Alternating sparse Bayesian compressed beamforming method in grid space

Abstract

This invention proposes an off-grid spatially alternating sparse Bayesian compressed beamforming method. Based on a beamforming model, this invention expands the manifold matrix using a first-order Taylor expansion to derive an off-grid beamforming model including DOA angle compensation. Based on a modified multi-snapshot model, it presents model assumptions for a three-layer Bayesian structure diagram and uses a spatial alternation method to obtain the update iterative formulas for hyperparameter variables. Finally, it uses the expectation-maximization method to derive the update equation for the DOA angle compensation vector. Specifically, this invention modifies the beamforming model by introducing an offset vector between the actual DOA and grid points, simultaneously improving the accuracy of DOA angle and target source signal estimation. Combined with spatial alternation technology, it avoids matrix inversion in each iteration, reducing the computational cost per iteration while preserving accelerated convergence characteristics.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, and in particular relates to a method for alternating sparse Bayesian compressed beamforming in a grid space. Background Technology

[0002] The use of sensor arrays for direction of arrival (DOA) and complex signal estimation of target sources is widely applied in radar, sonar, and remote sensing. This technique is used to determine the incident direction and complex amplitude of a target source relative to an antenna array. According to the Rayleigh criterion, the array aperture size limits the performance of traditional beamforming (CBF) methods, resulting in low resolution and excessive sidelobes, especially when multiple target sources are present. To improve resolution, researchers have proposed subspace-based methods, such as Multi-Signal Classification (MUSIC) and rotation-invariant techniques (ESPRIT). However, these methods require a large number of snapshots, require the target source signals to be uncorrelated, and cannot provide accurate complex amplitude estimates.

[0003] With the development of compressed sensing (CS) technology, numerous sparse signal reconstruction methods have emerged. For example, the l1-SVD method, which combines singular value decomposition (SVD) of the data matrix, uses the l1-norm to achieve sparsity and reduces noise sensitivity and computational complexity through SVD. The weighted subspace fitting sparse reconstruction (SRWSF) method improves the DOA estimation accuracy of l1-SVD through weighted subspace fitting. Furthermore, when the column vectors of the manifold matrix are highly correlated, most methods based on l1-SVD... p - Norm (0≤p≤1) optimization methods suffer from performance degradation, while sparse Bayesian learning (SBL) still exhibits satisfactory performance. Therefore, SBL is well-suited for solving DOA and complex signal estimation problems. For example, multi-snapshot models can be efficiently solved using maximum a posteriori (MAP) estimation within the SBL framework.

[0004] Traditional SBL beamforming methods employ a grid-based implementation (on-grid SBL). Due to the discrepancy between the actual angle and the predefined grid nodes, errors introduced by the finite grid are always observable, known as grid mismatch errors, which significantly limit resolution improvement. To address this, off-grid techniques can effectively overcome the mismatch errors caused by finite grid definitions. Examples include Sparse Cognitive Full Least Squares (S-TLS), Off-Grid Sparse Bayes Inference (OGSBI), and Perturbation Sparse Bayes Learning (PSBL).

[0005] Despite the superior performance of SBL, it requires matrix inversion in each iteration, and its convergence speed is slow when the signal-to-noise ratio is low. Therefore, some researchers have proposed fast SBL methods to improve computational efficiency, such as Fast Inverse-Free Sparse Bayesian Learning (IF-SBL). However, the accuracy of DOA and complex signal estimation remains limited due to the presence of mismatch error. To date, a method that simultaneously addresses grid mismatch error and computational efficiency has not been reported. Summary of the Invention

[0006] The purpose of this invention is to solve the problems in the prior art. It proposes a spatially alternating sparse Bayesian compressed beamforming method. The method introduces the DOA angle offset vector to correct the manifold matrix in the beamforming model to reduce mismatch error, and uses the spatial alternation method to solve the multi-level Bayesian model. This algorithm does not require matrix inversion, which not only effectively reduces the amount of computation per iteration, but also significantly accelerates the convergence speed.

[0007] This invention is achieved through the following technical solution: This invention proposes a method for alternating sparse Bayesian compressed beamforming in a grid space, the method specifically comprising:

[0008] Step 1: Based on the beamforming model, construct an off-grid beamforming model including DOA angle compensation based on acoustic echo measurement data;

[0009] Step 2: Based on the constructed off-grid beamforming model including DOA angle compensation, give the likelihood function and define the prior distribution;

[0010] Step 3: Establish the joint probability density function associated with the Bayesian structure diagram, and derive the approximate posterior distribution of the target source, i.e., the sound source signal X;

[0011] Step 4: Use the spatial alternation method to adjust the hyperparameter λ n γ n ρ and β are updated iteratively;

[0012] Step 5: Check convergence according to the predefined tolerance. End the iteration when the convergence condition is met or the maximum number of iterations is reached.

