Anti-pseudo peak frequency difference orientation estimation method using sparse Bayesian learning

Abstract

The invention provides an anti-pseudo peak frequency difference azimuth estimation method using sparse Bayesian learning, and relates to the technical field of underwater acoustic array signal processing. The method specifically comprises the steps of collecting signals, selecting processing frequency points, constructing a dictionary matrix and a joint spectrum matrix, quantifying the stability of signal intensity changing along with a reference high-frequency frequency point, optimizing the joint spectrum matrix according to the stability to eliminate false peaks, and obtaining an orientation estimation result. According to the technical scheme, false peaks can be effectively removed, the sidelobe height in the azimuth spectrum can be reduced, and the azimuth estimation accuracy of the target can be improved.

Description

Technical Field

[0001] This disclosure relates to the field of underwater acoustic array signal processing technology, and in particular to a method for anti-spurious peak frequency difference azimuth estimation using sparse Bayesian learning. Background Technology

[0002] Direction of Arrival (DOA) estimation refers to the process of finding the direction of a sound source from the output spatial spectrum of a receiving sensor array, and it is an important research topic in array signal processing. Conventional beamforming (CBF) is a widely used array data processing method. Its basic principle is a delay-summation approach, which has the advantages of low computational cost and good robustness. However, for sparse arrays, when the array element spacing is greater than half the wavelength of the received signal, grating lobes appear in the CBF method due to spatial aliasing, which seriously affects the target's azimuth estimation performance. In addition, due to the complex and variable marine environment, there may be sound velocity profile mismatch and array mismatch. High-frequency processing is more sensitive to mismatch and is prone to performance degradation.

[0003] Frequency Difference (FD) is a method that combines information from multiple frequency points to suppress grating lobes by reducing the operating frequency. The FD method simulates frequency difference by performing element-wise conjugate multiplication on a set of high-frequency signal array received data. The sound field characteristics at this frequency are improved by reducing the processing frequency to avoid spatial aliasing. The performance of frequency-difference beamforming (FDB) is related to the frequency... The results of the CBF method are comparable, providing a new solution for scenarios where traditional methods fail. In recent years, the FD concept has also been extended to matched field processing, and has been successfully applied to the localization of sound sources in shallow and deep seas. This has demonstrated from multiple perspectives that the FD method can effectively solve the spatial aliasing problem in array signal processing and exhibits good robustness in uncertain environments.

[0004] However, the reduced operating frequency after frequency differential processing increases the beamwidth of the direction finding beam, reducing the azimuth resolution of nearby targets. At the same time, the self-integration process amplifies the noise effect, leading to increased beam sidelobes and reduced detection performance under low signal-to-noise ratio conditions. In addition, in the case of multiple targets, the additional cross terms after signal self-integration can cause spurious peaks in the azimuth estimation results, causing significant interference to the detection of weak sources among strong sources. Summary of the Invention

[0005] This disclosure provides a method for azimuth estimation against spurious peak frequency difference using sparse Bayesian learning, including:

[0006] The array of elements collects acoustic signals to obtain multi-shot array signals.

[0007] L reference high-frequency points are selected in the high signal-to-noise ratio band of the acoustic signal and the difference frequency value is set to obtain L frequency pairs; where L is a positive integer greater than 1.

[0008] For each reference high frequency point, a dictionary matrix is ​​constructed to characterize the complex amplitude response of each array element to the acoustic signal in each grid direction, based on the array element position and azimuth search parameters. The azimuth search parameters include a preset scanning angle domain and the number of grid points. The grid direction refers to the direction obtained by discretizing the preset scanning angle domain according to the preset number of grid points.

[0009] Based on the multi-shot array signal, L frequency pairs and dictionary matrix, frequency difference sparse signal reconstruction is performed based on sparse Bayesian learning to construct a joint spectrum matrix characterizing the signal intensity of each reference high-frequency acoustic signal in each grid direction.

[0010] By quantizing the stability of signal strength variation with reference high frequency points, spurious signal strength generated by frequency difference cross terms in the joint spectrum matrix is ​​suppressed, resulting in an optimized joint spectrum matrix.

[0011] The optimized joint spectral matrix is ​​averaged in the frequency domain to obtain the azimuth spectrum, and then the azimuth estimation result is obtained.

[0012] The content described in this section is not intended to identify key or important features of the embodiments of this disclosure, nor does it constitute a limitation on the scope of this disclosure.

