are updated according to the weight vector to obtain the first parameter; Adaptive mesh refinement is performed based on the first parameter and the bipartite mesh interpolation method, and the parameters learned by sparse Bayesian learning are iteratively updated. The iteration ends when the preset convergence condition is met, and the DOA estimate is output.

[0009] Preferably, the covariance reconstruction and normalization are performed based on the sample covariance matrix and theoretical covariance matrix of the array received signal, and the off-network error is considered to construct a sparse reconstruction DOA estimation model under off-network conditions, including: For by M The array receiving signal model for a linear array composed of 10 array elements is used to obtain the theoretical covariance matrix under Gaussian white noise background. For the theoretical covariance matrix After vectorization, we obtain the first vector r: ; in, T This is a transpose operation; This is the vectorized dictionary matrix; For signal power vector, The variance of the noise; , i =1,.., M For one A column vector of dimension, where the first dimension is... i The row position is 1, and other positions are 0; vec(·) indicates vectorization; For the sample covariance matrix Vectorization is performed to obtain a second vector used to estimate the first vector r. : ; in, To estimate the error; Second vector Multiply both sides of the equation by the block diagonalized matrix The third vector is obtained. : ; By normalizing the matrix For the third vector After normalization, the fourth vector is obtained. : ; Let the normalized dictionary matrix The normalized error vector is the noise term. ,based on Discretize the spatial angle to obtain N A set of grid points with equal angular intervals , where the angle interval At the same time, ,in, Based on The dictionary matrix after angle discretization. Based on The vector after angle discretization; according to And take off-grid error into account The sparse reconstruction DOA estimation model under off-network conditions is obtained as follows: ; in, This is the guiding vector matrix after linear approximation; This is a vector diagonalization operation; for The partial derivative matrix; express It follows a mean of 0 and a variance of . The complex Gaussian distribution; It is the identity matrix; These are the variables used to approximate and correct model mismatch; when hour, This is a sparse reconstruction DOA estimation model for the ideal case.

[0010] Preferably, when When it is a random variable, the random variable The value of follows a Gamma distribution: ,c and d It is a constant, at this time For sparse reconstruction DOA estimation models used in real-world scenarios; random variable The update methods include: ; in, It is the Frobenius norm; E (·) indicates taking the expected value.

[0011] Preferably, the weight vector obtained based on the spatial smoothing Capon algorithm and the theoretical covariance matrix includes: For the second vector Perform redundancy removal operation to extract the second vector. Non-repeating elements in the data, ignoring estimation errors. The influence of this yields a data vector. , is represented as: ; in, For dictionary matrix The new guiding vector matrix obtained after rearrangement; It is a vector in which the element in the middle is 1 and all other elements are 0; According to data vectors The smoothed covariance matrix is ​​obtained by combining spatial smoothing algorithms. , satisfy For the new covariance matrix Eigenvalue decomposition is performed to obtain the smoothed covariance matrix. The expression: ; in, for The signal subspace; For noise subspace; For signal subspace eigenvalue matrix, Indicates the first i One eigenvalue; This is the conjugate transpose operation; calculate Inverse m Power of 1, we get: ; in, For matrix inversion, since By adjusting the coefficient m This yields the first expression: ; Based on the first expression, a noise subspace is constructed under the condition of an unknown number of sound sources, and the first weight is obtained. ,include: ; in, For angle The guiding vector below, , d represents the element spacing of the linear array; The wavelength of the signal; For the first weight Normalization is performed to obtain the weight vector. The weight vector of the first n item Calculation methods include: .

[0012] Preferably, the parameters of the sparse Bayesian learning in the sparse reconstruction DOA estimation model are updated according to the weight vector, and the first parameters include: The weights in the weight vector Sparse Bayesian learned vectors applied to sparse reconstruction DOA estimation models In the prior distribution of Gamma, the vector A two-stage hierarchical prior distribution is adopted: ; That is, vector Follows a mean of 0 and a variance of The complex Gaussian distribution; the first parameter for N One unknown hyperparameter The vector formed, the first parameter Follows a Gamma distribution: ; in, For the Gamma function, A constant greater than 0; First parameter hyperparameters in The update methods include: ; in, For vectors The n item; This is the operation for squaring the absolute value.