[0013] Further, step 1 specifically includes:

[0014] Step 1.1: Assuming the receiving array consists of M uniformly arranged arrays with a spacing of d, the model for receiving acoustic echo measurement data is represented as follows:

[0015] y = Ax + n (1)

[0016] in For acoustic echo measurement data vectors, It is a complex signal vector over a predefined angle θ, where θ = [θ1, θ2, ..., θ] N ] T , It is a Gaussian white noise vector, where N is the number of angular meshes. It is an array manifold matrix at a predefined angle, denoted as A(θ)=[a(θ1),a(θ2),…,a(θ)]. N )],in:

[0017] a(θ k )=[1,exp(-j2πfτ k ),···,exp(-j2πf(M-1)τ k )] T (2)

[0018] in,

[0019]

[0020] c represents the signal propagation speed; therefore, the model is given according to the snapshot order as follows:

[0021] y l =Ax l +n l ,l=1,2,···,L (4)

[0022] Where l is the snapshot number; taking each snapshot vector as a column, the multi-snapshot model is obtained as follows:

[0023] Y = AX + N (5)

[0024] in, For multiple snapshots of acoustic echo measurement data; X = [x1, x2, ..., x L [n1, n2, ..., n] represents the target source signal to be estimated from multiple snapshots; N = [n1, n2, ..., n] L Let the signal be Gaussian white noise, and the elements in the matrix be independent, satisfying the following condition: Where n ij For the element in the i-th row and j-th column, This represents a complex Gaussian distribution with zero mean and precision ρ.

[0025] Step 1.2: Apply a first-order Taylor series to the guiding vector a(θ) k Expanding, we get:

[0026]

[0027] Where υ represents the actual target source DOA perspective. Represents the node closest to the true angle, and the vector:

[0028]

[0029] Therefore, we can define:

[0030] B=[b(θ1),…,b(θ N (8)

[0031]

[0032]

[0033] Where, diag(β) represents a diagonal matrix with vector β as its diagonal element; r = θ2 - θ1 represents the spacing between the partition nodes; clearly, β represents the compensation vector for the introduced correction angle, for a specific When the true angle υ exists, there is Otherwise, the corresponding element β n =0; This yields the modified off-grid beamforming model:

[0034]

[0035] in, This is the corrected off-grid manifold matrix.

[0036] Furthermore, step 2 specifically includes:

[0037] Step 2.1: Assuming the target sources are independent, the nth predefined target source follows a complex Gaussian distribution with a mean of 0:

[0038]

[0039] Where λ=[λ1,λ2,…,λ N ] T It is the precision hyperparameter vector, I L It is an L×L identity matrix. To enhance population sparsity, λ is used at different snapshots. n They should remain the same;

[0040] Step 2.2: In the second layer of the Bayesian structure diagram, assume that the precision variables are independent and simultaneously follow a gamma distribution:

[0041]

[0042] Where Γ(a,b) represents the gamma distribution, with a and b representing the shape and scale parameters, respectively; in the third layer of the Bayesian structure diagram, given the hyperparameter vector γ = [γ1,γ2,…,γ...] N ] T The elements satisfy independent and equal distribution, that is:

[0043]

[0044] Where the given parameters are a0 = b0 = 10 -6 ;

[0045] Step 2.3: Based on the modified off-grid beamforming model, the expression for the likelihood function can be obtained:

[0046]

[0047] Where the noise accuracy ρ follows a gamma distribution:

[0048] p(ρ)=Γ(ρ|c0,d0) (16)

[0049] Wherein, the given parameter c0 = d0 = 10 -6 .

[0050] Furthermore, step 3 specifically includes:

[0051] Step 3.1: Use the set Θ = {X, λ, γ, ρ, β} to represent the latent variables, and for ease of expression, use Θ\X to represent the set of all other variables except variable X, i.e., {λ, γ, ρ, β}, and so on for other cases;

[0052] According to the Bayesian structure diagram, the joint probability function distribution is as follows:

[0053] p(Y,Θ)=p(Y|X,ρ,β)p(X|λ)p(λ|γ)p(γ)p(ρ)p(β) (17)

[0054] Assume β is in Uniformly distributed within, utilizing its non-informative and bounded nature, it satisfies:

[0055]

[0056] According to the variational method, the approximate true posterior satisfies the following independence assumptions:

[0057]

[0058] Therefore:

[0059]

[0060] Substituting (12) to (16) into (17) yields the logarithmic form of the joint probability function:

[0061]

