Vector array sparse Bayesian learning direction of arrival estimation method

Abstract

The invention provides a vector array sparse Bayesian learning direction of arrival estimation method. The method comprises the following steps: constructing a far-field vector sparse signal model; and establishing a noise covariance model under the vector sound field. And estimating a signal power hyper-parameter through a vector array sparse Bayesian learning process. And through a maximum likelihood estimation technology, noise power hyper-parameter estimation is realized. And finally, carrying out peak searching on the converged signal power hyper-parameter to obtain a direction of arrival estimation result. The method has the advantages that the vector array signal processing performance advantage is obtained, higher signal processing gain is obtained, and meanwhile the method has the capability of restraining the azimuth ambiguity problem; and by using the difference between the noise covariance matrix and the signal covariance matrix under the vector noise, the estimation precision of hyper-parameters such as the signal power and the noise power is remarkably improved. Compared with a traditional vector array DOA estimation method, the vector array DOA estimation method has a lower spectrum background and a sharper spatial spectrum peak, and the resolution and DOA estimation precision are remarkably superior to those of other methods.

Description

Technical Field

[0001] The invention belongs to the field of underwater acoustic detection, and mainly relates to a vector array sparse Bayesian learning direction of arrival estimation method. Background Art

[0002] Sparse Bayesian learning (SBL) is a classic sparse reconstruction algorithm. Traditional SBL algorithms use the expectation maximization (EM) algorithm to iteratively update hyperparameters (including source signal power and noise power), ultimately achieving DOA estimation using the resulting spatial spectrum reconstruction. Building on this foundation, numerous SBL-like algorithms have emerged, including the Off-Grid Sparse Bayesian Inference (OGSBI) method, which achieves high-precision DOA estimation using an off-grid model, the Root Sparse Bayesian Learning (Root-SBL) method for off-grid DOA estimation, the Grid Evolved DOA Estimation (GEDOA) method, which achieves efficient computation through grid evolution, and the Block Sparse Bayesian Learning (BSBL) method, which exploits intra-block correlations to improve algorithm performance. However, these sparse reconstruction methods using the EM algorithm for hyperparameter estimation suffer from the identification problem when applied to scalar arrays. This problem involves the algorithm being unable to distinguish the contributions of the source signal power and noise power hyperparameters to the objective function, resulting in the noise power estimate approaching zero. To address this problem, the multi-shot sparse Bayesian learning method (MSBL) designed a noise power estimation method based on maximum likelihood estimation (MLE), which improved the noise power estimation accuracy to a certain extent.

[0003] Research on sparse reconstruction DOA estimation methods has typically been conducted using underwater acoustic pressure sensors (APSs). With the development of sensors, underwater acoustic vector sensor (AVS) arrays have gradually emerged. Compared to APSs, AVSs incorporate a velocity channel that measures DOA information contained within the velocity field structure. This allows for more measurements and DOA information to be obtained without increasing the array aperture, effectively improving DOA estimation performance. Furthermore, studies of vector noise fields reveal that the noise received by the AVS pressure and velocity channels differs in correlation radius. This characteristic leads to significant differences in the noise covariance matrix structures between vector and scalar arrays, providing a new approach to addressing the identification problem. Many traditional DOA estimation methods, such as conventional beamforming (CBF), minimum variance distortionless response (MVDR), and multiple signal classification (MUSIC), have been applied to AVS arrays. Research results demonstrate that AVS arrays significantly improve the DOA estimation accuracy and resolution of the algorithms, effectively resolving azimuth ambiguities such as port / starboard ambiguity and spatial aliasing, and enabling omnidirectional detection for linear arrays. However, even with AVS arrays, CBF and MVDR still suffer from insufficient resolution at small apertures, and MUSIC is still affected by correlated signals. Unlike traditional DOA estimation methods such as CBF, MVDR, and MUSIC, sparse reconstruction methods offer both high resolution and high robustness. Therefore, combining sparse reconstruction methods with vector arrays is expected to overcome the performance bottleneck of existing underwater target DOA estimation methods. However, due to the high cost and maintenance difficulties of vector sensors, research on vector sensors in the field of DOA estimation, especially sparse reconstruction, is relatively limited.