[0013] Preferred options also include: After updating the first parameter Then, calculate the vector. covariance and posterior mean : ; ; According to covariance and posterior mean Update off-network error ; ; in, The interval is angular. and Based on posterior mean With covariance The auxiliary parameters obtained from the calculation.

[0014] Preferably, the adaptive mesh refinement based on the first parameter combined with the bipartite mesh interpolation method, and the iterative update of the parameters learned by the sparse Bayesian method, include: According to the first parameter Determining the local maximum value determines the corresponding grid angle in space. and the left and right grid angles and ;when and At that time, among them To determine the mesh refinement threshold, a bipartite mesh refinement method is used at the mesh angle. Insert new grid angles on both sides and : ; ; The corresponding hyperparameters are After inserting new grid points, , , The corresponding hyperparameters are , and ,satisfy ; when or At that time, the mesh refinement process ends; After completing adaptive mesh refinement, the guiding vector matrix is ​​reconstructed. and iteratively update the random variables. Weight vector First parameter covariance posterior mean Offline and offline errors .

[0015] Preferably, the preset convergence conditions include either a first condition or a second condition: The first condition includes: the first parameter The t +1 update value With the t The updated value Between satisfy , To preset the iteration convergence error, For 2-norm operations; The second condition includes: the number of iterations reaches a preset number.

[0016] The present invention also provides a DOA estimation device based on spatial smoothing weighted sparse Bayes algorithm, which is used in the method of the present invention. The device includes a first module, a second module and a third module. The first module is used to reconstruct and normalize the covariance based on the sample covariance matrix and the theoretical covariance matrix of the array received signal, and to construct a sparse reconstruction DOA estimation model under off-network conditions, taking off-network error into account. The second module is used to obtain the weight vector based on the spatial smoothing Capon algorithm and the theoretical covariance matrix; and to update the parameters of the sparse Bayesian learning in the sparse reconstruction DOA estimation model according to the weight vector to obtain the first parameter. The third module is used to perform adaptive grid refinement based on the first parameter and the bipartite grid interpolation method, and to iteratively update the parameters learned by sparse Bayesian learning; the iteration ends when the preset convergence condition is met, and the DOA estimate is output.

[0017] The present invention has the following beneficial effects: The DOA estimation method based on spatially smoothed weighted sparse Bayesian algorithm of this invention significantly enhances the sparsity of signal recovery in sparse Bayesian learning when processing finite aperture array data by introducing a spatially smoothed Capon weighting mechanism based on subspace projection. By autonomously constructing weight vectors through the spatially smoothed Capon algorithm, fully automatic DOA estimation can be achieved in scenarios with an unknown number of targets. This frees the method from the limitation of the number of information sources, giving it greater autonomy in complex non-cooperative detection tasks and greatly expanding its application scope in practical underwater combat environments. The spatially smoothed Capon weighting mechanism can effectively suppress the influence of non-target interference on DOA estimation, providing more accurate grid refinement location information. Using this region as the search center to guide the adaptive iteration of the bipartite grid refinement algorithm can improve DOA estimation performance.

[0018] The DOA estimation device based on the spatially smooth weighted sparse Bayesian algorithm of the present invention, when used in the method of the present invention, has the same beneficial effects as the method of the present invention.

[0019] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0020] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a schematic diagram of the method flow of a preferred embodiment of the present invention.

[0021] Figure 2 This is a DOA orientation spectrum comparison diagram of a preferred embodiment of the present invention.

[0022] Figure 3 This is a schematic diagram of the mean square error of DOA estimation for different signal-to-noise ratios under the ideal sparse reconstruction DOA estimation model of the preferred embodiment of the present invention, with a snapshot number L=1000.

[0023] Figure 4 This is a schematic diagram of the success resolution probability curves of DOA estimation for different signal-to-noise ratios under the ideal sparse reconstruction DOA estimation model of the preferred embodiment of the present invention, when the number of snapshots L=1000.

[0024] Figure 5 This is a schematic diagram of the mean square error of DOA estimation for different snapshot numbers under the ideal sparse reconstruction DOA estimation model of the preferred embodiment of the present invention, when the signal-to-noise ratio is -8dB.