[0062] Among them, ||·|| F Denotes the Frobenius norm;

[0063] Step 3.2: According to the variational method, the expectation step in the expectation-maximization algorithm requires calculating the target source x. n The approximate posterior logarithm:

[0064]

[0065] in,

[0066]

[0067]

[0068] <ρ>=E q(ρ) [ρ] (25)

[0069] The expectation operator is abbreviated as <·>, and tr[·] represents the trace operation. express The nth column vector, Remove The matrix after that is denoted as X (removing the nth row vector) The matrix after that is denoted as

[0070] According to equation (22), the target source signal distribution q(x) n The distribution follows a Gaussian distribution, with variance and mean as follows:

[0071]

[0072] Furthermore, the hyperparameter λ n The update is as follows:

[0073] First update λ n Collective (21) all containing λ n The approximate posterior of the terms is:

[0074]

[0075] It can be obtained in:

[0076]

[0077] Furthermore, the hyperparameter γ n The update is as follows:

[0078] Update γ n :

[0079]

[0080] Therefore, there is in,

[0081]

[0082] Furthermore, the hyperparameter ρ update specifically involves:

[0083] Updating the noise parameter ρ, we get:

[0084]

[0085] Furthermore, the hyperparameter β update specifically involves:

[0086] To update the angle compensation vector β, the following expectation needs to be calculated, while retaining terms related to β:

[0087]

[0088] Therefore, the update formula for β is:

[0089]

[0090]

[0091] Where, β -n This represents the nth element β excluding β. n The newly formed vector; Λ nn Represents the nth element on the diagonal of matrix Λ; (Λ n ) -n Let represent the vector formed by removing the nth element from the nth column vector of matrix Λ, and:

[0092]

[0093]

[0094] in, This represents the operator for taking the real part.

[0095] This invention proposes an electronic device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the off-grid spatial alternating sparse Bayesian compressed beamforming method.

[0096] This invention proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the off-grid spatial alternating sparse Bayesian compressed beamforming method.

[0097] The present invention has the following beneficial effects:

[0098] 1. This invention adopts the idea of ​​sparse reconstruction off-grid. By performing a first-order Taylor expansion of the manifold matrix in terms of angle, an angle offset vector is introduced to compensate for the inherent bias of the original beamforming model, effectively reducing mismatch error and significantly improving the estimation accuracy of complex signals.

[0099] 2. This invention employs the spatial alternation method to solve the modified beamforming model, and combines it with the off-grid angle offset vector to address the mismatch error problem. From an implementation perspective, the calculation process of the target source covariance matrix is ​​reduced to a scalar scale, avoiding tedious matrix inversion, significantly reducing the computational load, and retaining the performance of fast convergence.

[0100] 3. The OGSA-MSBL method proposed in this invention maintains estimation accuracy while ensuring running speed under low signal-to-noise ratio conditions. More importantly, it still guarantees the estimation accuracy of the target source when the predefined number of grids is low, while further reducing the computational load. Therefore, it has greater development potential than traditional grid implementation methods. Attached Figure Description

[0101] Figure 1 This is a flowchart of the OGSA-MSBL method proposed in this invention;

[0102] Figure 2 The figures show the reconstruction results of various methods at a frequency of 109 Hz. Among them, (a) is the reconstruction result of CBF at f = 109 Hz; (b) is the reconstruction result of IF-SBL at f = 109 Hz; (c) is the reconstruction result of OGSA-MSBL at f = 109 Hz; (d) is the reconstruction result of SAVE-MSBL at f = 109 Hz; (e) is the reconstruction result of OGSBI at f = 109 Hz; (f) is the reconstruction result of VSBL at f = 109 Hz; and (g) is the reconstruction result of C-BCS at f = 109 Hz.

[0103] Figure 3 The figures show the reconstruction results of various methods at a frequency of 127Hz. (a) is the reconstruction result using CBF at f=127Hz; (b) is the reconstruction result using IF-SBL at f=127Hz; (c) is the reconstruction result using OGSA-MSBL at f=127Hz; (d) is the reconstruction result using SAVE-MSBL at f=127Hz; (e) is the reconstruction result using OGSBI at f=127Hz; (f) is the reconstruction result using VSBL at f=127Hz; and (g) is the reconstruction result using C-BCS at f=127Hz.

[0104] Figure 4The figures show the reconstruction results of various methods at a frequency of 145Hz. (a) is the reconstruction result using CBF at f=145Hz; (b) is the reconstruction result using IF-SBL at f=145Hz; (c) is the reconstruction result using OGSA-MSBL at f=145Hz; (d) is the reconstruction result using SAVE-MSBL at f=145Hz; (e) is the reconstruction result using OGSBI at f=145Hz; (f) is the reconstruction result using VSBL at f=145Hz; and (g) is the reconstruction result using C-BCS at f=145Hz.