[0004] To solve the above problems, the present invention proposes a vector array sparse Bayesian learning direction of arrival estimation method. Summary of the Invention

[0005] The purpose of the present invention is to overcome the deficiencies of the prior art and to provide a vector array sparse Bayesian learning direction of arrival estimation method.

[0006] The object of the present invention is achieved by the following technical solution: A vector array sparse Bayesian learning direction of arrival estimation method, comprising the following steps:

[0007] Step 1: Construct a far-field vector sparse signal model received by the array;

[0008] Step 2: Construct the noise covariance matrix model under the vector sound field:

[0009] Step 3: Estimate the signal power hyperparameters through the vector array sparse Bayesian learning process; by introducing it into the vector sparse Bayesian learning process, the recognition problem in sparse Bayesian learning is effectively solved, and high-precision estimation of the signal power hyperparameters is achieved.

[0010] Step 4: The maximum likelihood estimation method is used to achieve high-precision estimation of the noise power hyperparameters, further improving the algorithm resolution.

[0011] Step 5: Iterate the hyperparameter update formula until convergence. After convergence, perform peak search on the signal power hyperparameter to obtain the direction of arrival estimation result.

[0012] Furthermore, in step 1, the signal model expression is obtained by using the sound pressure and vibration velocity channels of the vector sensor to receive signals simultaneously. Where y(t) represents the array receiving signal at time t, Φ is the vector overcomplete dictionary set, is the spatial sparse source signal, and n(t) is the additive white Gaussian noise.

[0013] Furthermore, in step 2, it is assumed that the noise n(t) has a mean of 0 and a variance of σ 2 Σ n Gaussian distribution, by analyzing the correlation between sound pressure and vibration velocity in the vector noise field, Σ n expression.

[0014] Furthermore, in step 3, Φ and Σ n The traditional sparse Bayesian learning process is introduced to utilize the difference between the signal and noise covariance matrices in the vector sound field to effectively solve the identification problem that leads to the decrease of hyperparameter estimation accuracy. Then, the update formula of the signal power hyperparameter γ is obtained through the expectation maximization method.

[0015] Furthermore, in step 4, the σ under the conditions of infinite snapshot and finite snapshot is comprehensively considered. 2 The maximum likelihood estimation result is obtained, σ 2 The update formula of .

[0016] Furthermore, in step 5, by continuously iterating the hyperparameters γ and σ 2 The update formula makes the hyperparameters converge gradually, and the iteration termination threshold is set to determine whether to terminate the iteration; after the iteration is terminated, the γ convergence result is output as the spatial spectrum estimation result, and the peak is searched to obtain the target wave arrival direction estimation value

[0017] The beneficial effects of the present invention are:

[0018] This paper proposes a vector array sparse Bayesian learning direction of arrival (DOA) estimation method. This study addresses the performance limitations of traditional DOA estimation methods and the insufficient accuracy of hyperparameter estimation in scalar array sparse reconstruction DOA estimation methods. By combining the characteristics of the vector acoustic field environment, vector array signal processing technology, and sparse Bayesian learning methods, a vector array sparse Bayesian learning DOA estimation method is proposed. This method effectively improves DOA estimation performance, such as target resolution and direction-finding accuracy, and provides an effective solution for omnidirectional, high-resolution, and highly reliable detection of small-aperture arrays. The advantages of this method over common scalar array sparse reconstruction DOA estimation methods are:

[0019] (1) The signal processing performance advantage of the vector array is obtained. Under the same array shape and array aperture conditions, it achieves higher signal processing gain than the scalar array, while also having the ability to suppress azimuth ambiguity problems;

[0020] (2) By utilizing the difference between the noise covariance matrix and the signal covariance matrix under vector noise, the influence of the recognition problem is overcome and the estimation accuracy of hyperparameters such as signal power and noise power is significantly improved.

[0021] The advantages of this method over the traditional vector array DOA estimation method are:

[0022] (1) It has lower spectral background and sharper spatial spectral peak, which significantly improves the resolution and DOA estimation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art or ordinary technicians, other drawings can be obtained based on these drawings without paying any creative work.