[0013] Other features of this disclosure will be described in detail in the following description to aid understanding. Attached Figure Description

[0014] Figure 1 This is a schematic flowchart of an embodiment of the present disclosure of a method for anti-spurious peak frequency difference azimuth estimation using sparse Bayesian learning;

[0015] Figure 2 This is a schematic diagram of the process flow of a frequency difference sparse signal reconstruction method based on sparse Bayesian learning provided in one embodiment of the present disclosure;

[0016] Figure 3 This is a schematic flowchart of a method for quantifying the stability of signal strength as a reference high-frequency point varies, according to an embodiment of this disclosure.

[0017] Figure 4 This is a schematic flowchart of an embodiment of the present disclosure of a method for iteratively removing false signal strength;

[0018] Figures 5 to 17 These are simulation results diagrams of some embodiments of this disclosure. Detailed Implementation

[0019] The present disclosure will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the embodiments provided below are merely exemplary. Furthermore, for the sake of brevity and clarity, common knowledge has been omitted from the description of the following embodiments.

[0020] In this document, terms such as "first," "second," and "third" are used only to distinguish identical or similar descriptive objects and are not intended to limit the specific order or sequence of the described objects, nor are they used to limit the importance of the described objects. At the same time, in order to enable those skilled in the art to clearly understand the technical solutions provided in this disclosure, expressions such as "red," "yellow," and "blue," as well as the specific colors in the accompanying drawings, are also used only to distinguish identical or similar descriptive objects and do not represent the color attributes possessed by the descriptive objects when this solution is actually deployed.

[0021] This disclosure provides a method for azimuth estimation that is resistant to spurious peak frequency difference using sparse Bayesian learning, such as Figure 1 As shown, the specific steps include:

[0022] Step S101: The array element acquires acoustic wave signals to obtain multi-shot array signals.

[0023] The receiver array consists of M receiver elements, where M is a positive integer greater than 1.

[0024] Step S102: Select L reference high-frequency points in the high signal-to-noise ratio frequency band of the acoustic signal and set the difference frequency value to obtain L frequency pairs;

[0025] L is a positive integer greater than 1.

[0026] High signal-to-noise ratio (SNR) frequency band acoustic signals, where the signal components dominate the observation data (compared to noise and interference), can provide high-quality signals for subsequent processing, which is beneficial to improving the accuracy of azimuth estimation results.

[0027] The setting of the difference frequency should satisfy the spatial sampling theorem (Nyquist sampling theorem), that is... To avoid the formation of grid lobes, Indicates the reference speed of sound. This indicates the element spacing of the receiving array elements.

[0028] Step S103: For each reference high frequency point, construct a dictionary matrix that characterizes the complex amplitude response of each element to the acoustic signal in each grid direction, based on the element position and orientation search parameters of the array element array.

[0029] The orientation search parameters include a preset scanning angle range. And the number of grid points H.

[0030] The orientation search parameters are designed to define the spatial range of the orientation search. The grid direction specifically refers to the direction obtained by discretizing the preset scanning angle domain according to the preset number of grid points.

[0031] Based on the physical meaning of the dictionary matrix, it can be understood that the dimension of the dictionary matrix for each frequency point is MxH.

[0032] Step S104: Based on the multi-snap array signal, L frequency pairs and dictionary matrix, perform frequency difference sparse signal reconstruction based on sparse Bayesian learning to construct a joint spectrum matrix that characterizes the signal intensity of each reference high-frequency acoustic signal in each grid direction.

[0033] Based on the physical meaning of the joint spectral matrix, it can be understood that the dimension of the joint spectral matrix is ​​LxH.

[0034] Step S105: By quantizing the stability of the signal strength as the reference high frequency point changes, identify and remove the spurious signal strength generated by the frequency difference cross term in the joint spectrum matrix to obtain the optimized joint spectrum matrix.

[0035] Step S106: Perform frequency domain averaging on the optimized joint spectrum matrix to obtain the azimuth spectrum, and then obtain the azimuth estimation result.

[0036] It should be noted that the cross term in multi-frequency differential signal processing can produce spurious signal strength. The spurious signal strength fluctuates greatly with frequency and has poor stability, while the real signal strength has better consistency with frequency.

[0037] Therefore, by quantifying the stability of signal strength as it changes with the reference high frequency point, spurious signal strengths in the joint spectral matrix can be effectively identified and removed, thereby improving the accuracy of azimuth estimation results.

[0038] The following description, in conjunction with some embodiments of this disclosure, further illustrates the technical solutions of this disclosure to aid understanding.

