A block-sparse bayesian learning robust matching field positioning method based on environmental disturbance

Abstract

The application discloses a block sparse Bayesian learning robust matched field localization method based on environmental disturbance and belongs to the field of underwater acoustic array signal processing. A plurality of groups of environmental parameters are randomly sampled in an uncertain environmental parameter space, a corresponding normalized copy field vector is calculated for each candidate position in a search area, and an environmental disturbance constraint matrix is constructed. Singular value decomposition is performed on the environmental disturbance constraint matrix, and a main left singular vector is extracted to represent the first-order and second-order statistical characteristics of the random environmental parameters. A block dictionary matrix with multiple constraints is constructed, a block sparse observation model is established in combination with array multi-shot receiving data, a matched field localization problem is converted into a block multi-shot sparse signal recovery problem, a block sparse Bayesian learning model is established, two kinds of block internal correlation structures, namely a simple correlation model and an autoregressive correlation model, are respectively constructed, and sound source localization processing is realized. The application has strong localization robustness under the condition of environmental parameter mismatch.

Description

Technical Field

[0001] This invention relates to a robust matching field localization method based on block sparse Bayesian learning under environmental perturbation, belonging to the field of underwater acoustic array signal processing. Background Technology

[0002] Matched field processing (MRP) is an important method for sound source localization that utilizes the spatial coherence structure of the acoustic field in a marine waveguide. Compared with traditional beamforming methods, MRP can fully utilize multipath propagation information in the marine environment, offering higher localization accuracy and better long-range detection capabilities. Therefore, it has broad application prospects in underwater sound source localization, target tracking, and environmental inversion. Traditional MRP localization methods calculate the copy field at different candidate locations using an acoustic propagation model and match the measured received acoustic field of the array with the copy field to estimate the sound source location. However, these methods are highly dependent on the accuracy of environmental parameters, such as water depth, sound velocity profiles, and seabed acoustic parameters. When the actual marine environment changes dynamically or there are estimation errors in environmental parameters, environmental mismatch can easily occur between the copy field and the measured acoustic field, leading to a significant decrease in localization performance.

[0003] In recent years, compressed sensing theory has provided a new approach to overcome the performance bottleneck of traditional matched-field processing. Matched-field localization methods based on compressed sensing utilize the sparsity of the spatial distribution of sound sources, transforming the localization problem into a sparse signal recovery problem, thereby improving resolution and noise resistance to some extent. Among these methods, sparse Bayesian learning has attracted widespread attention due to its insensitivity to sparsity parameters, high resolution, and strong robustness. However, existing matched-field localization methods based on sparse Bayesian learning typically still construct dictionary matrices based on fixed prior environmental parameters, meaning their performance remains highly dependent on the accuracy of the environmental model. When the marine environment undergoes dynamic changes or environmental parameters are uncertain, the constructed dictionary matrix inevitably mismatches with the real sound field, leading to a decline in sparse reconstruction performance and even localization failure. Therefore, how to construct a more adaptable compressed sensing method under environmental mismatch conditions has become an important issue in current underwater sound source localization research. Summary of the Invention

[0004] The purpose of this invention is to provide a robust matched-field localization method based on block sparse Bayesian learning under environmental perturbation, in order to address the problem that existing compressed sensing matched-field localization methods are prone to environmental mismatch and degraded localization performance under dynamic and uncertain conditions of marine environmental parameters.

[0005] To solve the above-mentioned technical problems, the present invention includes the following steps:

[0006] Step 1: Input array parameters, measured multi-snap data of the array, search area parameters, and the uncertainty range of marine environmental parameters. Preprocess the array received data to obtain the array multi-snap received data matrix at the target frequency. The array parameters include the number of array elements, element depth, array geometry, and sampling frequency; the search area parameters include the distance search range, depth search range, and discrete grid interval; the uncertainty range of marine environmental parameters includes one or more of water depth, seabed parameters, and sound velocity profile parameters. Obtain the target frequency information of the sound source signal through time-frequency analysis and other techniques to form a frequency domain multi-snap received data matrix.