[0024] Figure 1 It is the particle velocity decomposition model;

[0025] Figure 2 Receive signal model for the array;

[0026] Figure 3 Schematic diagram of the change of noise correlation coefficient with sensor spacing;

[0027] Figure 4 It is a far-field spatial spectrum of sparse reconstruction algorithm;

[0028] Figure 5 Normalize the far-field spatial spectrum for the vector array algorithm;

[0029] Figure 6 Schematic diagram of RMSE-σ changing with SNR;

[0030] Figure 7 Schematic diagram of RMSE-θ changing with SNR;

[0031] Figure 8 Schematic diagram of how the probability of successful resolution of each algorithm changes with the angular interval. DETAILED DESCRIPTION

[0032] The technical solutions in the embodiments of the present invention are described clearly and completely below. Obviously, the described embodiments 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 of the present invention without inventive effort are within the scope of protection of the present invention.

[0033] The present invention proposes a vector array sparse Bayesian learning direction of arrival estimation method, which includes the following steps:

[0034] Step 1: Construct a far-field vector sparse signal model for array reception

[0035] AVS consists of a sound pressure sensor and a particle velocity sensor, which can measure the sound pressure and the particle velocity of the medium at a certain point in space. The decomposition model of the particle velocity is shown in the attached figure. Figure 1 As shown in the figure, θ represents the horizontal angle, It can be seen from the figure that the orthogonal components of the particle velocity V can be expressed as

[0036]

[0037] Where u is the unit direction vector pointing from the sound source to the vector sensor, and |·| represents the modulus of the vector. According to the Euler equation, assuming that the signal received by the sensor is a plane wave, the relationship between sound pressure and vibration velocity can be expressed as

[0038]

[0039] Where ρ0 represents the density of the medium and c is the sound velocity of the medium. ρ0c is often called the acoustic impedance. To simplify the model and facilitate calculation, ρ0c is usually set to 1. At this time, the noisy signal y received by the sound pressure sensor is P (t) can be expressed as

[0040]

[0041] where n P (t) represents the noise received by the sound pressure sensor. The noisy signal y received by the particle velocity sensor V (t) can be expressed as

[0042]

[0043] where y V x(t),y V y(t),y V z(t) represents the vibration velocity signal at the adjacent Figure 1 Projection on the x, y and z axes of the model, n V (t) is the noise received by the vibration velocity sensor, (·) T In this case, the noisy signal y(t) received by a single three-dimensional (3-D) AVS can be expressed as

[0044]

[0045] Will be used to receive y P (t),y Vx (t),y Vy (t),y Vz The channels of (t) are called P, Vx, Vy and Vz channels. It is worth noting that the two-dimensional (2-D) AVS does not include the Vz channel, and the remaining channels are the same as those of the 3-D AVS. In addition, for far-field target signals, since the distance between the target and the sensor can be regarded as infinite, the pitch angle approaches 0, so under the far-field plane wave signal model, the direction vector of 2-D AVS can be equivalent to

[0046] u=[cosθ,sinθ] T

[0047] Consider K independent narrowband far-field plane wave signals s k (t), k=1,…,K from different angles θ k The signal is incident on a 2-D AVS uniform linear array (ULA) with M elements. The element spacing is half a wavelength d = λ2, where λ is the signal wavelength. The array receiving signal model is shown in the attached figure. Figure 2 As shown in the figure, the numbered circles represent vector sensors. The Vx channels of all vector sensors point from element 1 to element M, and the Vy channels point orthogonally to Vx. At this time, the array output y(t) at time t can be expressed as

[0048] y(t)=As(t)+n(t)

[0049] Where n(t) is the mean of the array received, which is 0, and the variance is σ 2 Σ n Isotropic Gaussian white noise, A=[a(θ1),…,a(θ K )] is the array manifold, a(θ k ) is the steering vector corresponding to the kth far-field target signal, defined as

[0050] a(θ k )=[a P (θ k ),a Vx (θ k ),a Vy (θ k )] T

[0051]

[0052] a Vx (θ k )=a P (θ k )cosθ k

[0053] a Vy (θ k )=a P (θ k )sinθ k

[0054] The far-field spatial domain range [0°~360°] is uniformly discretized into a set of grid points Θ=[Θ1,…,Θ I ], where I represents the number of grid points, and K < < I. At this time, the array output can be expanded to a sparse signal model as follows

[0055]

[0056] where Φ=[a(Θ1),…,a(Θ I )] is an overcomplete dictionary set, and its columns are called basis functions. Obtained by filling s(t) with zero values, assuming is the distance θ k The nearest grid point, at this time Satisfaction properties

[0057]

[0058] Furthermore, consider the multi-snapshot model with the number of snapshots L as follows

[0059]

[0060] Where Y=[y(1),…,y(L)], N=[n(1),…,n(L)].