[0105] Figure 5 The figures show the reconstruction results of various methods at a frequency of 163Hz. (a) is the reconstruction result using CBF at f=163Hz; (b) is the reconstruction result using IF-SBL at f=163Hz; (c) is the reconstruction result using OGSA-MSBL at f=163Hz; (d) is the reconstruction result using SAVE-MSBL at f=163Hz; (e) is the reconstruction result using OGSBI at f=163Hz; (f) is the reconstruction result using VSBL at f=163Hz; and (g) is the reconstruction result using C-BCS at f=163Hz.

[0106] Figure 6 The figures show the reconstruction results of various methods at a frequency of 198Hz. (a) is the reconstruction result using CBF at f=198Hz; (b) is the reconstruction result using IF-SBL at f=198Hz; (c) is the reconstruction result using OGSA-MSBL at f=198Hz; (d) is the reconstruction result using SAVE-MSBL at f=198Hz; (e) is the reconstruction result using OGSBI at f=198Hz; (f) is the reconstruction result using VSBL at f=198Hz; and (g) is the reconstruction result using C-BCS at f=198Hz.

[0107] Figure 7 The figures show the reconstruction results of various methods at a frequency of 232Hz. (a) is the reconstruction result using CBF at f=232Hz; (b) is the reconstruction result using IF-SBL at f=232Hz; (c) is the reconstruction result using OGSA-MSBL at f=232Hz; (d) is the reconstruction result using SAVE-MSBL at f=232Hz; (e) is the reconstruction result using OGSBI at f=232Hz; (f) is the reconstruction result using VSBL at f=232Hz; and (g) is the reconstruction result using C-BCS at f=232Hz.

[0108] Figure 8The graphs show the relationship between different algorithms and the number of snapshots, along with their running times; where (a) represents the RMSE of different algorithms relative to the number of snapshots. θ (a) Relationship curve; (b) RMSE of different algorithms relative to the number of snapshots X Relationship curves; (c) shows the running time of different algorithms relative to the number of snapshots;

[0109] Figure 9 The graphs show the relationship between different algorithms and SNR, along with their running times; where (a) represents the RMSE of different algorithms relative to SNR. θ (a) Relationship curve; (b) RMSE of different algorithms relative to SNR X Relationship curves; (c) shows the running time of different algorithms relative to SNR;

[0110] Figure 10 The graphs show the relationship between different algorithms and the number of receiving array elements, along with their running times; where (a) represents the RMSE of different algorithms relative to the number of receiving array elements. θ (a) Relationship curves; (b) RMSE of different algorithms relative to the number of receiving array elements. X Relationship curves; (c) shows the running time of different algorithms relative to the number of receiving array elements;

[0111] Figure 11 The graphs show the relationship between different algorithms and sparsity, along with their running times; where (a) represents the RMSE of different algorithms relative to sparsity. θ (a) Relationship curve; (b) RMSE of different algorithms relative to sparsity. X Relationship curves; (c) shows the running time of different algorithms relative to sparsity;

[0112] Figure 12 The graphs show the relationship between different algorithms and the number of grid nodes, along with their running times; where (a) represents the RMSE of different algorithms relative to the number of grid nodes. θ (a) Relationship curve; (b) RMSE of different algorithms with respect to the number of grid nodes X Relationship curves; (c) represents the running time of different algorithms relative to the number of grid nodes. Detailed Implementation

[0113] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0114] This embodiment provides an off-grid spatial alternating sparse Bayesian compressed beamforming method. By introducing the deviation between the actual angle and the predefined grid nodes, a multi-snapshot off-grid beamforming model is established. The joint distribution of latent variables is calculated using a multi-level structure and variational Bayesian learning. The variables are iteratively updated using the spatial alternation method, thereby effectively compensating for grid adaptation errors and improving the accuracy of angle and complex signal estimation while ensuring the efficiency of iterative calculation.

