Underwater signal direction estimation method based on compressed sensing under inconsistency of array element signal-to-noise ratio

Abstract

The present application relates to the technical field of underwater acoustic engineering and array signal processing, and particularly relates to an underwater signal direction estimation method based on compressed sensing under the condition of inconsistent array element SNR, which comprises the following steps: firstly, estimating the noise power of each array element by means of noise subspace method, constructing a whitening matrix to perform whitening preprocessing on the observation data and the steering vector dictionary, and converting the non-uniform noise problem into a standard compressed sensing problem under the condition of uniform noise; and then, designing a weighted sparse reconstruction algorithm to obtain high-precision direction estimation by using the spatial sparsity of signals, wherein the RMSE of the direction estimation of the method is 0.45° under the condition of 12dB noise non-uniformity, which is improved by 85% compared with CBF and improved by 62.5% compared with standard CS. The calculation time is about 9.2ms, which meets the processing constraints of real-time sonar systems and has strong substitutability for the CBF algorithm in engineering.

Description

Technical Field

[0001] This invention relates to the fields of underwater acoustic engineering and array signal processing technology, specifically to a method for underwater signal orientation estimation based on compressed sensing under inconsistent array element signal-to-noise ratios. Background Technology

[0002] Underwater target location estimation is one of the core functions of a sonar system. Conventional beamforming (CBF) is widely used in engineering practice due to its simple structure, low computational cost, and good robustness to model mismatch. The spatial spectrum estimation formula for CBF is:

[0003] (1)

[0004] in, for Directional guidance vector, Let H be the sample covariance matrix of the data received by the array, where the superscript H indicates the conjugate transpose.

[0005] The derivation of CBF implicitly assumes a key assumption: the noise power of each array element is the same, that is, the noise covariance matrix is ​​a scalar matrix. However, in actual underwater environments, the signal-to-noise ratio of each array element often varies significantly, mainly due to the following reasons:

[0006] (1) Uneven sensor aging: Hydrophones that have been immersed in seawater for a long time will gradually lose sensitivity due to corrosion, deterioration of the seal, and other factors. The aging rate of different array elements is different.

[0007] (2) Spatial non-uniformity of environmental noise: Marine environmental noise is affected by factors such as seabed topography, ocean currents, and biological activities, and is spatially non-uniformly distributed. The environmental noise power received by array elements at different locations varies.

[0008] (3) Cable and connector attenuation: The cable lengths of array elements at different positions in the drag array are different, resulting in different signal transmission attenuation, which effectively causes inconsistency in SNR between array elements;

[0009] (4) Local occlusion and multipath effect: The uneven distribution of carrier self noise and local flow noise on the array makes the array elements closer to the noise source more disturbed.

[0010] The factors mentioned above cause the array's noise covariance matrix to no longer be a scalar matrix, but rather a diagonal matrix that is not equal to the original matrix:

[0011] ,in (2)

[0012] Define noise nonuniformity index In actual engineering, The value range is typically 6~20dB. When the signal-to-noise ratio of the array elements is inconsistent, CBF exhibits the following performance degradation:

[0013] (1) Beam pattern distortion: The sidelobe level increases significantly when When the value is 12dB, the side lobe elevation can reach 4~8dB;

[0014] (2) Decreased azimuth estimation accuracy: Non-uniform noise effectively changes the array weighting, leading to increased beam pointing deviation and estimation deviation;

[0015] (3) Array gain loss: Array elements with high noise power effectively reduce the signal-to-noise ratio gain of the entire array. When the gain is 15dB, the array gain loss can reach 3~5dB.

[0016] In existing technologies, the methods for handling inconsistencies in array element SNR mainly include the following categories:

[0017] Option 1: Adaptive Beamforming (MVDR / Capon method). This method adaptively adjusts the weighting coefficients using the minimum variance criterion, theoretically allowing for automatic adaptation to non-uniform noise. However, MVDR is extremely sensitive to steering vector errors and is prone to signal self-cancellation under low signal-to-noise ratio and insufficient snapshot counts, making its robustness far inferior to CBF. In practical sonar systems, the failure probability of MVDR is much higher than that of CBF.