[0061] Assuming that the far-field sound source signals and noise are independent of each other, the array output covariance matrix can be expressed as

[0062]

[0063] in(·) H represents the conjugate transpose, E{·} represents the expectation, Indicates is a diagonal matrix with diagonal elements, Represents the signal power at each grid point, that is, the far-field spatial spectrum.

[0064] Step 2: Construct the noise covariance matrix model under the vector sound field

[0065] The array receiving noise can be expressed as the superposition of plane waves propagating from all possible directions. Assume that each plane wave is narrowband, with a corresponding wavelength of λ, and the displacement between the two vector sensors is d (d = |d| represents the distance). Taking array element 1 and array element 2 in the array receiving signal model as an example, define ρ C1,C2 (d) shows the correlation coefficient between the received noise of channel C1 of array element 1 and channel C2 of array element 2, where C1, C2 = P, Vx, Vy (i.e., C1 and C2 can represent any channel among P, Vx and Vy). In an isotropic noise field, the correlation coefficient ρ C1,C2 (d) can be expressed as

[0066] ρ P,P (d) = J0(|l|)

[0067]

[0068]

[0069]

[0070] Where l=2πd / λ,V1,V2=Vx,Vy,J N (·) represents the Nth-order spherical Bessel function. It represents the angle between the direction of the V1 channel and the displacement d. The noise correlation coefficient varies with the sensor distance as shown in the attached figure. Figure 3 As shown in the figure, in the isotropic noise field, when d / λ=1 / 2, although the noise received by each array element P channel is independent of each other, there is still a clear correlation between the velocity channels of each array element. At this time, the variance matrix of the array element receiving noise ∑ n It can be expressed as

[0071]

[0072] in

[0073]

[0074] In the formula, C1, C2 = P, Vx, Vy. It is worth noting that ∑ n is a positive definite Hermitian matrix.

[0075] Step 3: Estimate signal power hyperparameters through vector array sparse Bayesian learning process

[0076] In the noise Under the conditions, Represents Gaussian distribution, assuming that the signals are independent of each other in each snapshot, the likelihood function can be obtained as

[0077]

[0078] where Y ·,l represents the lth column of the matrix Y, and exp(·) represents the exponential with the natural number e as the base.

[0079] Also assume Each column has the same sparse structure, that is,

[0080]

[0081] Where I L represents the L×L unit matrix, Γ=diag(γ), γ=[γ1,…,γ I ] can be regarded as the spatial distribution of signal power. According to the Bayesian formula, Furthermore, there The variance Σ and the mean It can be expressed as

[0082]

[0083] in for The point estimate of To obtain Then we need to estimate the hyperparameters γ and σ.

[0084] The estimated cost function is

[0085]

[0086] where Λ=σ 2 ∑ n +ΦΓΦ H It is worth noting that Λ has the same expression as the signal covariance matrix R. Λ is the main factor causing the scalar matrix SBL identification problem. Specifically, σ 2 The contribution of γ to Λ is consistent and cannot be separated statistically, that is, the scalar matrix SBL can be obtained by adding a set of hyperparameter vectors γ add , so that Φdiag(γ add )Φ H ≈σ 2 I M , at this time σ 2The estimated value of approaches 0, and the estimated value of γ becomes γ+γ add , the hyperparameter estimation accuracy is greatly reduced. Since the estimation accuracy of noise power will affect the sharpness of the spatial spectrum peak, σ 2 The increase of estimation error will lead to the reduction of resolution of SBL method, and γ add The introduction of will cause more pseudo peaks to appear in the spatial spectrum, which will lead to false alarms in subsequent detections.

[0087] In the vector array model of the present invention, the influence of the recognition problem is effectively suppressed. n By multiple ∑ C1,C2 (C1, C2 = P, Vx, Vy). Under the condition of half-wave distribution between array elements, only ∑ P,P =I M is a diagonal matrix, ∑ P,Vx ,∑ Vx,Vx and ∑ Vy,Vy The matrices are all non-diagonal matrices. In this case, it is difficult for the present invention to add a set of γ add Satisfy Φdiag(γ add )Φ H ≈σ 2 ∑ n , thus effectively avoiding the influence of the identification problem and significantly improving the estimation accuracy of hyperparameters in SBL.