[0025] Figure 6 This is a schematic diagram of the success resolution probability curves of DOA estimation corresponding to different snapshot numbers under the ideal sparse reconstruction DOA estimation model of the preferred embodiment of the present invention, when the signal-to-noise ratio is -8dB.

[0026] Figure 7 This is a schematic diagram of the mean square error of DOA estimation for different signal-to-noise ratios under the modified sparse reconstruction DOA estimation model of the preferred embodiment of the present invention, with a snapshot number L=1000.

[0027] Figure 8 This is a schematic diagram of the success resolution probability curves of DOA estimation for different signal-to-noise ratios under the modified sparse reconstruction DOA estimation model of the preferred embodiment of the present invention, when the number of snapshots L=1000.

[0028] Figure 9This is a schematic diagram of the mean square error of DOA estimation for different snapshot numbers under the modified sparse reconstruction DOA estimation model of the preferred embodiment of the present invention, when the signal-to-noise ratio is -8dB.

[0029] Figure 10 This is a schematic diagram of the success resolution probability curves of DOA estimation corresponding to different snapshot numbers under the modified sparse reconstruction DOA estimation model of the preferred embodiment of the present invention, when the signal-to-noise ratio is -8dB. Detailed Implementation

[0030] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings, but the present invention can be implemented in many different ways as defined and covered by the claims.

[0031] See Figure 1 In a preferred embodiment of the present invention, a DOA estimation method based on a spatially smooth weighted sparse Bayesian algorithm is provided, comprising: Q1. Based on the sample covariance matrix and theoretical covariance matrix of the array received signal, perform covariance reconstruction and normalization, and consider off-network error to construct a sparse reconstruction DOA estimation model under off-network conditions. Q1 specifically includes: For by M The array receiving signal model for a linear array composed of 10 array elements is used to obtain the theoretical covariance matrix under Gaussian white noise background. For the theoretical covariance matrix After vectorization, we obtain the first vector r: ; in, T This is a transpose operation; This is the vectorized dictionary matrix; For signal power vector, The variance of the noise; , i =1,.., M For one A column vector of dimension, where the first dimension is... i The row position is 1, and other positions are 0; vec(·) indicates vectorization; For the sample covariance matrix Vectorization is performed to obtain a second vector used to estimate the first vector r. : ; in, To estimate the error; Second vector Multiply both sides of the equation by the block diagonalized matrix To remove the influence of unknown noise variance on the estimation accuracy, a third vector is obtained. : ; By normalizing the matrix For the third vector After normalization, the fourth vector is obtained. : ; Let the normalized dictionary matrix The normalized error vector is the noise term. ,based on Discretize the spatial angle to obtain N A set of grid points with equal angular intervals , where the angle interval At the same time, ,in, Based on The dictionary matrix after angle discretization. Based on The vector after angle discretization; according to And take off-grid error into account The sparse reconstruction DOA estimation model under off-network conditions is obtained as follows: ; in, This is the guiding vector matrix after linear approximation; This is a vector diagonalization operation; for The partial derivative matrix; express It follows a mean of 0 and a variance of . The complex Gaussian distribution; It is the identity matrix; These are the variables used to approximate and correct model mismatch; when hour, For the sparse reconstruction DOA estimation model used in the ideal case; noise term Under the condition of a large number of snapshots, it approximately follows a mean of 0 and a variance of . The standard Gaussian distribution.

[0032] In a preferred embodiment of the present invention, when When it is a random variable, the random variable The value of follows a Gamma distribution: , c and d It is a constant, at this time A sparse reconstruction DOA estimation model for practical applications; random variables The update methods include: ; in, It is the Frobenius norm; E (·) indicates taking the expected value.

[0033] In a preferred embodiment of the present invention, the model mismatch problem caused by the finite number of snapshots and ocean non-Gaussian white noise is addressed, i.e., the sample covariance matrix is... It will deviate significantly from the theoretical covariance matrix Noise item No longer meeting the ideal mean of 0 and variance of The standard Gaussian distribution of the noise term in the DOA estimation model leads to mismatch and reduces its performance. This is why the noise term in the sparse reconstruction of the DOA estimation model is affected. Introducing random variables into the variance of the distribution Approximate corrections are made to the model mismatch, i.e., noise terms. Follows a mean of 0 and a variance of The Gaussian distribution.