[0115] Example 1

[0116] Combination Figures 1-12 This invention proposes a method for alternating sparse Bayesian compressed beamforming in a grid space, the method specifically comprising:

[0117] Step 1: Based on the beamforming model, construct an off-grid beamforming model including DOA angle compensation based on acoustic echo measurement data;

[0118] Step 1 specifically involves:

[0119] Step 1.1: Without loss of generality, assuming the receiving array consists of M uniformly arranged arrays with a spacing of d, the model for receiving acoustic echo measurement data is represented as follows:

[0120] y = Ax + n (1)

[0121] in For acoustic echo measurement data vectors, It is a complex signal vector over a predefined angle θ, where θ = [θ1, θ2, ..., θ] N ] T , It is a Gaussian white noise vector, where N is the number of angular meshes. It is an array manifold matrix at a predefined angle, denoted as A(θ)=[a(θ1),a(θ2),…,a(θ)]. N )],in:

[0122] a(θ k )=[1,exp(-j2πfτ k ),···,exp(-j2πf(M-1)τ k )] T (2)

[0123] in,

[0124]

[0125] c represents the signal propagation speed; therefore, the model is given according to the snapshot order as follows:

[0126] y l =Axl +n l ,l=1,2,···,L (4)

[0127] Where l is the snapshot number; taking each snapshot vector as a column, the multi-snapshot model is obtained as follows:

[0128] Y = AX + N (5)

[0129] in, For multiple snapshots of acoustic echo measurement data; X = [x1, x2, ..., x L [n1, n2, ..., n] represents the target source signal to be estimated from multiple snapshots; N = [n1, n2, ..., n] L Let the signal be Gaussian white noise, and the elements in the matrix be independent, satisfying the following condition: Where n ij For the element in the i-th row and j-th column, This represents a complex Gaussian distribution with zero mean and precision ρ.

[0130] Step 1.2: Apply a first-order Taylor series to the guiding vector a(θ) k Expanding, we get:

[0131]

[0132] Where υ represents the actual target source DOA perspective. Represents the node closest to the true angle, and the vector:

[0133]

[0134] Therefore, we can define:

[0135] B=[b(θ1),…,b(θ N (8)

[0136]

[0137]

[0138] Where, diag(β) represents a diagonal matrix with vector β as its diagonal element; r = θ2 - θ1 represents the spacing between the partition nodes; clearly, β represents the compensation vector for the introduced correction angle, for a specific When the true angle υ exists, there is Otherwise, the corresponding element β n =0; This yields the modified off-grid beamforming model:

[0139]

[0140] in, This is the corrected off-grid manifold matrix.

[0141] Step 2: Based on the constructed off-grid beamforming model including DOA angle compensation, give the likelihood function and define the prior distribution;

[0142] Step 2 specifically involves:

[0143] Step 2.1: Assuming the target sources are independent, the nth predefined target source follows a complex Gaussian distribution with a mean of 0:

[0144]

[0145] Where λ=[λ1,λ2,…,λ N ] T It is the precision hyperparameter vector, I L It is an L×L identity matrix. To enhance population sparsity, λ is used at different snapshots. n They should remain the same;

[0146] Step 2.2: In the second layer of the Bayesian structure diagram, assume that the precision variables are independent and simultaneously follow a gamma distribution:

[0147]

[0148] Where Γ(a,b) represents the gamma distribution, with a and b representing the shape and scale parameters, respectively; in the third layer of the Bayesian structure diagram, given the hyperparameter vector γ = [γ1,γ2,…,γ...] N ] T The elements satisfy independent and equal distribution, that is:

[0149]

[0150] To ensure the randomness of γ, the given parameters are a0 = b0 = 10. -6 ;

[0151] Step 2.3: Based on the modified off-grid beamforming model, the expression for the likelihood function can be obtained:

[0152]

[0153] Where the noise accuracy ρ follows a gamma distribution:

[0154] p(ρ)=Γ(ρ|c0,d0) (16)

[0155] Wherein, the given parameter c0 = d0 = 10 -6 .

[0156] Step 3: Establish the joint probability density function associated with the Bayesian structure diagram, and derive the approximate posterior distribution of the target source, i.e., the sound source signal X;

[0157] Step 3 specifically involves:

[0158] Step 3.1: Use the set Θ = {X, λ, γ, ρ, β} to represent the latent variables, and for ease of expression, use Θ\X to represent the set of all other variables except variable X, i.e., {λ, γ, ρ, β}, and so on for other cases;

[0159] According to the Bayesian structure diagram, the joint probability function distribution is as follows:

[0160] p(Y,Θ)=p(Y|X,ρ,β)p(X|λ)p(λ|γ)p(γ)p(ρ)p(β) (17)

[0161] Assume β is in Uniformly distributed within, utilizing its non-informative and bounded nature, it satisfies:

[0162]

[0163] According to the variational method, the approximate true posterior satisfies the following independence assumptions:

[0164]

[0165] Therefore:

[0166]

[0167] Substituting (12) to (16) into (17) yields the logarithmic form of the joint probability function:

[0168]

[0169] Among them, ||·|| F Denotes the Frobenius norm;

[0170] Step 3.2: According to the variational method, the expectation step in the expectation-maximization algorithm requires calculating the target source x. n The approximate posterior logarithm:

[0171]

[0172] in,

[0173]

[0174]