[0088] By using the EM method, the hyperparameters γ and σ can be obtained 2 The update formula is

[0089]

[0090] in Representation matrix The i-th row of n -12 ∑ n -1 The positive square root of n -1 =∑ n -12 (∑ n -12 ) H , due to ∑ n is a positive Hermitian matrix, so ∑ n -12 In the present invention, the above σ is used 2 The vector array sparse Bayesian learning method of the update formula is referred to as SBL-V, which is the first form of the present invention.

[0091] Step 4: Estimation of noise power hyperparameters using maximum likelihood estimation techniques

[0092] The σ update formula derived from the EM method in this paper mitigates identification issues to a certain extent and improves hyperparameter estimation accuracy. Furthermore, this paper combines the MSBL method with additional DOA information received by the vector array velocity channel to further improve noise power estimation accuracy. The following describes the process of obtaining the noise power estimation formula based on maximum likelihood estimation (MLE).

[0093] Known noise power σ 2 The MLE is

[0094]

[0095] where tr(·) represents the trace of the matrix, represents the Frobenius norm, MLE, Under the condition of unlimited snapshot, The expression can be updated to

[0096]

[0097] Then we can get the noise power σ 2 The update formula is

[0098]

[0099] In the formula is the data covariance matrix under finite snapshots, in is the MLE of array flow type A. In the present invention, the above σ is used 2 The vector matrix sparse Bayesian learning method of the iterative formula is referred to as MSBL-V, which is the second form of the present invention.

[0100] Step 5: Iterate the hyperparameter update formula until convergence to obtain the direction of arrival estimation result

[0101] Comprehensively build the model and formula to Σ、 γ, σ 2 Perform cyclic iterations. After multiple iterations, the hyperparameters γ and σ 2 Gradually converge. The present invention finally outputs the hyperparameter γ as the spatial spectrum The estimation results of Peak search to obtain DOA estimation results In order to avoid wasting computation time due to infinite iteration of hyperparameters, a threshold of iteration number G is usually set. ε and tolerance threshold The number of iterations is limited, and the tolerance of the present invention is Defined as

[0102]

[0103] where ||·||2 represents the 2-norm, γ old Represents the estimated value of γ in the previous iteration. When the number of iterations ε≥G ε or tolerance , stop the iteration.

[0104] The vector array sparse Bayesian learning direction of arrival estimation method designed in the present invention is verified by simulation, and the results are explained.

[0105] The vector array sparse Bayesian learning direction-of-arrival (DOA) estimation method of the present invention can be specifically represented by two new algorithms: SBL-V and MSBL-V. Simulation results compare the performance of these two algorithms with scalar array SBL, MSBL, the sparse iterative covariance estimation method (SPICE), and vector array CBF, MVDR, and MUSIC (hereinafter referred to as CBF-V, MVDR-V, and MUSIC-V). The simulations analyze each method's spatial spectrum results, hyperparameter estimation accuracy, DOA estimation accuracy, and resolution.

[0106] Simulation 1 first compares the spatial spectra of various comparison methods within the detection range of [0° to 360°] to verify the effectiveness of the vector array method of the present invention. The comparison methods are scalar array SBL, MSBL, SPICE and the SBL-V and MSBL-V methods of the present invention. Assume that K = 2 far-field target signals are incident on the ULA of M = 5 from 60° and 260° respectively, the signal-to-noise ratio (SNR) is 0dB, the number of snapshots T = 200, the far-field grid spacing α = 2°, and the termination condition of the sparse reconstruction method is G ε =500. The far-field spatial spectrum results of each algorithm are in the attached Figure 4 As can be seen from the figure, the spatial spectrum of each comparison method has sharp peaks in the target direction (60 ° and 260 °), which shows that each comparison algorithm can effectively realize target direction estimation. It is worth noting that the scalar array algorithm is affected by the starboard and starboard ambiguity, and there are obvious pseudo peaks on the starboard and starboard ambiguity angles (300 ° and 100 °) of the target direction, while the SBL-V and MSBL-V methods proposed in the present invention benefit from the starboard and starboard ambiguity suppression capabilities of the vector array, and only form sharp peaks in the target direction, effectively reducing the detection false alarm. At the same time, the target signal power estimation value of the scalar array algorithm has obvious deviations, while the target signal power estimation value of the algorithm proposed in the present invention is more accurate than the scalar array algorithm. This result proves the effective improvement of the present invention in the accuracy of signal power super parameter estimation.