[0039] In one embodiment of this disclosure, it is assumed that the sensor array for acquiring signals is a uniform linear array, and it is considered that... A non-correlated far-field narrowband plane wave underwater acoustic signal from Direction of incidence A uniform linear array of elements, with the element spacing of the receiving elements being... Each array element satisfies the condition of isotropy.

[0040] The normal direction of the array is Then the first The received signal of each array element can be expressed as:

[0041]

[0042] in,

[0043] Indicates the first One incident signal;

[0044] Indicates signal frequency;

[0045] Indicates the reference speed of sound;

[0046] This indicates that, relative to the reference array element, the incident signal is... The signal arrived at the first The latency of each array element;

[0047] Represents the imaginary unit;

[0048] Indicates the first Additive Gaussian noise received by each array element that is uncorrelated with the signal;

[0049] The array output can be expressed in matrix form as follows:

[0050]

[0051] in,

[0052] For the received signal matrix, ;in, Indicates the number of snapshots;

[0053] The source signal matrix, ;

[0054] For the noise matrix, ;

[0055] For array manifold matrix, , Elements The expression is:

[0056]

[0057] It should be noted that Formulas 1 to 3 are mathematical models of actual sound source signals, and the purpose of deploying the technical solution disclosed herein is to... An approximation fit is performed, and then the azimuth estimation result is obtained based on the final azimuth spectrum.

[0058] Scanning angle domain After setting the number of grid points H, the dictionary matrix corresponding to each reference high-frequency point can be calculated by combining the array element positions of the receiving array elements. Its elements can be represented as:

[0059]

[0060] It should be noted that the array element position of the receiving array element is used to determine the phase difference and amplitude attenuation when the signal arrives at different array elements. Formula 4 is the dictionary matrix element representation under the premise of uniform linear array in this embodiment.

[0061] In the actual deployment of the technical solution disclosed herein, the sensor array can also be any array such as a circular array. The element expression of its dictionary matrix may be different from Formula 4, but the physical meaning of the dictionary matrix is ​​the same, that is, the complex amplitude response caused by a unit amplitude signal from a specific direction at a specific frequency when it reaches a specific array element.

[0062] One embodiment of this disclosure provides a frequency difference sparse signal reconstruction method based on sparse Bayesian learning, such as... Figure 2 As shown, the specific steps include:

[0063] Step S201: For each frequency pair, construct a differential feature matrix based on the multi-shot array signals of its two corresponding frequency points.

[0064] The expression for the difference characteristic matrix is:

[0065]

[0066] in, Indicates frequency of The received signal matrix is ​​taken as conjugate.

[0067] Step S202: Initialize the sparse Bayesian hyperparameters of each reference high-frequency point.

[0068] Sparse Bayesian hyperparameters include signal strength hyperparameters and noise estimation hyperparameters. When actually deploying the technical solution disclosed herein, initial values ​​can be assigned through uniform initialization, random initialization, or initialization using prior information, etc. This disclosure does not impose any restrictions on this.

[0069] Step S203: For each reference high-frequency point, construct the cross-covariance matrix based on its dictionary matrix and the current sparse Bayesian hyperparameters.

[0070] The expression for the cross-covariance matrix is:

[0071]

[0072] in,

[0073] Represents the identity matrix;

[0074] This represents the noise estimation hyperparameter for the l-th frequency point;

[0075] This represents a diagonal matrix, where the diagonal elements are the current signal strength hyperparameters corresponding to the grid direction at that frequency point. ;

[0076] This represents the conjugate transpose of the dictionary matrix for that frequency point.

[0077] Step S204: Using the evidence maximization framework based on sparse Bayesian learning, the hyperparameter iterative formula derived from the likelihood function is maximized using the fixed-point iterative method, and the signal strength hyperparameter and noise estimation hyperparameter are iterated to a preset number of times.

[0078] The iterative formula for signal strength hyperparameters is as follows:

[0079]

[0080] in, This represents the h-th column of the frequency point dictionary matrix.

[0081] The iterative formula for noise estimation hyperparameters is as follows:

[0082]

[0083] in,

[0084] The number of sound sources is estimated, and its value can be obtained by existing source number estimation (SNE) methods. This disclosure does not limit this.

[0085] , Indicates according to The extracted peak value of the complex amplitude response in the dictionary matrix The matrix formed by the corresponding column vectors;

[0086] .

[0087] Step S205: Construct the joint spectrum matrix based on the signal strength hyperparameters iterated to a preset number of times.