[0007] Step 2: Based on historical sea trial data, environmental statistics, or empirical environmental parameter ranges, establish an uncertain environmental parameter space, and randomly sample multiple sets of environmental parameter vectors within this space. For each candidate location within the search area, calculate the normalized copy field vector corresponding to each set of random environmental parameters. The multiple sets of normalized copy field vectors corresponding to the same candidate location constitute an environmental perturbation constraint matrix. Perform singular value decomposition on the environmental perturbation constraint matrix corresponding to each candidate location, and extract the previous... The principal left singular vectors corresponding to the maximal singular values ​​are used to characterize the first and second-order statistical features of the stochastic environment parameters. Specifically, the first left singular vector is used to characterize the principal first-order statistical features of the stochastic environment parameters, while the remaining left singular vectors are used to characterize the principal second-order statistical features of the stochastic environment parameters.

[0008] The specific formula is: for candidate positions Corresponding environmental disturbance constraint matrix Perform singular value decomposition:

[0009] ,

[0010] In the formula, It is the environmental disturbance matrix. and These are left singular and right singular matrices, respectively. It is a diagonal matrix, and the elements on its diagonal are non-negative singular values. (Take the first...) The left singular vectors corresponding to the maximal singular values ​​constitute the principal left singular vector matrix. .

[0011] Step 3: Use the principal left singular vector matrix corresponding to each candidate position within the search area as a dictionary block, and concatenate them column-wise to construct a block dictionary matrix with multiple constraints. The block dictionary matrix consists of the principal left singular vector matrices corresponding to all candidate positions within the search area, with each candidate position corresponding to a matrix of principal left singular vectors. A dictionary block consisting of a main left singular vector.

[0012] The block dictionary matrix is ​​represented as follows:

[0013] ,

[0014] In the formula, The total number of candidate locations after discretizing the search region, where each candidate location corresponds to a [number of locations]. A dictionary block consisting of a main left singular vector.

[0015] Compared with traditional dictionaries consisting of only a single copy of the field vector, the block dictionary matrix constructed in this invention can simultaneously represent the main subspace information of candidate positions under environmental perturbation conditions, thus exhibiting stronger environmental adaptability and better mismatch robustness.

[0016] Step 4: Based on the block dictionary matrix and the array multi-shot received data matrix, establish a multi-shot block sparse observation model, transforming the matched field localization problem into a block multi-shot sparse signal recovery problem. In underwater sound source localization, the actual number of sound sources in the search area is usually much smaller than the number of search grids, therefore the spatial distribution to be estimated is sparse. Based on the block dictionary matrix constructed in Step 3, establish a multi-shot block sparse observation model, where the block sparse signal matrix to be estimated is divided into blocks, and each block structure contains... There are 100 elements, and only a few blocks are non-zero blocks, with different snapshots sharing the same block support. Therefore, the matching field localization problem is transformed into a block-multiple-snapshot sparse signal recovery problem.

[0017] Step 5: Establish a block sparse Bayesian learning model. Assume that the block sparse signal to be estimated satisfies the block structure complex Gaussian prior distribution, and solve the block sparse signal matrix by iteratively updating the block sparse control parameters, noise variance, and intra-block correlation matrix.

[0018] The noise variance is iteratively updated based on the system residual energy.

[0019] ,

[0020] In the formula, It is the cross-spectral density matrix of the received signal. The number of array elements It is the covariance matrix of the marginal distribution of the observed data. It is a block diagonal matrix. It is a copy field dictionary matrix.

[0021] Within the block-sparse Bayesian learning framework, it is assumed that the signal to be estimated and the noise in different snapshots are independent of each other, and that each block structure follows a zero-mean complex Gaussian prior distribution. The block sparsity control parameter is a non-negative hyperparameter used to control the sparsity of the corresponding block. The noise is modeled as zero-mean complex Gaussian white noise, and the marginal distribution of the observed data follows a zero-mean complex Gaussian distribution.

[0022] By constructing a joint log-likelihood function, the block sparse control parameters are updated, and the noise variance is updated based on the system residual energy. The noise update formula does not require estimation of the source sparsity; when the source sparsity is known and the source signal is determined only by a few dominant blocks, the noise variance can also be updated using an approximate update rule composed of the sub-dictionary matrices corresponding to the dominant blocks.