[0107] Simulation 2 compares the spatial spectra of various vector array methods within the detection range of [0° to 360°] to verify the performance advantage of the vector array sparse reconstruction DOA estimation method of the present invention over the existing vector array DOA estimation algorithm. The comparison methods are CBF-V, MVDR-V, MUSIC-V and the present invention's SBL-V and MSBL-V. The rest of the simulation conditions are the same as those in Simulation 1. The normalized far-field spatial spectra of each vector array algorithm are shown in the attached figure. Figure 5 As shown in the figure, each comparison method can achieve effective estimation of the target direction. Among them, CBF-V has the highest background level, followed by MVDR-V and MUSIC-V. There are obvious pseudo peaks in the spatial spectrum of MVDR-V. This is because this algorithm does not consider the correlation between the receiving noise of the sound pressure channel and the vibration velocity channel. The SBL-V and MSBL-V methods of the present invention design a noise covariance model for a specific vector noise field, effectively reducing the estimation error of the noise signal power, and improving the peak value (target signal power) estimation accuracy while reducing the pseudo peaks in the spatial spectrum.

[0108] Simulation 3 uses W=200 Monte Carlo experiments to statistically calculate the root mean square error (RMSE) of the noise power hyperparameter σ of each sparse reconstruction method to verify the improvement of the noise power estimation accuracy of the present invention, where the RMSE of the hyperparameter σ is expressed as RMSE-σ. The comparison methods are scalar array SBL, MSBL, SPICE and the SBL-V and MSBL-V methods of the present invention. The detection range of this simulation is [0°~360°], considering K=2 far-field target signals incident on the ULA of M=5 from θ1=60° and θ2=120°, the number of snapshots T=200, and the SNR gradually increases from -10dB to 10dB. The far-field grid spacing of each sparse reconstruction method is α=2°, and the termination condition is G ε =500. The RMSE-σ of each algorithm changes with SNR as shown below Figure 6 As shown in the figure, due to the influence of the recognition problem, the noise power estimation values of the SBL and SPICE methods are close to 0, and the error is large. The SBL-V of the present invention effectively suppresses the influence of the recognition problem through the difference between the vector array signal and the noise covariance model, and the noise power estimation accuracy is significantly improved. The MSBL and MSBL-V methods estimate the noise power based on MLE, and their estimation accuracy is significantly better than other methods. Among them, the RMSE-σ of MSBL-V is significantly smaller than that of MSBL, which further verifies the improvement of the vector array on the accuracy of hyperparameter estimation.

[0109] Simulation 4 uses W=200 Monte Carlo tests to statistically calculate the RMSE (abbreviated as RMSE-θ) of the angle estimation results of each vector array DOA estimation method to compare the DOA estimation accuracy of each method. The comparison methods are CBF-V, MVDR-V, MUSIC-V and the SBL-V and MSBL-V methods of the present invention. It is worth noting that since the scalar array SBL, MSBL and SPICE methods are seriously affected by the starboard and starboard ambiguity, it is difficult to accurately judge the true peak of the target, so the RMSE-θ comparison is not included. The detection range of this simulation is [0°~360°]. Under the premise of avoiding the influence of resolution, it is assumed that K=1 far-field target signals are incident from θ1 to the ULA of M=5, the number of snapshots T=200, and the SNR gradually increases from -10dB to 10dB. In each Monte Carlo test, θ1 is randomly generated within the detection range. The far-field grid spacing of each sparse reconstruction method is α=2°, and the termination condition is G ε =500. The RMSE-θ of each comparison algorithm changes with SNR as shown below Figure 7 As shown in the figure. It can be seen that the RMSE-θ of each algorithm gradually decreases as the SNR increases. Among them, the DOA estimation error of MVDR-V is relatively large, and it is difficult to accurately measure the direction. This is because the correlation between the receiving noise of the sound pressure channel and the vibration velocity channel under the isotropic vector noise field causes the distortion of the MVDR-V beam, making it easy for pseudo peaks with peaks higher than the target spectrum peak to appear in the spatial spectrum, resulting in the failure of DOA estimation. When SNR<0dB, the SBL-V and MSBL-V methods of the present invention effectively reduce the influence of noise model mismatch by constructing and introducing noise covariance models under various isotropic noise fields. The RMSE-θ is significantly smaller than that of other algorithms, and has obvious advantages in DOA estimation accuracy.