[0088] For each high-frequency point, a hyperparameter vector will be obtained after executing step S204. By concatenating the hyperparameter vectors of all frequency points, the joint spectral matrix can be obtained, and its expression is: index set .

[0089] The frequency-difference sparse signal reconstruction method (or multi-shot frequency-difference sparse Bayesian learning, FDSBL) provided in this embodiment applies the evidence maximization framework of sparse Bayesian learning to the FD sparse signal reconstruction problem. It estimates more accurate signal strength hyperparameters and noise estimation hyperparameters through fixed-point iteration, thereby improving the accuracy of azimuth estimation.

[0090] One embodiment of this disclosure provides a method for quantifying the stability of signal strength as a function of a reference high-frequency point, such as... Figure 3 As shown, the specific steps include:

[0091] Step S301: Set a hard threshold, set the elements in the joint spectrum matrix that are greater than or equal to the hard threshold to 1, and retain the original values ​​of the remaining elements to obtain a partially binarized joint spectrum matrix.

[0092] Hard threshold By traversing all high-frequency points, the elements in the joint spectral matrix are partially binarized to obtain a partially binarized joint spectral matrix. The partially binarized expression is:

[0093]

[0094] Retaining the original value of elements smaller than the hard threshold is beneficial for detecting lower intensity signals, ultimately improving the accuracy of orientation estimation.

[0095] Step S302: For the grid column vectors in the partially binarized joint spectrum matrix, randomly select at least one of the remaining grid column vectors, multiply them element by element in turn, and take the average of the results to obtain the updated partially binarized joint spectrum matrix.

[0096] This step aims to suppress the influence of randomness on the azimuth estimation results through random multiplication. In this embodiment, the number of random multiplications is equal to the number of reference high-frequency points L. In the updated partial binarized azimuth spectrum, the vector expression corresponding to each reference high-frequency point is:

[0097]

[0098] Step S303: Perform frequency domain summation on the updated partial binarized azimuth spectrum to obtain the pseudo-spectrum.

[0099] The expression for the pseudospectrum is:

[0100]

[0101] Step S304: Calculate the stability threshold based on the pseudo-spectrum to quantify the stability.

[0102] In this embodiment, the stability threshold expression is:

[0103]

[0104] One embodiment of this disclosure provides a method for iteratively removing spurious signal strength, such as... Figure 4 As shown, the specific steps include:

[0105] Step S401: Based on the stability quantization, remove the grid column vectors corresponding to the false signal strength from the current dictionary matrix to obtain the updated dictionary matrix.

[0106] It should be noted that this embodiment adopts the idea of ​​iterative optimization, gradually tightening the requirements for signal stability according to the iteration process. Specifically, Formula 12 is changed to:

[0107]

[0108] Where t represents the number of iterations, initialized to 1.

[0109] Get all values ​​less than in the pseudospectrum Grid index set Its expression is as follows:

[0110]

[0111] Remove dictionary matrix In, corresponding to The vector (grid column vector) is obtained , This enables the updating of the dictionary matrix.

[0112] Step S402: Based on the updated dictionary matrix, estimate the sparse Bayesian hyperparameters corresponding to the true signal strength in the current joint spectrum matrix, and assign a minimum value to the signal strength hyperparameters corresponding to the false signal strength, thus obtaining the updated joint spectrum matrix.

[0113] In this embodiment, the sparse Bayesian hyperparameters corresponding to the true signal intensity in the current joint spectral matrix are estimated once, specifically by performing the hyperparameter estimation process as described in steps S203 to S204 above.

[0114] In removing the corresponding After the vector, in the azimuth spectrum matrix The dimension will be reduced accordingly; in this embodiment, it will correspond to... The grid index position elements are assigned a minimum value to obtain the complete azimuth spectrum, and its expression is:

[0115]

[0116] After multiple iterations and updates, when the dictionary matrix... When the number of vectors indexed by the grid is less than or equal to the preset remaining entries Q, output The azimuth spectrum estimation result is obtained by frequency domain averaging, and its expression is:

[0117]

[0118] Output The position of the larger spectral peak is used as the DOA estimate of the acoustic signal to obtain the orientation estimation result.

[0119] This embodiment provides an iterative method for removing false signal strength, which uses the number of dictionary matrix vectors as the termination condition for iteration based on the aforementioned FDSBL, or it can be called an iterative refined dictionary matrix method (Iterative Refined Dictionary-FDSBL, IRD-FDSBL).