[0175] <ρ>=E q(ρ) [ρ] (25)

[0176] The expectation operator is abbreviated as <·>, and tr[·] represents the trace operation. express The nth column vector, Remove The matrix after that is denoted as X (removing the nth row vector) The matrix after that is denoted as

[0177] According to equation (22), the target source signal distribution q(x) n The distribution follows a Gaussian distribution, with variance and mean as follows:

[0178]

[0179] Step 4: Use the spatial alternation method to adjust the hyperparameter λ n γ n ρ and β are updated iteratively;

[0180] The hyperparameter λ n The update is as follows:

[0181] First update λ n Collective (21) all containing λ n The approximate posterior of the terms is:

[0182]

[0183] It can be obtained in:

[0184]

[0185] hyperparameter γ n The update is as follows:

[0186] Update γ n :

[0187]

[0188] Therefore, there is in,

[0189]

[0190] The hyperparameter ρ update is specifically as follows:

[0191] Updating the noise parameter ρ, we get:

[0192]

[0193] The hyperparameter β update is specifically as follows:

[0194] To update the angle compensation vector β, the following expectation needs to be calculated, while retaining terms related to β:

[0195]

[0196] Therefore, the update formula for β is:

[0197]

[0198]

[0199] Where, β -n This represents the nth element β excluding β. n The newly formed vector; Λ nn Represents the nth element on the diagonal of matrix Λ; (Λ n ) -n Let represent the vector formed by removing the nth element from the nth column vector of matrix Λ, and:

[0200]

[0201]

[0202] in, This represents the operator for taking the real part. Although structurally the matrix Λ is a positive semi-definite matrix, due to μμ H The rank is 1, and in most cases the target source to be estimated is sparse, and the matrix Λ is a singular matrix in most cases.

[0203] Step 5: Check convergence according to the predefined tolerance. End the iteration when the convergence condition is met or the maximum number of iterations is reached.

[0204] The performance of the proposed method was verified using publicly available data from SwellEx-96 acoustic experiments. Two sound sources were used in the experiments: one deep source and one shallow source. This invention focuses on analyzing the shallow source. The method described in this invention selects six frequencies of radiation from the shallow sound source: 109, 127, 145, 163, 198, and 232 Hz. Seven methods were employed to process data from 87 snapshots: conventional beamforming (CBF), spatial alternation method SAVE-MSBL without off-grid techniques, the proposed OGSA-MSBL, variational sparse Bayesian learning VSBL, off-grid method OGSBI, inverse-free fast implementation IF-SBL, and C-BCS. Figures 2-7As shown, SAVE-MSBL, OGSA-MSBL, VSBL, OGSBI, IF-SBL, and C-BCS have significant advantages in resolution improvement, especially IF-SBL, OGSA-MSBL, and SAVE-MSBL, and these three methods are more outstanding in noise suppression. However, IF-SBL does not always achieve good performance at all frequencies, such as 232Hz. Theoretically, OGSA-MSBL has higher accuracy than SAVE-MSBL, but the difference is not significant in this comparison. The main reason is that the DOA angle offset vector β is too small, or some non-zero terms of β correspond to smaller terms of the signal source, which have little effect on the recovery matrix, resulting in insignificant compensation.

[0205] Example 2

[0206] This example verifies the performance of OGSA-MSBL through simulation experiments, comparing six Bayesian compressed beamforming methods: SAVE-MSBL, OGSA-MSBL, VSBL, OGSBI, IF-SBL, and C-BCS. OGSA-MSBL is the improved method proposed in this invention. In the simulation, the accuracy of various algorithms in angle estimation and complex signal estimation is analyzed under different snapshot numbers, SNR, number of sensors, sparsity, and grid points. The relative mean square error (RMSE) is used to measure these accuracy values, defined as follows:

[0207] (1) DOA Angle Estimation RMSE θ

[0208]

[0209] Where, θ and represents the actual target source angle and the DOA estimation result, respectively. T represents the number of Monte Carlo simulations, and L represents the number of snapshots.

[0210] (2) Target source signal estimation RMSE X

[0211]

[0212] Among them, X and These represent the actual target source signal and the estimation result, respectively.

[0213] according to Figure 8The simulation results show that the estimation accuracy of grid-based methods, including SAVE-MSBL, VSBL, IF-SBL, and C-BCS, is not high, especially when the target source deviates from the grid points. Off-grid methods, however, achieve better performance in angle and complex signal estimation. With an increasing number of snapshots, the accuracy of OGSA-MSBL approaches that of OGSBI. However, in terms of runtime, OGSA-MSBL is significantly faster than OGSBI.