[0034] In a preferred embodiment of the present invention, the noise term of the model is estimated through sparse reconstruction DOA. variance Introducing modified random variables And use conjugate Gamma priors for random variables Adaptive adjustments can reduce the impact of small snapshots and ocean non-Gaussian noise on the DOA estimation model, thereby improving DOA estimation performance.

[0035] Q2. Obtain the weight vector based on the spatial smoothing Capon algorithm and the theoretical covariance matrix; update the parameters of the sparse Bayesian learning in the sparse reconstruction DOA estimation model according to the weight vector to obtain the first parameter.

[0036] To enhance the sparsity-induced performance of the signal in the spatial spectrum, a hyperparameter update weight is designed based on the spatial smoothing Capon algorithm.

[0037] In a preferred embodiment of the present invention, the weight vector obtained based on the spatial smoothing Capon algorithm and the theoretical covariance matrix includes: For the second vector Perform redundancy removal operation to extract the second vector. Non-repeating elements in the data, ignoring estimation errors. The influence of this yields a data vector. , is represented as: ; in, For dictionary matrix The new guiding vector matrix obtained after rearrangement; It is a vector in which the element in the middle is 1 and all other elements are 0; According to data vectors The smoothed covariance matrix is ​​obtained by combining spatial smoothing algorithms. , satisfy For the new covariance matrix Eigenvalue decomposition is performed to obtain the smoothed covariance matrix. The expression: ; in, for The signal subspace; For noise subspace; For signal subspace eigenvalue matrix, Indicates the first i One eigenvalue; This is the conjugate transpose operation; calculate Inverse m Power of 1, we get: ; in, For matrix inversion, since By adjusting the coefficient m This yields the first expression: ; Based on the first expression, a noise subspace is constructed under the condition of an unknown number of sound sources, and the first weight is obtained. ,include: ; in, For angle The guiding vector below, , ; d The element spacing of a linear array; The wavelength of the signal; For the first weight Normalization is performed to obtain a weight vector used to enhance signal sparsity. The weight vector of the first n item Calculation methods include: ; In a preferred embodiment of the present invention, the parameters of the sparse Bayesian learning in the sparse reconstruction DOA estimation model are updated according to the weight vector to obtain the first parameters, including: The weights in the weight vector Sparse Bayesian learned vectors applied to sparse reconstruction DOA estimation models In the prior distribution of Gamma, the vector A two-stage hierarchical prior distribution is adopted: ; That is, vector Follows a mean of 0 and a variance of The complex Gaussian distribution; the first parameter for N One unknown hyperparameter The vector formed, the first parameter Follows a Gamma distribution: ; in, For the Gamma function, A constant greater than 0; First parameter hyperparameters in The update methods include: ; in, For vectors The nth term; This is the operation for squaring the absolute value.

[0038] The weighting mechanism of the preferred embodiment of the present invention does not require prior knowledge of the number of signal sources, effectively improving the ability to resolve the orientation of multiple targets.

[0039] In a preferred embodiment of the present invention, it further includes: After updating the first parameter Then, calculate the vector. covariance and posterior mean : ; ; According to covariance and posterior mean Update off-network error ; ; in, The interval is angular. and Based on posterior mean With covariance The auxiliary parameters obtained from the calculation.

[0040] In a preferred embodiment of the present invention, by using covariance posterior mean Offline and offline errors By incorporating iterative processes, the negative impact of mismatch between sparse reconstruction DOA estimation models and DOA estimation accuracy is systematically reduced.

[0041] Q3. Based on the first parameter, perform adaptive mesh refinement using the bipartite mesh interpolation method, and iteratively update the parameters learned by sparse Bayesian learning; when the preset convergence condition is met, the iteration ends and the DOA estimate is output.