[0120] The following simulation examples illustrate the effectiveness of the technical solution disclosed herein.

[0121] Calculation example 1:

[0122] A 27-element uniform linear array with a spacing of 9 m and an array aperture of 243 m was used. The sound velocity c was set to 1500 m / s. According to the Nyquist sampling theorem, the maximum signal frequency at which no grating lobes appear corresponding to this element spacing is 83 Hz. The sine value of the azimuth angle was then... The area is uniformly divided into 501 points, and each array element receives independent and identically distributed Gaussian white noise. The signal-to-noise ratio of the broadband signal is defined as:

[0123]

[0124] The ratio of trust to action is:

[0125]

[0126] in,

[0127] , and These correspond to the frequency points. The target signal power, noise power, and interference signal power.

[0128] Simulation A:

[0129] Simulate targets at three azimuth angles of -10°, 30°, and 60°, with a signal-to-noise ratio of 10 dB for each. Simulate frequency. and For broadband signals, construct the difference-frequency self-integration point by point, i.e. A total of 51 high-frequency pairs were identified, and the minimum number of iterations for the hyperparameters was set. .

[0130] Figure 5 To illustrate the initial azimuth estimation results obtained by using the FDSBL method for self-integration at different high frequencies, targets are marked with white circles. It can be seen that when there are multiple targets, spurious peaks appear in the azimuth estimation results. At the same time, the sine value of the spurious peak changes linearly with frequency, while the azimuth angle of the real target remains stable with frequency. Figure 6 This is the azimuth spectrum obtained by directly averaging the FDSBL results at different frequency points in the frequency domain. Figure 7 The results after updating the dictionary matrix six times using the IRD-FDSBL method show that the spurious peaks are almost completely eliminated and the azimuth spectrum background is cleaner, proving the effectiveness of the method.

[0131] Simulation B:

[0132] Based on simulation A, a target with a signal-to-noise ratio of 5 dB is set to arrive at an angle of -10°. Two interferences with different intensities are set to arrive at angles of 30° and 60° respectively, with signal-to-interference ratios of -5 dB and -15 dB. The performance of the proposed algorithm in estimating the target's azimuth under strong interference is analyzed.

[0133] Figure 8 The frequency domain average result after 5 updates of IRD-FDSBL shows that the spurious peaks are almost completely removed and the target can be significantly identified, verifying that the proposed algorithm can effectively remove spurious peaks and significantly improve the target direction finding accuracy under strong interference.

[0134] Simulation C:

[0135] Based on simulation A, two targets are set to arrive at angles of -10° and -13° respectively, with a signal-to-noise ratio of 5 dB. An interference target is set to arrive at an angle of 60°, with a signal-to-interference ratio of -5 dB. The direction-finding performance of the algorithm for nearby targets under strong interference conditions is analyzed.

[0136] Figure 9 The DOA estimation results of the IRD-FDSBL method can clearly distinguish two neighboring targets and effectively remove spurious peaks, demonstrating good direction-finding performance.

[0137] Simulation D:

[0138] An interference signal with a constant azimuth over time was simulated, while two targets with azimuths changing over time were present. The signal-to-interference ratios were -5 dB and -10 dB, respectively. Azimuth estimation was performed every 20 snapshots as one frame, and a total of 121 frames of data were processed.

[0139] Figure 10 The orientation history map obtained using the IRD-FDSBL method was plotted. False peaks were completely removed in most snapshots, and all target trajectories were clear, enabling accurate estimation of target orientation.

[0140] Calculation example 2:

[0141] To quantitatively analyze the direction-finding performance of the proposed method in different scenarios, the root mean square error is defined. Monte Carlo independent experiments were used for statistical comparison:

[0142]

[0143] in,

[0144] It is the estimated direction of the k-th signal in the g-th independent experiment;

[0145] K is the number of target signals;

[0146] G represents the number of independent Monte Carlo experiments.

[0147] FDB stands for Conventional Frequency Differential Beamforming, FA-FDSBL represents the azimuth estimation result obtained by directly averaging FDSBL results at different frequencies in the frequency domain, and MF-FDSBL sets up data containing L sets of self-integrations. For all Applying the same sparsity constraint, we obtain the update rule:

[0148]

[0149] The azimuth spectrum estimation results are obtained by directly processing multiple sets of self-integrations. SBLFDH is a method proposed in existing literature. It uses the full Hadamard product to construct a dictionary matrix, applies the SBL method to estimate the two-dimensional hyperparameter matrix, and obtains the azimuth spectrum estimate by extracting the diagonal elements of the result.