[0214] Figure 9 The estimation results are presented under different signal-to-noise ratio (SNR) conditions. The recovery performance of all methods is enhanced at higher SNRs. It can be seen that OGSA-MSBL is close to OGSBI in terms of angle and amplitude estimation accuracy, but OGSA-MSBL still has high computational efficiency under low SNR conditions.

[0215] Figure 10 The relationship between recovery performance and the number of array elements is given when the signal-to-noise ratio (SNR) is 20 dB. From... Figure 10 (a) and Figure 10 (b) Results show that the RMSE of OGSA-MSBL deteriorates when the number of array elements is small. This indicates that the error caused by the assumption of uncorrelated target source vectors introduced in the spatial alternation method is highly sensitive to the number of array elements. When the number of array elements increases, OGSA-MSBL shows a significant performance advantage, with accuracy comparable to OGSBI and a faster running speed.

[0216] Figure 11 This indicates that all algorithms achieve high accuracy in DOA estimation at low sparsity. Furthermore, off-grid methods generally outperform grid-based methods. When the number of target sources is large, the complex signal estimation error of the OGSA-MSBL algorithm is significantly lower than that of other algorithms.

[0217] Figure 12 The relationship between the algorithm estimation performance and the number of defined grid points is presented. Results show that the DOA estimation accuracy of all six algorithms improves with increasing grid number. Furthermore, from... Figure 12 (b) It can be seen that OGSA-MSBL has a significant advantage in target source signal estimation when the number of grid cells is small. Figure 12 (c) It can be seen that when the number of grids is large, the runtime of OGSBI increases rapidly, while OGSA-MSBL has a lower computational cost while maintaining recovery performance.

[0218] This invention proposes an electronic device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the off-grid spatial alternating sparse Bayesian compressed beamforming method.

[0219] This invention proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the off-grid spatial alternating sparse Bayesian compressed beamforming method.

[0220] The memory in this application embodiment can be volatile memory or non-volatile memory, or it can include both volatile and non-volatile memory. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as static random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDRSDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous linked dynamic random access memory (SLDRAM), and direct rambus RAM (DR RAM). It should be noted that the memory used in the methods described in this invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0221] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. The available media may be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., high-density digital video discs (DVDs)), or semiconductor media (e.g., solid-state disks (SSDs)).

[0222] In implementation, each step of the above method can be completed by integrated logic circuits in the processor's hardware or by instructions in software. The steps of the method disclosed in the embodiments of this application can be directly implemented by a hardware processor, or by a combination of hardware and software modules in the processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, detailed descriptions are omitted here.

[0223] It should be noted that the processor in the embodiments of this application can be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method embodiments can be completed by the integrated logic circuitry in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this application can be directly embodied as being executed by a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads the information in the memory and, in conjunction with its hardware, completes the steps of the above methods.

[0224] The above provides a detailed description of the off-grid spatial alternating sparse Bayesian compressed beamforming method proposed in this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. An off-grid space-time alternating sparse Bayesian compressive beamforming method, characterized in that, The method specifically comprises: Step 1: on the basis of a beam forming model, constructing an off-grid beam forming model containing DOA angle compensation according to sound echo measurement data; Step 2: giving a likelihood function according to the constructed off-grid beam forming model containing DOA angle compensation, and defining a prior distribution; Step 3: establishing a joint probability density function associated with a Bayesian structure diagram, and deducing an approximate posterior distribution of a target source, i.e. a sound source signal X; Step 4: Iterative update of hyperparameters λ, γ, ρ, and β using the space-alternating method n n Step 4: Iterative update of hyperparameters λ, γ, ρ, and β using the space-alternating method n n Step 4: Step 5: checking convergence according to a predefined tolerance, and ending iteration when a convergence condition is met or a maximum iteration number is reached; The hyperparameter λ n The updating is in particular: First update λ n Collect all terms in the log form of the joint probability function that contain λ n The approximate posterior is: obtained wherein: The hyper-parameter γ n The updating is specifically: Update gamma n : Thus there is wherein, The super parameter ρ updating is specifically as follows: The noise parameter ρ is updated to obtain: The super parameter β updating is specifically as follows: In order to realize the angle compensation vector β updating, the following expectation needs to be calculated, and the terms related to β are retained: Therefore, the updating formula of β is as follows: where β -n denotes the nth element of the vector β n the new vector formed; Λ nn denotes the nth element of the diagonal of the matrix Λ; (Λ n ) -n denotes the vector formed by removing the nth element of the nth column vector of the matrix Λ, and: wherein denotes the real part operator.