[0023] Furthermore, the intra-block correlation model in step 5 includes simple correlation model and autoregressive correlation model.

[0024] In the simple correlation model, all intra-block correlation matrices are fixed as identity matrices, meaning that the components within a block are considered approximately independent. This model has a simple structure and avoids overfitting under conditions of low signal-to-noise ratio or few snapshots, making it the first robust block sparse Bayesian learning processor.

[0025] In the autoregressive correlation model, a parametric averaging strategy is employed to ensure that all blocks share the same covariance structure, and the elements within each block are modeled as a first-order autoregressive process, thus obtaining the intra-block correlation matrix with a conjugate Toeplitz structure. The autoregressive coefficients can be estimated based on the average of the main diagonal and secondary diagonal elements of the covariance matrix. This model can explicitly utilize intra-block correlation structure information and can constitute a second type of robust block sparse Bayesian learning processor.

[0026] Step 6: Determine the sound source location based on the obtained block sparse solution and output the matching field localization result.

[0027] After completing the iterative solution in step 5, the sound source location is determined based on the sparse control parameters corresponding to each block. For the single-source case, the candidate location corresponding to the largest sparse control parameter is taken as the sound source location estimation result. For the multi-source case, the locations corresponding to multiple significant non-zero blocks are selected as the multi-target localization result.

[0028] Compared with the prior art, the advantages of the present invention are as follows:

[0029] This invention reduces dependence on single prior environmental parameters by constructing an environmental perturbation constraint matrix and extracting its principal left singular vector subspace, and then using this subspace to construct a block dictionary matrix. Furthermore, by combining a multi-buzzer block sparse observation model and block sparse Bayesian learning, robust matching field localization under environmental mismatch conditions is achieved. This invention is applicable to underwater sound source localization scenarios where environmental parameters are uncertain and the number of buzzers is limited. Attached Figure Description

[0030] Figure 1 This is a flowchart of a robust matching field localization method based on block sparse Bayesian learning under environmental perturbation according to the present invention.

[0031] Figure 2This is a schematic diagram of the environment and the space of uncertain environmental parameters in the demonstration experiment of this invention;

[0032] Figure 3 This refers to the correct positioning probability of the four processors under different signal-to-noise ratios when the number of snapshots is 20 in the embodiment.

[0033] Figure 4 This represents the correct positioning probability of the four processors under different signal-to-noise ratios when the number of snapshots is 40 in the embodiment. Detailed Implementation

[0034] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0035] like Figure 1 The diagram shows a flowchart of a robust matched-field localization method based on block sparse Bayesian learning for environmental perturbation, according to the present invention. This method first constructs an environmental perturbation constraint matrix under conditions of environmental uncertainty, and extracts the main environmental perturbation subspace through singular value decomposition, thereby constructing a block dictionary matrix. Then, a multi-buzzer block sparse observation model is established, and a block sparse Bayesian learning algorithm is used to iteratively solve for the block sparse signal. Finally, the sound source location is determined based on the block sparse solution. The specific implementation includes the following steps:

[0036] Step 1: Input parameters and perform preprocessing.

[0037] The input parameters include array parameters, array multi-shot measured data, search area parameters, and the uncertainty range of environmental parameters. Array parameters include the number of array elements, element depth, array geometry, and sampling frequency; search area parameters include the distance search range, depth search range, and discrete grid interval; and the uncertainty range of environmental parameters includes the uncertain intervals of water depth, seabed parameters, and sound velocity profile parameters.

[0038] The measured array data is preprocessed, and the target frequency information of the sound source signal is obtained through techniques such as time-frequency analysis, ultimately forming a frequency domain multi-snapshot received data matrix. ,in For the first A quick snapshot 3D array observation vector, This represents the number of snapshots.

[0039] Step 2: Construct the environmental perturbation constraint matrix and perform singular value decomposition to extract the first-order and second-order statistical features of the random environmental parameters.