[0042] In a preferred embodiment of the present invention, adaptive mesh refinement based on the first parameter combined with bipartite mesh interpolation, and iterative updating of the parameters learned by sparse Bayesian learning, include: According to the first parameter Determining the local maximum value determines the corresponding grid angle in space. and the left and right grid angles and ;when and At that time, among them To determine the mesh refinement threshold, a bipartite mesh refinement method is used at the mesh angle. Insert new grid angles on both sides and : ; ; The corresponding hyperparameters are After inserting new grid points, , , The corresponding hyperparameters are , and ,satisfy This enables rapid and precise location of potential targets; when or At that point, the mesh refinement process ends.

[0043] After completing adaptive mesh refinement, the guiding vector matrix is ​​reconstructed. and iteratively update the random variables. Weight vector First parameter covariance posterior mean Offline and offline errors .

[0044] In a preferred embodiment of the present invention, the preset convergence condition includes a first condition or a second condition: The first condition includes: the first parameter The t +1 update value With the t The updated value Between satisfy , To preset the iteration convergence error, For 2-norm operations; The second condition includes: the number of iterations reaches a preset number.

[0045] The DOA estimation method based on spatially smoothed weighted sparse Bayesian algorithm of this invention significantly enhances the sparsity of signal recovery in sparse Bayesian learning when processing finite aperture array data by introducing a spatially smoothed Capon weighting mechanism based on subspace projection. By autonomously constructing weight vectors through the spatially smoothed Capon algorithm, fully automatic DOA estimation can be achieved in scenarios with an unknown number of targets. This frees the method from the limitation of the number of information sources, giving it greater autonomy in complex non-cooperative detection tasks and greatly expanding its application scope in practical underwater combat environments. The spatially smoothed Capon weighting mechanism can effectively suppress the influence of non-target interference on DOA estimation, providing more accurate grid refinement location information. Using this region as the search center to guide the adaptive iteration of the bipartite grid refinement algorithm can improve DOA estimation performance.

[0046] In a preferred embodiment of the present invention, a DOA estimation device based on a spatially smooth weighted sparse Bayesian algorithm is also provided for use in the method of the present invention. The device includes a first module, a second module, and a third module. The first module is used to reconstruct and normalize the covariance based on the sample covariance matrix and the theoretical covariance matrix of the array received signal, and to construct a sparse reconstruction DOA estimation model under off-network conditions, taking off-network error into account. The second module is used to obtain the weight vector based on the spatial smoothing Capon algorithm and the theoretical covariance matrix; and to update the parameters of the sparse Bayesian learning in the sparse reconstruction DOA estimation model according to the weight vector to obtain the first parameter. The third module is used to perform adaptive grid refinement based on the first parameter and the bipartite grid interpolation method, and to iteratively update the parameters learned by sparse Bayesian learning; the iteration ends when the preset convergence condition is met, and the DOA estimate is output.

[0047] The DOA estimation device based on the spatially smooth weighted sparse Bayesian algorithm of the present invention, when used in the method of the present invention, has the same beneficial effects as the method of the present invention.

[0048] Verification section: In a preferred embodiment of the present invention, eight array elements arranged in an equally spaced half-wavelength array were used for the experiment, with a signal sampling frequency of 4kHz. In the simulation, the azimuth angle of the signal source was set to -30°, -18°, and -1°, while the azimuths of the three targets changed slowly and randomly with an angular deviation of 0.2 degrees. When simulating the root mean square error and resolution probability under different signal-to-noise ratios, the number of snapshots L=1000, the signal-to-noise ratio range was set from -10dB to 10dB, and incremented in 2dB steps; when simulating the root mean square error and resolution probability under different number of snapshots, the number of snapshots varied from 500 to 4500, increasing in 500 steps, the signal-to-noise ratio was set to -8dB, and the Monte Carlo simulation was performed N=500 times.