[0018] Option 2: Noise Power Equalization. This method estimates the noise power of each array element and then normalizes it. While simple in principle, the accuracy of noise power estimation is limited by the number of snapshots and signal leakage. Furthermore, simple equalization does not utilize prior knowledge of signal sparsity, resulting in limited improvement at low SNR.

[0019] Option 3: Standard Compressed Sensing DOA Estimation. This method utilizes the sparsity of spatial signals to... Norm minimization yields high-resolution DOA estimates. However, the standard CS algorithm assumes uniform white noise, and when the element SNRs are inconsistent, the effective RIP condition of the sensing matrix deteriorates, significantly reducing reconstruction accuracy.

[0020] Option 4: Subarray Processing Method. The array is divided into multiple subarrays, processed separately, and then fused. This method reduces the influence range of non-uniform noise, but sacrifices the array aperture, resulting in a decrease in angular resolution.

[0021] In summary, existing technical solutions suffer from an inherent contradiction in balancing accuracy, speed, and robustness when dealing with the inconsistency of array element SNR. This invention aims to propose a novel orientation estimation method based on compressed sensing theory. While maintaining the robustness and real-time processing capabilities of CBF (Compressed-Band Forced-Flight) algorithm, it effectively improves the orientation estimation accuracy under non-uniform noise conditions through noise-aware weighted sparse reconstruction, achieving a strong alternative to the CBF algorithm in engineering applications. Summary of the Invention

[0022] To address the shortcomings of existing technologies, the present invention aims to provide an underwater signal orientation estimation method based on compressed sensing under conditions of inconsistent array element signal-to-noise ratios.

[0023] To achieve the above objectives, the present invention provides the following technical solution: a method for underwater signal azimuth estimation based on compressed sensing under inconsistent array element signal-to-noise ratios, comprising the following steps:

[0024] (1) Receive multi-shot observation data from an N-element underwater acoustic array Establish a signal model containing non-uniform noise. The noise covariance matrix A matrix that is diagonal but not equal;

[0025] (2) Estimate the noise power of each array element by using the eigenvalue decomposition of the sample covariance matrix. Construct a noise power diagonal matrix ;

[0026] (3) Constructing the whitening matrix The observation data and the steering vector dictionary are whitened to eliminate the noise power difference between array elements;

[0027] (4) Design a K-column complete dictionary in the angle domain, and construct a whitening dictionary matrix using the whitened guiding vectors. Establish a sparse representation model for the whitened observation data. ;

[0028] (5) Use the weighted sparse reconstruction algorithm to solve for the sparse coefficient vector. The weighting coefficients are designed based on the correlation between the whitened steering vector and the observed data;

[0029] (6) Based on the sparsity coefficient The amplitude is used to construct a spatial spectrum, and the orientation estimate of the underwater signal is obtained by searching for spectral peaks.

[0030] In some embodiments, the noise power estimation in step (2) adopts the noise subspace method: the sample covariance matrix is ​​decomposed into eigenvalues, and the noise subspace eigenvectors and corresponding eigenvalues ​​are used to construct a weighted estimate of the noise power of each array element.

[0031] In some embodiments, the whitening transformation in step (3) makes the transformed noise covariance matrix approach the identity matrix, thus transforming the orientation estimation problem under non-uniform noise into a standard compressed sensing reconstruction problem under uniform white noise.

[0032] In some embodiments, the weighted sparse reconstruction algorithm in step (5) is a weighted algorithm. Norm minimization or weighted orthogonal matching pursuit algorithm; weighting coefficients ,in For compression parameters, is the regularization constant.

[0033] In some embodiments, the method further includes step (7): fusing the compressed sensing spatial spectrum with the conventional beamforming spatial spectrum according to a preset weight to obtain a fused spatial spectrum output that has both high resolution and strong robustness.

[0034] In some embodiments, the noise power estimation in step (2) is implemented with an online adaptive update using a sliding window mechanism, where the window length and sliding step size are adaptively adjusted according to the noise change rate.

[0035] In some embodiments, the method is applicable to narrowband and wideband signal processing; wideband signals employ a strategy of noncoherent accumulation after independent frequency band processing.