[0110] Simulation 5 uses W=200 Monte Carlo tests to statistically analyze the resolution of each vector array DOA estimation method. The detection range of this simulation is [0°~360°], considering K=2 far-field target signals incident on the ULA of M=5 from θ1 and θ2 respectively, and the number of snapshots T=200. This simulation studies the impact of the target angle interval on the probability of successful resolution of the algorithm. When comparing the impact of the algorithm resolution on the target angle interval, the SNR=0dB is fixed, and in each Monte Carlo test, θ1 is randomly generated within the detection range, θ2=θ1+△θ, and △θ gradually changes from 2° to 20°. The far-field grid spacing α=2° for each sparse reconstruction method, and the termination condition is G ε=500. Considering the low DOA estimation accuracy of MVDR-V in isotropic noise field and the problem that the preset maximum target interval in this simulation is less than the Rayleigh limit, this simulation comparison method excludes MVDR-V and CBF-V. The rest of the comparison method is the same as Simulation 3. The successful resolution probability and RMSE-θ of each comparison algorithm with target angle when SNR is fixed at 0dB are shown in the attached figure. Figure 8 As shown in the figure, the probability of successful resolution for each algorithm increases with increasing angular interval. The successful resolution curves for SBL-V and MSBL-V are highly similar, with a minimum resolvable angle of approximately 8°. In contrast, the MUSIC-V method fails to achieve effective resolution within an angular interval of ≤20°, effectively demonstrating the resolution advantages of the SBL-V and MSBL-V methods of the present invention.

[0111] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the scope of the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A vector array sparse Bayesian learning direction of arrival estimation method, characterized by: The steps are as follows: Step 1: Construct a far-field vector sparse signal model received by the array; Step 2: Construct the noise covariance matrix model under the vector sound field: Step 3: Estimate signal power hyperparameters through a vector array sparse Bayesian learning process; Step 4: Estimation of noise power hyperparameters is achieved through maximum likelihood estimation method; Step 5: Iterate the hyperparameter update formula until convergence. After convergence, perform peak search on the signal power hyperparameter to obtain the direction of arrival estimation result.

2. The vector array sparse Bayesian learning direction of arrival estimation method according to claim 1, characterized in that: In step 1, the signal model expression is obtained by using the sound pressure and vibration velocity channels of the vector sensor to receive signals simultaneously. Where y(t) represents the array receiving signal at time t, Φ is the vector overcomplete dictionary set, is the spatial sparse source signal, and n(t) is the additive white Gaussian noise.

3. The vector array sparse Bayesian learning direction of arrival estimation method according to claim 2, characterized in that: In step 2, it is assumed that the noise n(t) has a mean of 0 and a variance of σ 2 Σ n Gaussian distribution, by analyzing the correlation between sound pressure and vibration velocity in the vector noise field, Σ n expression.

4. The vector array sparse Bayesian learning direction of arrival estimation method according to claim 3, characterized in that: In step 3, Φ and Σ n The traditional sparse Bayesian learning process is introduced to utilize the difference between the signal and noise covariance matrices in the vector sound field to effectively solve the identification problem that leads to the decrease of hyperparameter estimation accuracy. Then, the update formula of the signal power hyperparameter γ is obtained through the expectation maximization method.

5. The vector array sparse Bayesian learning direction of arrival estimation method according to claim 4, characterized in that: In step 4, considering the σ under the conditions of infinite snapshot and finite snapshot, 2 The maximum likelihood estimation result is obtained, σ 2 The update formula of .

6. The vector array sparse Bayesian learning direction of arrival estimation method according to claim 5, characterized in that: In step 5, by continuously iterating the hyperparameters γ and σ 2 The update formula makes the hyperparameters converge gradually, and the iteration termination threshold is set to determine whether to terminate the iteration; after the iteration is terminated, the γ convergence result is output as the spatial spectrum estimation result, and the peak is searched to obtain the target wave arrival direction estimation value

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