2. The method of claim 1, wherein, The step 1 is specifically as follows: Step 1.1: assuming that a receiving array is an equal-interval array containing M uniformly arranged equal-interval arrays with a spacing d, and a model for receiving sound echo measurement data is represented as: y = Ax + n (1) wherein is a vector of acoustic echo measurement data, is a vector of complex signals over a predefined angle θ, θ = [θ1, θ2, …, θ N ] T , is a vector of Gaussian white noise, N is the number of divided angle grids, is a matrix of array manifold over a predefined angle, denoted as A(θ) = [a(θ1), a(θ2), …, a(θ N )], wherein: a(θ k ) = [1, exp(-j2πfτ k ),···, exp(-j2πf(M-1)τ k )] T (2) Wherein, c is the propagation speed of a signal; therefore, the model is given according to a snapshot order as: y l = Ax l + n l , l = 1,2, ···, L (4) Wherein, l is a snapshot label; taking each snapshot vector as a column, a multi-snapshot model is obtained as: Y = AX + N (5) wherein, is the multi-shot acoustic echo measurement data; X = [x1, x2,..., x L is the multi-shot target source signal to be estimated; N = [n1, n2,..., n L is assumed to be a Gaussian white noise signal, with elements in the matrix being independent of each other, satisfying wherein n ij is the element in the i-th row and j-th column, denotes a complex Gaussian distribution with zero mean and precision p; Step 1.2: Expanding the steering vector a(θ k ) using a first order Taylor series gives: where υ is the true target source DOA angle, θ nk represents the node closest to the true angle, and the vector: Therefore, the following is defined: B = [b(θ1),..., b(θ N )] (8) where diag(β) denotes a diagonal matrix with vector β as its diagonal elements; r = θ2- θ1denotes the distance between the divided nodes; obviously, β denotes the compensation vector of the introduced correction angle, and for a specific When the real angle υ exists, there is Otherwise, the corresponding element β n = 0; thus, the corrected off-grid beamforming model is obtained: wherein is the modified off-lattice manifold matrix.

3. The method of claim 2, wherein, The step 2 is specifically as follows: Step 2.1: in the case that target sources are independent of each other, the nth predefined target source is given to be subject to a complex Gaussian distribution with a mean value of 0: where λ = [λ1, λ2,..., λN]Tis the precision vector, and N ] T is the precision hyperparameter vector, I L is the L x L identity matrix, and to enhance the sparsity of the population, λ n should be kept the same across different snapshots. Step 2.2: in the second layer of the Bayesian structure diagram, it is assumed that precision variables are independent and subject to a gamma distribution at the same time: where Γ(a, b) denotes a gamma distribution with shape parameter a and scale parameter b; at the third layer of the Bayesian structure graph, given the hyperparameter vector γ = [γ1, γ2, …, γN] T each element of which satisfies an independent equal distribution, i.e.: where the given parameters a0 = b0 = 10 -6 ; Step 2.3: the expression of a likelihood function is obtained according to the modified off-grid beam forming model: Wherein, the noise precision ρ is subject to a gamma distribution: p(ρ) = Γ(ρ|c0,d0) (16) where the given parameters are c0= d0= 10 -6 .

4. The method of claim 3, wherein, The step 3 is specifically as follows: Step 3.1: using a set Θ = {X, λ, γ, ρ, β} to represent hidden variables, and in order to facilitate expression, using Θ\X to represent a set of all other variables except the variable X, i.e. {λ, γ, ρ, β}, and other cases are similar; According to the Bayesian structure diagram, the joint probability function distribution is as follows: p(Y, Θ) = p(Y|X, ρ, β) p(X|λ) p(λ|γ) p(γ) p(ρ) p(β) (17) Assume that β is uniformly distributed within and using its non-informativeness and boundedness, we have that: According to the variational method, the approximate true posterior satisfies the following independent assumption: Therefore, there is: Substituting (12) to (16) into (17) obtains a logarithmic form of the joint probability function: where || · || F denotes the Frobenius norm; Step 3.2: The step of computing the expectation in the expectation-maximization algorithm requires computing the log of the approximate posterior of the target source x n given the data y. Wherein, The desired operator is simply written as <·>, and tr[·] denotes the trace operation, denotes the nth column vector of X, The matrix obtained by removing the nth column vector of X is denoted by The matrix obtained by removing the nth row vector of X is denoted by The matrix obtained by removing the nth row vector of X is denoted by According to equation (22), the target source signal distribution q(x n ) is subject to a Gaussian distribution with variance and mean 5.An electronic device comprising a memory and a processor, the memory storing a computer program, wherein, The processor realizes the steps of the method of any one of claims 1 to 4 when executing the computer program.

6. A computer readable storage medium for storing computer instructions, characterized in that, The computer instructions realize the steps of the method of any one of claims 1 to 4 when executed by the processor.

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