[0049] The performance of the method of this invention (named SSWGRSBL) was compared with that of Off-grid Sparse Bayesian Learning (OGSBI), Multiple Signal Classification (MUSIC), Spatial Smoothing Multiple Signal Classification (SSMUSIC), Sparse Bayesian Learning Based on Covariance Matrix (OGSBICOV), and Adaptive Mesh Refinement Sparse Bayesian Learning Based on Covariance Model (AGRCMSBL). AGRCMSBL is a method based on OGSBICOV with a bipartite mesh refinement strategy. Quantitative analysis was performed on the noise term under different signal-to-noise ratios and snapshot numbers. Follows a mean of 0 and a variance of Under standard Gaussian distribution (i.e.) The ideal sparse reconstruction DOA estimation model with =1) and the noise term Follows a mean of 0 and a variance of Below (i.e.) The corrected sparse reconstruction DOA estimation model (using random variables) demonstrates its DOA estimation accuracy and spatial resolution under multi-target conditions. See the simulation-generated DOA orientation spectrum comparison diagram. Figure 2 .

[0050] Under the ideal sparse reconstruction DOA estimation model, with a snapshot number L=1000, the mean square error of DOA estimation and the probability of successful resolution for different signal-to-noise ratios are shown in the following figures. Figure 3 and Figure 4 .Depend on Figure 3 It is evident that the mean square error performance of AGRCMSBL is poor at low signal-to-noise ratios (SNR). This is because bipartite mesh refinement cannot effectively distinguish between signal components and noise disturbances at low SNR, resulting in inaccurate mesh refinement and a decline in its mean square error performance. In contrast, the SSWGRSBL of this invention significantly enhances the sparse recovery capability of the signal by introducing a weighting mechanism, suppresses non-target direction noise interference, and, combined with the bipartite mesh refinement algorithm, significantly improves the mean square error performance at low SNR. Figure 4The multi-target resolution success rates of various algorithms were further compared. Simulation results show that the SSWGRSBL algorithm of this invention has a significant advantage in spatial resolution capability, achieving a resolution success rate of 90% even in a low signal-to-noise ratio environment of -6 dB.

[0051] Under the ideal sparse reconstruction DOA estimation model, with a signal-to-noise ratio of -8dB, the mean square error of DOA estimation and the probability of successful resolution for different number of snapshots are shown in the following figures. Figure 5 and Figure 6 . Figure 5 and Figure 6 The impact of varying snapshot count on the mean square error and resolution probability of each algorithm was further analyzed under a signal-to-noise ratio of -8dB. Experimental results show that SSWGRSBL exhibits the best convergence accuracy with a large number of snapshots; however, its mean square error is slightly inferior to SSMUSIC when the number of snapshots is below 1000. This is because the sample covariance is lower with a small number of snapshots. Compared with theoretical value Significant biases exist between them, leading to noise terms in the sparse reconstruction DOA estimation model. The distribution deviates significantly from the ideal Gaussian distribution, resulting in model mismatch. Nevertheless, in terms of resolution, the resolution probability of the method in this invention is consistently higher than that of other comparative algorithms across different snapshots.

[0052] Under the modified sparse reconstruction DOA estimation model, with a snapshot number L=1000, the mean square error of DOA estimation and the success resolution probability curves for different signal-to-noise ratios are shown below. Figure 7 and Figure 8 . Figure 7 and Figure 8 The graphs show the mean squared error and multi-target resolution probability of each algorithm as a function of signal-to-noise ratio under the modified sparse reconstruction DOA estimation model. Their overall trend is similar to... Figure 3 and Figure 4 Consistent results were observed. Within the signal-to-noise ratio (SNR) range (SNR > 0 dB), the modified AGRCMSBL, thanks to its mesh refinement strategy, outperforms OGSBICOV in terms of mean square error. However, at low SNR, AGRCMSBL performs worse than OGSBICOV. In contrast, the SSWGRSBL of this invention, by introducing a weighting mechanism, suppresses noise interference from non-target directions. Combined with a bipartite mesh refinement algorithm, this SSWGRSBL consistently maintains the best estimation performance compared to other methods. In a low SNR environment of -6 dB, its multi-target success rate reaches 98%, higher than the success rate under the ideal model, effectively improving the estimation performance of the SSWGRSBL of this invention.