[0036] To achieve the above objectives, the present invention also provides the following technical solution: an underwater signal orientation estimation system based on compressed sensing under element signal-to-noise ratio inconsistency, comprising:

[0037] The array data acquisition module is used to receive multi-shot observation data from an N-element underwater acoustic array;

[0038] The noise power estimation module is used to estimate the noise power of each array element based on the eigenvalue decomposition of the sample covariance matrix.

[0039] The whitening preprocessing module is used to construct a whitening matrix based on the estimated noise power and perform whitening transformation on the data and dictionary;

[0040] A sparse dictionary building module for generating an overcomplete whitening guide vector dictionary in the angular domain;

[0041] The weighted sparse reconstruction module is used to perform weighted l1 minimization or weighted OMP algorithms to solve for sparse orientation spectra.

[0042] The azimuth estimation output module is used to search for spatial spectrum peaks and output the azimuth estimation results.

[0043] Compared with the prior art, the beneficial effects of the present invention are:

[0044] (1) Compared with conventional beamforming (CBF): Without significantly increasing the computational burden, the accuracy of azimuth estimation under non-uniform noise is greatly improved through noise whitening and sparse reconstruction. At κ=12dB, the RMSE is reduced from 3.0° in CBF to 0.45°, an improvement of 85%.

[0045] (2) Compared with the MVDR / Capon method: it maintains the robustness of CBF-like methods and avoids the signal self-cancellation problem of MVDR under low snapshot number and model mismatch. Under the condition of snapshot number T=50, the failure probability of the method of this invention is less than 2%, while that of MVDR is as high as 15%.

[0046] (3) Compared with standard compressed sensing DOA: Through noise whitening preprocessing and weighted sparse reconstruction, it is specially adapted to non-uniform noise scenarios, and the reconstruction accuracy is improved by 40~60%. The effective RIP constant of the sensing matrix is ​​improved from 0.85 in standard CS to 0.45.

[0047] (4) Compared with the subarray processing method: the complete array aperture is maintained and the angular resolution is not lost; at the same time, the computational complexity O(NKL) is much lower than that of subarray fusion O(N²K).

[0048] (5) Engineering substitutability: The single-frame processing delay of this method is about 9.2ms (32 elements, 360° scan), which is on the same order of magnitude as CBF's 2.1ms. It meets the 20ms processing constraint of real-time sonar system and is suitable for engineering deployment.

[0049] Details of one or more embodiments of this application are set forth in the following drawings and description to make other features, objects and advantages of this application more readily apparent. The embodiments of this application will provide a detailed description and understanding of the application. Attached Figure Description

[0050] Figure 1 This is a flowchart illustrating the overall workflow of the method of the present invention;

[0051] Figure 2 This is a schematic diagram of the architecture of a weighted compressed sensor orientation estimation system.

[0052] Figure 3 This diagram illustrates the comparison between the effects of uniform noise and non-uniform noise on array performance.

[0053] Figure 4 Comparison of spatial spectrum estimation under non-uniform noise with simulation results (32 elements, source: -15°, 25°).

[0054] Figure 5 Comparison of RMSE for location estimation under different signal-to-noise ratios (noise non-uniformity κ=12dB).

[0055] Figure 6 Comparison of azimuth estimation RMSE and array gain loss under different noise nonuniformity conditions;

[0056] Figure 7 Comparison of single-frame computation time for each method (32-element array, 360° scan). Detailed Implementation

[0057] 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.

[0058] This invention proposes an underwater signal azimuth estimation method based on compressed sensing under conditions of inconsistent signal-to-noise ratio among array elements. The core idea is as follows: first, estimate the noise power of each array element; then, use the noise power information to perform whitening preprocessing on the observation data and sensor dictionary, transforming the non-uniform noise problem into a standard CS reconstruction problem under uniform noise; finally, obtain high-precision azimuth estimation through sparse reconstruction. Specifically, the method includes the following steps:

[0059] Specifically, the following steps are included:

[0060] Step S1: Array signal reception and data modeling.