[0040] An uncertain environmental parameter space is established based on historical sea trial data, environmental statistics, or empirical environmental parameter ranges. Monte Carlo random sampling is then used to generate the uncertain environmental parameter space. Group random environment parameter vector: For any candidate location within the search area The sound propagation model is used to calculate its first... Group random environment parameters The copied field vector is then normalized to obtain... The corresponding candidate positions The normalized copy field vectors are combined column-wise to form the environmental perturbation constraint matrix:

[0041] ,

[0042] In the formula, It is the environmental perturbation matrix, reflecting the candidate locations under random perturbation of environmental parameters. The set of changes in the copy field.

[0043] Under moderate environmental uncertainty, the column space of the environmental perturbation constraint matrix typically has an approximately low-rank structure. Singular value decomposition of the environmental perturbation constraint matrix only requires retaining the first few columns. The 100 maximal singular values ​​and their corresponding left singular vectors can effectively characterize the main change patterns of environmental disturbances, such as:

[0044] ;

[0045] In the formula, and These are left singular and right singular matrices, respectively. It is a diagonal matrix, and the elements on its diagonal are non-negative singular values. (Take the first...) The left singular vectors corresponding to the maximal singular values ​​constitute the principal left singular vector matrix. .

[0046] In this invention, Zhang Cheng's subspace reflects the most significant direction of change in the copy field under environmental disturbances. The first left singular vector usually corresponds to the strongest dominant mode, mainly reflecting the first-order statistical principal characteristics; subsequent left singular vectors mainly characterize the main second-order statistical changes of environmental disturbances.

[0047] Step 3: Construct a block dictionary matrix with multiple constraints.

[0048] For all candidate locations within the search area The corresponding principal left singular vector matrices are obtained respectively. Each candidate position Treat it as a dictionary block, and concatenate it column-wise to obtain a block dictionary matrix:

[0049] ,

[0050] In the formula, , This represents the total number of candidate locations after discretizing the search region. At this point, each candidate location no longer corresponds to a single copy of the field dictionary, but rather to a dictionary composed of... A block structure composed of main left singular vectors. This block structure can simultaneously carry the main subspace information of the location under environmental perturbation conditions, thus exhibiting better environmental robustness compared to traditional dictionaries.

[0051] Step 4: Establish a multi-fast block sparse observation model.

[0052] In underwater sound source localization, the actual number of sound sources within the search area is usually much smaller than the number of search grids, thus the spatial distribution to be estimated is sparse. Based on the block dictionary matrix constructed in step 3, the following multi-bucket sparse observation model can be established:

[0053] ,

[0054] In the formula, For multi-shot data receiving matrix, For block dictionary matrix, Let be the sparse signal matrix of the block to be estimated. This is the noise matrix. For each column vector... It can be represented as:

[0055] ,

[0056] In the formula, each block structure All include 1 element, and Only one in each block Each block is a non-zero block. There are only a few non-zero blocks, and the same block support is shared across multiple snapshots.

[0057] Therefore, the matching field localization problem is transformed into a multi-block sparse signal recovery problem.

[0058] Step 5: Establish a block sparse Bayesian learning model and solve iteratively.

[0059] Within the block sparse Bayesian learning framework, assuming different snapshots and They are mutually independent, and the first Block structure If the prior distribution satisfies a zero-mean complex Gaussian distribution, then:

[0060]

[0061] In the formula, and These are unknown hyperparameters. It is a non-negative parameter used to control Block sparsity. When At that time, the first Each block becomes zero. It is a positive definite matrix used to capture the first... The related structure of each block.

[0062] at this time, The prior can be written as:

[0063] ,

[0064] In the formula, It is a block diagonal matrix.

[0065] The noise is modeled as zero-mean complex Gaussian white noise:

[0066] ,

[0067] In the formula, express An identity matrix of order 1. Define the parameter set. When the parameters are estimated and hour, The maximum a posteriori estimate can be obtained from the posterior mean.

[0068] Easy to prove, observation data The marginal distribution of follows a zero-mean complex Gaussian distribution, with the following:

[0069] ,

[0070] In the formula, the covariance matrix Therefore, the joint log-likelihood function under different snapshots can be written as:

[0071] ,

[0072] In the formula, It is a parameter Irrelevant constant terms.