[0053] Under the modified sparse reconstruction DOA estimation model, with a signal-to-noise ratio of -8dB, the mean square error of DOA estimation and the success resolution probability curves for different number of snapshots are shown below. Figure 9 and Figure 10 . Figure 9 and Figure 10 The curves showing the mean square error and multi-target resolution probability of each method as a function of the number of snapshots are presented under the condition of a signal-to-noise ratio of -8dB. It can be observed that the experimental results exhibit a similar pattern to those of other methods. Figure 5 and Figure 6 Consistent statistical patterns. At different snapshot numbers, the estimation performance of the SSWGRSBL algorithm of this invention is superior to other comparative methods. Compared to Figure 5 Even under conditions of small snapshots, the SSWGRSBL of the present invention can still maintain the lowest mean square error level, further verifying the robustness of the method of the present invention under a finite number of snapshots.

[0054] This invention possesses the ability to adaptively refine grid division and resist environmental mismatch interference, enabling high-precision, high-resolution DOA estimation for multiple targets, thereby achieving high-performance detection of the orientation of multiple targets in complex underwater environments.

[0055] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A DOA estimation method based on spatially smooth weighted sparse Bayesian algorithm, characterized in that, include: Based on the sample covariance matrix and theoretical covariance matrix of the array received signal, covariance reconstruction and normalization are performed, and off-network error is considered to construct a sparse reconstruction DOA estimation model under off-network conditions. The weight vector is obtained based on the spatial smoothing Capon algorithm and the theoretical covariance matrix; the parameters of the sparse Bayesian learning in the sparse reconstruction DOA estimation model are updated according to the weight vector to obtain the first parameter; Adaptive mesh refinement is performed based on the first parameter and the bipartite mesh interpolation method, and the parameters of the sparse Bayesian learning are iteratively updated; the iteration ends when the preset convergence condition is met, and the DOA estimate is output.

2. The DOA estimation method based on spatially smooth weighted sparse Bayesian algorithm according to claim 1, characterized in that, Based on the sample covariance matrix and theoretical covariance matrix of the received signal from the array, covariance reconstruction and normalization are performed. Considering off-network error, a sparse reconstruction DOA estimation model under off-network conditions is constructed, including: For the array receiving signal model of a linear array consisting of M elements, the theoretical covariance matrix is ​​obtained under Gaussian white noise background. For the theoretical covariance matrix After vectorization, we obtain the first vector r: ； in, T This is a transpose operation; This is the vectorized dictionary matrix; For signal power vector, The variance of the noise; , i =1,.., M For one A column vector of dimension, where the first dimension is... i The row position is 1, and other positions are 0; vec(·) indicates vectorization; For the sample covariance matrix Vectorization is performed to obtain a second vector for estimating the first vector r. : ； in, To estimate the error; In the second vector Multiply both sides of the equation by the block diagonalized matrix The third vector is obtained. : ； By normalizing the matrix For the third vector After normalization, the fourth vector is obtained. : ； Let the normalized dictionary matrix The normalized error vector is the noise term. ,based on Discretize the spatial angle to obtain N A set of grid points with equal angular intervals , where the angle interval At the same time, ,in, Based on The dictionary matrix after angle discretization. Based on The vector after angle discretization; according to And take off-grid error into account The sparse reconstruction DOA estimation model under off-network conditions is obtained as follows: ； in, This is the guiding vector matrix after linear approximation; This is a vector diagonalization operation; for The partial derivative matrix; express It follows a mean of 0 and a variance of . The complex Gaussian distribution; It is the identity matrix; These are the variables used to approximate and correct model mismatch; when hour, This is a sparse reconstruction DOA estimation model for the ideal case.

3. The DOA estimation method based on spatially smooth weighted sparse Bayesian algorithm according to claim 2, characterized in that, when When it is a random variable, the random variable The value of follows a Gamma distribution: , c and d It is a constant, at this time For sparse reconstruction DOA estimation models used in real-world scenarios; random variable The update methods include: ； in, It is the Frobenius norm; E (·) indicates taking the expected value.