[0061] Consider an N-element uniform linear array (ULA) with element spacing... The system receives L far-field narrowband signals in the receiving space. The received signal model for the i-th element is:

[0062] (3)

[0063] Among them, s I (t) is the th The complex envelope of a signal source, Its azimuth angle, For the first The noise of each array element has a variance of . Stack all element signals into a vector form:

[0064] (4)

[0065] in For array manifold matrix, As the guide vector, ,in .

[0066] Step S2: Online estimation of array element noise power.

[0067] The noise power of each array element is estimated using the sample covariance matrix of the received data from the array. First, the sample covariance matrix is ​​calculated:

[0068] (5)

[0069] Where T is the number of snapshots. Since the covariance matrix of the far-field signal has a Toeplitz structure (for ULA), and the noise contribution is only reflected on the diagonal, the noise power can be estimated using the following strategy:

[0070] Strategy A (Diagonal Extraction Method): When the signal power is much smaller than the noise power or the signal source is sparse, the diagonal of the covariance matrix mainly reflects the noise power.

[0071] (6)

[0072] in Through the Perform eigenvalue decomposition and take the mean estimate of the eigenvalues ​​in the signal subspace.

[0073] Strategy B (Noise Subspace Method): Eigenvalue decomposition of the covariance matrix. A more accurate estimate of noise power can be constructed using the eigenvectors of the noise subspace:

[0074] (7)

[0075] in For the i-th element of the k-th noise feature vector, The corresponding characteristic value. This strategy does not require known signal power and is more robust to signal leakage.

[0076] Step S3: Noise whitening pretreatment.

[0077] Constructing the whitening matrix:

[0078] (8)

[0079] Perform whitening transformation on the received data:

[0080] (9)

[0081] Whitened noise The covariance matrix is:

[0082] (10)

[0083] That is, after whitening, the noise becomes uniform white noise, eliminating the influence of SNR inconsistency between array elements. Simultaneously, the equivalent steering vector after whitening becomes... The equivalent manifold matrix becomes .

[0084] Step S4: Design an overcomplete sparse dictionary.

[0085] A complete dictionary was designed in the angle domain. The azimuth space [-90°, 90°] was discretized into K uniform grid points (K >> N), with a grid spacing of... Construct the whitened overcomplete dictionary matrix:

[0086] (11)

[0087] in This is the whitened steering vector. The whitened observation data is represented as:

[0088] (12)

[0089] in It is a K-dimensional sparse coefficient vector, with only L non-zero elements corresponding to the actual signal source direction (L < 0.05). <K), This represents the model error and the uniform noise after whitening.

[0090] Step S5: Solve for orientation estimation using weighted sparse reconstruction.

[0091] Average measurement vector using multi-shot data This invention establishes a sparse optimization problem. A weighted average is used. Norm minimization (weighted LASSO):

[0092] (13)

[0093] in For weighted matrices, These are noise margin parameters. The design criteria for the weighting coefficients are:

[0094] (14)

[0095] in This is the compression parameter (default p=0.5). To prevent division by zero of small positive numbers (default) This weighting strategy results in smaller weights in the signal direction (encouraging non-zero values) and larger weights in the no-signal direction (suppressing spurious peaks), significantly improving the accuracy of sparse reconstruction.

[0096] Alternatively, the Weighted Orthogonal Matching Pursuit (W-OMP) algorithm can be used for a faster solution:

[0097] (a) Initialization: Residual Support set Number of iterations ;

[0098] (b) Weighted matching: Calculate the weighted correlation value Select the index corresponding to the maximum value. ;

[0099] (c) Support set update: ;

[0100] (d) Least squares estimation: ;

[0101] (e) Residual update: ;

[0102] (f) Termination judgment: when Or the number of iterations reaches Stop when the time comes.

[0103] Step S6: Spatial spectrum estimation and orientation output.

[0104] Based on the sparsity coefficient estimate Constructing the spatial spectrum:

[0105] (15)

[0106] Azimuth estimation is obtained by searching for peaks in the spatial spectrum:

[0107] (16)

[0108] To enhance robustness, the CS spatial spectrum and the CBF spatial spectrum can be weighted and fused:

[0109] (17)

[0110] in Represents the normalized spatial spectrum. For fusion weights (default) This fusion strategy combines the high resolution of CS with the robustness of CBF.