[0073] The sparse control parameters can be obtained by differentiating the joint log-likelihood function under different snapshot conditions. Update expression:

[0074] ,

[0075] Based on system residual energy estimation, noise variance The update formula is:

[0076] ,

[0077] In the formula, It is the cross-spectral density matrix of the received signal, and the noise variance update process does not require pre-setting the source sparsity. If the sparsity of the sound source is known. ,noise The update rule can be further approximated as:

[0078] ,

[0079] In the formula, It consists of a complete dictionary matrix In A submatrix consisting of columns corresponding to each dominant block. for The generalized Moore-Penrose inverse.

[0080] In this invention, the following two types of intra-block correlation models can be constructed:

[0081] (a) Simple correlation model

[0082] Let all intra-block correlation matrices be fixed as identity matrices: This model is used to describe the case where the components within a block are approximately independent. It has a simple structure and avoids overfitting under conditions of low signal-to-noise ratio or few snapshots. It can constitute the first robust block sparse Bayesian learning processor.

[0083] (b) Autoregressive correlation model

[0084] A parametric averaging strategy is adopted, meaning that all blocks share the same covariance structure. .at this time, The update formula is:

[0085] ,

[0086] Simultaneously, the elements within the block are modeled as a first-order autoregressive process to characterize intra-block correlations. At this point, the covariance matrix... It has a conjugate Toeplitz matrix structure of the following form:

[0087] ,

[0088] In the formula, These are the autoregressive coefficients. For matrix The average of the elements on the main diagonal. For matrix The average value of the second diagonal elements. This model can explicitly utilize intra-block correlation structure information, and can constitute a second type of robust block sparse Bayesian learning processor.

[0089] Step 6: Output the sound source location based on the block sparse solution.

[0090] After completing the iteration in step 5, the sparsity control parameters corresponding to each block can be used as a basis. Determine the location of the sound source. For a single source, the following can be considered:

[0091] ,

[0092] This is the result of sound source location estimation. For multi-source cases, the locations corresponding to multiple significant non-zero blocks can be selected as the multi-target localization results.

[0093] The following example of a shallow sea matching field positioning method illustrates the processing procedure of the present invention.

[0094] Figure 2 A general mismatch benchmark scenario provided by Workshop'93 is presented. Almost all environmental parameters in this scenario are only roughly known, including water depth, sound velocity profile, and sediment parameters. The model is a typical three-layer downward-refracting shallow underwater acoustic channel, consisting of a water column, sediment, and a bottom half-space. The receiving array is a 20-element vertical linear array, with elements uniformly distributed across a depth range of 5 m to 100 m and spaced 5 m apart. The sound source emits a narrowband signal at a frequency of 250 Hz, located at a depth of 70 m and a horizontal distance of 5.9 km from the receiving array. The range search is... The search step size is 100 m, and the depth search range is... The search step size is 5 m. Under this partitioning, a total of 861 candidate sound source locations were generated.

[0095] To evaluate the effectiveness of each processor, we use the Probability of Correct Location (PCL) metric to quantify performance. Running For sub-independent Monte Carlo simulations, the PCL calculation method is as follows:

[0096] ,

[0097] In the formula, and These represent the actual distances to the sound source. and depth The estimated value. and These represent the permissible deviations in the distance and depth directions, respectively, which are taken as 200m and 5m here. In each Monte Carlo simulation, the environmental parameters used to generate the simulation signal are all from... Figure 2 The parameters are obtained by random sampling in the space of uncertain parameters shown.

[0098] Figure 3 and Figure 4The correct localization probability of four processors was evaluated under different signal-to-noise ratios (SNRs) and snapshot numbers of 20 and 40. 300 independent Monte Carlo simulations were performed for each SNR condition. For the MV-EPC and two BSBL processors, the previous... The constraint space was reconstructed using the order maximal singular values ​​and singular vectors. Results showed that, under both snapshot number conditions, when the signal-to-noise ratio (SNR) was above -4 dB, the PCL performance of the two BSBL processors outperformed the traditional MV-EPC and EPB processors. Furthermore, when the snapshot number increased from 20 to 40, the PCL performance of MV-EPC improved significantly, but it still lagged behind the two BSBL processors under high SNR conditions.