4. The DOA estimation method based on spatially smooth weighted sparse Bayesian algorithm according to claim 3, characterized in that, The weight vector obtained based on the spatial smoothing Capon algorithm and the theoretical covariance matrix includes: For the second vector Perform a redundancy removal operation to extract the second vector. Non-repeating elements in the data, ignoring estimation errors. The influence of this yields a data vector. , is represented as: ； in, For dictionary matrix The new guiding vector matrix obtained after rearrangement; It is a vector in which the element in the middle is 1 and all other elements are 0; According to the data vector The smoothed covariance matrix is ​​obtained by combining spatial smoothing algorithms. , satisfy For the new covariance matrix Eigenvalue decomposition is performed to obtain the smoothed covariance matrix. The expression: ； in, for The signal subspace; For noise subspace; For signal subspace eigenvalue matrix, Indicates the first i One eigenvalue; This is the conjugate transpose operation; calculate Inverse m Power of 1, we get: ； in, For matrix inversion, since By adjusting the coefficient m This yields the first expression: ； Based on the first expression, a noise subspace is constructed under the condition of an unknown number of sound sources, and the first weight is obtained. ,include: ； in, For angle The guiding vector below, , ; d The element spacing of a linear array; The wavelength of the signal; For the first weight Normalization is performed to obtain the weight vector. The weight vector of the first n item Calculation methods include: 。 5. The DOA estimation method based on spatially smooth weighted sparse Bayesian algorithm according to claim 4, characterized in that, The parameters of the sparse Bayesian learning in the sparse reconstruction DOA estimation model are updated based on the weight vector to obtain the first parameters, including: The weights in the weight vector Sparse Bayesian learned vectors applied to sparse reconstruction DOA estimation models In the prior distribution of Gamma, the vector A two-stage hierarchical prior distribution is adopted: ； That is, vector Follows a mean of 0 and a variance of The complex Gaussian distribution; the first parameter for N One unknown hyperparameter The vector formed, the first parameter Follows a Gamma distribution: ； in, For the Gamma function, A constant greater than 0; The first parameter hyperparameters in The update methods include: ； in, For vectors The n item; This is the operation for squaring the absolute value.

6. The DOA estimation method based on spatially smooth weighted sparse Bayesian algorithm according to claim 5, characterized in that, Also includes: After updating the first parameter Then, calculate the vector. covariance and posterior mean : ； ； Based on the covariance and posterior mean Update the off-network error ; ； in, The angular interval; and Based on posterior mean With covariance The auxiliary parameters obtained from the calculation.

7. The DOA estimation method based on spatially smooth weighted sparse Bayesian algorithm according to claim 6, characterized in that, Adaptive mesh refinement is performed based on the first parameter using a bipartite mesh interpolation method, and the parameters learned by sparse Bayesian learning are iteratively updated, including: According to the first parameter Determining the local maximum value determines the corresponding grid angle in space. and the left and right grid angles and ;when and At that time, among them To determine the mesh refinement threshold, a bipartite mesh refinement method is used at the mesh angle. Insert new grid angles on both sides and : ； ； The corresponding hyperparameters are After inserting new grid points, , , The corresponding hyperparameters are , and ,satisfy ; when or At that time, the mesh refinement process ends; After completing adaptive mesh refinement, the guiding vector matrix is ​​reconstructed. and iteratively update the random variable. The weight vector The first parameter The covariance The posterior mean and the aforementioned off-grid error .

8. The DOA estimation method based on spatially smooth weighted sparse Bayesian algorithm according to claim 7, characterized in that, The preset convergence condition includes either a first condition or a second condition: The first condition includes: the first parameter The t +1 update value With the t The updated value Between satisfy , To preset the iteration convergence error, For 2-norm operations; The second condition includes: the number of iterations reaches a preset number.

9. A DOA estimation device based on spatially smooth weighted sparse Bayesian algorithm, used in the method described in any one of claims 1 to 8, characterized in that, The device includes a first module, a second module, and a third module; The first module is used to perform covariance reconstruction and normalization based on the sample covariance matrix and theoretical covariance matrix of the array received signal, and to construct a sparse reconstruction DOA estimation model under off-network conditions, taking off-network error into account. The second module is used to obtain a weight vector based on the spatial smoothing Capon algorithm and the theoretical covariance matrix; and to update the parameters of the sparse Bayesian learning in the sparse reconstruction DOA estimation model according to the weight vector to obtain the first parameter; The third module is used to perform adaptive grid refinement based on the first parameters and the bipartite grid interpolation method, and iteratively update the parameters of the sparse Bayesian learning; when the preset convergence condition is met, the iteration ends and the DOA estimate is output.

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