[0111] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0112] Example 1: 32-element passive sonar linear array

[0113] The following explanation uses a 32-element linear array with uniform half-wavelength spacing as an example. Assume the array's operating center frequency f0 = 5kHz, the speed of sound in water c = 1500m / s, and the element spacing... Assume there are two far-field narrowband signal sources in space, located at... and Direction and signal power are both 0dB.

[0114] Assume the noise power of the 32 array elements is non-uniformly distributed: most elements have a noise power of 0dB ( However, the noise power of the fourth array element increased to 9dB due to sensor aging. The 8th element is 7dB ( The noise power of the 16th element increased to 10.8 dB due to its proximity to the carrier noise source. =12), the 23rd element is 7.8dB ( =6), the 29th array element is 10dB ( =10). Overall noise nonuniformity .

[0115] Perform according to the method of this invention:

[0116] (1) Collect T=200 snapshots and calculate the sample covariance matrix. ;

[0117] (2) Strategy B (noise subspace method) is used to estimate the noise power of each array element, and the number of signal sources is determined to be L=2 by the MDL criterion;

[0118] (3) Constructing the whitening matrix The data is whitened.

[0119] (4) Design an overcomplete angle dictionary with K=360 columns (-90° to 89°, interval) Construct the whitened dictionary matrix ];

[0120] (5) Use the weighted OMP algorithm and set the compression parameters. Maximum number of iterations residual threshold After three iterations, the algorithm converges, yielding the sparse coefficients. ;

[0121] (6) Constructing the spatial spectrum The search peak is used to obtain a directional estimate.

[0122] Simulation results are as follows Figure 4 As shown, the spatial spectrum of the method of this invention (weighted CS-DOA) exhibits sharp spectral peaks in both signal source directions, and its sidelobe suppression is significantly better than CBF and standard CS. Specific performance indicators are as follows: CBF has an RMSE of 3.0°, standard CS has an RMSE of 1.2°, and this invention has an RMSE of 0.45°; CBF has a sidelobe level of -5.2dB, standard CS has an RMSE of -8.5dB, and this invention has an RMSE of -12.5dB.

[0123] Example 2: Actual Deployment Scenario of Trailed Linear Array

[0124] This invention is applied to a 64-element towed linear array system. Due to the long-distance towing causing uneven cable attenuation, coupled with the spatial variation of marine environmental noise, the measured noise non-uniformity of this system is approximately [value missing]. =15dB. Operating frequency band: 200Hz~2kHz.

[0125] A frequency-band processing strategy is adopted: the working frequency band is divided into 10 sub-bands, and the weighted CS azimuth estimation of this invention is performed independently in each sub-band. Finally, the spatial spectrum of each sub-band is incoherently accumulated. The processing delay of each sub-band is about 15ms, and the total delay of parallel processing of 10 sub-bands is only about 18ms (including data scheduling overhead), which meets the real-time requirements.

[0126] exist Under the condition of 15dB, the broadband azimuth estimation RMSE of the method of the present invention is 0.65°, which is an improvement of 85.6% compared with CBF 4.5° and an improvement of 67.5% compared with standard CS 2.0°.

[0127] Example 3: Adaptive processing of dynamic changes in non-uniformity

[0128] In real marine environments, the noise power of array elements changes dynamically over time. This invention addresses this by employing a sliding window estimation method (window length W) in step S2. est =500 snapshots, sliding step size S step =100 snapshots) to achieve adaptive tracking of noise power.

[0129] Simulation verification: The noise non-uniformity was assumed to vary sinusoidally between 0 dB and 20 dB (period of 60 seconds), with a sampling interval of 0.5 seconds. Results show that the method of this invention can adapt to changes in noise characteristics within 2-3 sliding windows (approximately 1-1.5 seconds), maintaining an azimuth estimation accuracy consistently within 0.8°. In contrast, the standard CS method without noise power updates rapidly degrades in accuracy to over 3° after noise changes.