Claims

1. A robust matching field localization method based on block sparse Bayesian learning with environmental perturbation, characterized in that, Includes the following steps: Step 1: Input array parameters, array multi-snap measured data, search area parameters, and the uncertainty range of marine environmental parameters, preprocess the array received data, and obtain the array multi-snap received data matrix at the target frequency; Step 2: Based on historical sea trial data, environmental statistics, or empirical environmental parameter ranges, establish an uncertain environmental parameter space, and randomly sample multiple sets of environmental parameter vectors within this space. For each candidate location within the search area, calculate the normalized copy field vector corresponding to each set of random environmental parameters. The multiple sets of normalized copy field vectors corresponding to the same candidate location constitute an environmental perturbation constraint matrix. Perform singular value decomposition on the environmental perturbation constraint matrix corresponding to each candidate location, and extract the previous... The principal left singular vector corresponding to the maximum singular value is used to characterize the first and second order statistical features of the random environment parameters; Step 3: Take the main left singular vector matrix corresponding to each candidate position in the search area as a dictionary block, and concatenate them column by column to construct a block dictionary matrix with multiple constraints; Step 4: Based on the block dictionary matrix and the array multi-shot received data matrix, establish a multi-shot block sparse observation model to transform the matching field localization problem into a block multi-shot sparse signal recovery problem; Step 5: Establish a block sparse Bayesian learning model. Assume that the block sparse signal to be estimated satisfies the block structure complex Gaussian prior distribution, and solve the block sparse signal matrix by iteratively updating the block sparse control parameters, noise variance and intra-block correlation matrix. Step 6: Determine the sound source location based on the obtained block sparse solution and output the matching field localization result.

2. The robust matching field localization method based on block sparse Bayesian learning with environmental perturbation as described in claim 1, characterized in that: In step 2, candidate positions are... Corresponding environmental disturbance constraint matrix Perform singular value decomposition: ， In the formula, It is the environmental disturbance matrix. and These are left singular and right singular matrices, respectively. It is a diagonal matrix whose diagonal elements are non-negative singular values; take the first... The left singular vectors corresponding to the maximal singular values ​​constitute the principal left singular vector matrix. The first left singular vector is used to characterize the first-order statistical principal feature of the random environment parameter, and the remaining left singular vectors are used to characterize the principal second-order statistical feature of the random environment parameter.

3. The robust matching field localization method based on block sparse Bayesian learning with environmental perturbation as described in claim 2, characterized in that: The block dictionary matrix mentioned in step 3 is represented as follows: ， In the formula, The total number of candidate locations after discretizing the search region, where each candidate location corresponds to a [number of locations]. A dictionary block consisting of a main left singular vector.

4. The robust matching field localization method based on block sparse Bayesian learning with environmental perturbation as described in claim 3, characterized in that: In step 5, the noise variance is iteratively updated based on the system residual energy: ， In the formula, It is the cross-spectral density matrix of the received signal. The number of array elements It is the covariance matrix of the marginal distribution of the observed data. It is a block diagonal matrix. It is a copy field dictionary matrix.

5. The robust matching field localization method based on block sparse Bayesian learning with environmental perturbation as described in claim 1, characterized in that: In step 5, a simple correlation model is used, and the correlation matrices within all blocks are fixed as identity matrices.

6. The robust matching field localization method based on block sparse Bayesian learning with environmental perturbation as described in claim 1, characterized in that: In step 5, an autoregressive correlation model is used, all blocks share the same covariance structure, and the elements within the blocks are modeled as a first-order autoregressive process to construct the intra-block correlation matrix with a conjugate Toeplitz structure; the autoregressive coefficients are determined based on the average of the main diagonal and secondary diagonal elements of the covariance matrix.

7. The robust matching field localization method based on block sparse Bayesian learning with environmental perturbation as described in claim 1, characterized in that: In step 6, the sound source location is determined based on the sparse control parameters corresponding to each block. For the single-source case, the candidate location corresponding to the largest sparse control parameter is taken as the sound source location estimation result. For the multi-source case, the locations corresponding to multiple significant non-zero blocks are selected as the multi-target localization result.

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