[0130] Through the technical solution of this application

[0131] (1) Under the conditions of noise nonuniformity κ=12dB and SNR=10dB, the azimuth estimation RMSE is 0.45°, which is 85% better than CBF's 3.0° and 62.5% better than standard CS's 1.2°.

[0132] (2) The array gain loss was reduced from -3.0dB of CBF and -1.6dB of standard CS to only -0.5dB, effectively restoring the array gain.

[0133] (3) The sidelobe level improved from -5.2dB to -12.5dB in CBF, which is close to the ideal value of -13.2dB under uniform noise.

[0134] (4) When the noise non-uniformity varies over a wide range from 0 to 24 dB, the performance degradation curve is smooth, which reflects strong robustness.

[0135] (5) The calculation time is about 9.2ms, which meets the real-time processing requirements and has strong engineering substitutability for CBF.

[0136] The above embodiments merely illustrate several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

[0137] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for underwater signal azimuth estimation based on compressed sensing under inconsistent signal-to-noise ratios of array elements, characterized in that: Includes the following steps: (1) Receive multi-shot observation data from an N-element underwater acoustic array Establish a signal model containing non-uniform noise. The noise covariance matrix A matrix that is diagonal but not equal; (2) Estimate the noise power of each array element by using the eigenvalue decomposition of the sample covariance matrix. Construct a noise power diagonal matrix ; (3) Constructing the whitening matrix The observation data and the steering vector dictionary are whitened to eliminate the noise power difference between array elements; (4) Design a K-column complete dictionary in the angle domain, and construct a whitening dictionary matrix using the whitened guiding vectors. Establish a sparse representation model for the whitened observation data. ; (5) Use the weighted sparse reconstruction algorithm to solve for the sparse coefficient vector. The weighting coefficients are designed based on the correlation between the whitened steering vector and the observed data; (6) Based on the sparsity coefficient The amplitude is used to construct a spatial spectrum, and the orientation estimate of the underwater signal is obtained by searching for spectral peaks.

2. The method according to claim 1, characterized in that, The noise power estimation in step (2) adopts the noise subspace method: the sample covariance matrix is ​​decomposed into eigenvalues, and the noise subspace eigenvectors and corresponding eigenvalues ​​are used to construct a weighted estimate of the noise power of each array element.

3. The method according to claim 1, characterized in that, The whitening transformation described in step (3) makes the transformed noise covariance matrix approach the identity matrix, thus transforming the orientation estimation problem under non-uniform noise into a standard compressed sensing reconstruction problem under uniform white noise.

4. The method according to claim 1, characterized in that, The weighted sparse reconstruction algorithm described in step (5) is a weighted... Norm minimization or weighted orthogonal matching pursuit algorithm; weighting coefficients ,in For compression parameters, is the regularization constant.

5. The method according to claim 1, characterized in that, It also includes step (7): fusing the compressed sensing spatial spectrum with the conventional beamforming spatial spectrum according to a preset weight to obtain a fused spatial spectrum output that has both high resolution and strong robustness.

6. The method according to claim 1, characterized in that, In step (2), the noise power estimation uses a sliding window mechanism to achieve online adaptive updates, with the window length and sliding step size adaptively adjusted according to the noise change rate.

7. The method according to any one of claims 1 to 6, characterized in that, The method is applicable to both narrowband and wideband signal processing; wideband signals are processed independently by frequency band and then noncoherently accumulated.

8. An underwater signal orientation estimation system based on compressed sensing under inconsistent signal-to-noise ratios of array elements, characterized in that, include: The array data acquisition module is used to receive multi-shot observation data from an N-element underwater acoustic array; The noise power estimation module is used to estimate the noise power of each array element based on the eigenvalue decomposition of the sample covariance matrix. The whitening preprocessing module is used to construct a whitening matrix based on the estimated noise power and perform whitening transformation on the data and dictionary; A sparse dictionary building module for generating an overcomplete whitening guide vector dictionary in the angular domain; The weighted sparse reconstruction module is used to perform weighted l1 minimization or weighted OMP algorithms to solve for sparse orientation spectra. The azimuth estimation output module is used to search for spatial spectrum peaks and output the azimuth estimation results.

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