[0150] First, we verify the performance of different methods at different frequency points, with a fixed frequency. The remaining conditions are the same as in simulation B. One hundred Monte Carlo simulations are performed, with the number of high-frequency pairs ranging from 51 to 501, and a step size of 50. Under the same conditions, the root mean square error of the results from different methods is statistically analyzed. The average time taken to output one frame is as follows: Figure 11 .

[0151] from Figure 11 As can be seen, when the number of high-frequency pairs is less than 200, the FDB, FA-FDSBL, and MF-FDSBL methods all have large errors in target direction finding. In contrast, IRD-FDSBL and SBLFDH still have high direction finding accuracy with fewer frequency points. When the number of high-frequency pairs is greater than 150, the error of the MF-FDSBL method in target direction finding is significantly reduced. When the number of high-frequency pairs is greater than 250, all methods can successfully estimate the target azimuth, with the SBL-based method having higher direction finding accuracy. Figure 11 (b) It can be seen that in order to achieve higher resolution and lower sidelobes, the overall running time of SBL-type methods is higher than that of FDB, SBLFDH takes the longest time, and IRD-FDSBL can complete the removal of pseudo-peaks with only a few updates. At the same time, as the number of vectors contained in the dictionary matrix decreases with each iteration, the time of one iteration also decreases. Therefore, the time consumed is much less than that of SBLFDH, and the computational efficiency is relatively high.

[0152] To analyze the performance of the proposed method under different signal-to-noise ratios (SNRs) and signal-to-interference ratios (SINRs), based on Simulation B, the target SNR was changed from -20 dB to 30 dB in 5 dB increments. One hundred independent Monte Carlo replicate experiments were conducted, and the results of different algorithms were statistically analyzed. like Figure 12It can be seen that when the signal-to-noise ratio (SNR) is less than -10 dB, the direction finding results of several frequency difference methods have relatively large errors. The MF-FDSBL method assumes a common sparse mode across frequencies and processes multi-frequency data together, resulting in the lowest root mean square error. SBLFDH and IRD-FDSBL can achieve high-precision direction finding when the SNR is greater than -5 dB, exhibiting relatively good direction finding performance. When the SNR is greater than 5 dB, MF-FDSBL can achieve robust target azimuth estimation. FDB and FA-FDSBL suppress spurious peaks through frequency domain averaging. When the SNR is low, the overall root mean square error of FA-FDSBL is lower than that of FDB, and when the SNR is greater than 10 dB, it can achieve robust azimuth estimation.

[0153] Based on simulation B, the power of the interference from 60° was varied to increase the signal-to-interference ratio from -30dB to 25dB in 5dB increments. One hundred independent Monte Carlo experiments were conducted to statistically analyze the azimuth estimation results of different algorithms. like Figure 13 For the FDB, FA-FDSBL, and MF-FDSBL methods, they all exhibit large direction-finding errors and almost completely fail when the signal-to-interference ratio (SIR) is less than -10dB. The MF-FDSBL method can achieve robust azimuth estimation when the SIR is greater than -5dB. The proposed IRD-FDSBL and SBLFDH methods can accurately estimate the azimuth of the target and interference when the SIR is greater than -20dB, demonstrating good direction-finding performance.

[0154] Calculation example 3:

[0155] The performance of different methods was verified using data received from the HLA North array in the S59 experiment on a SwellEx96. During the S59 experiment, in addition to the target vessel, there was a strong interference signal (noise from nearby vessels), which could be used to verify the performance of the IRD-FDSBL method in a multi-target scenario. The horizontally non-uniform linear array HLA North has 27 effective elements and an array aperture of 240 m. Its array structure is shown in Figure 14(a). The array is deployed at a depth of 213 m underwater. The underwater sound velocity profile is shown in Figure 14(a). Figure 14 As shown in (b):

[0156] The array received signal sampling rate was 3276.8 Hz, with each 4096 sampling points divided into a snapshot (1.25 seconds). The average of 8 snapshots was used as the azimuth estimation result for one frame. The scanning angle range was 0°~360°, and the grid spacing was 0.5°. The MVDR beamforming method was used to estimate the azimuth of the array received signal over a duration of approximately 64 minutes, processing the frequency band from 1000 to 1100 Hz. The azimuth history diagram is shown below. Figure 15As shown, the trajectories of the two targets in the current time period roughly coincide with the GPS recording results. However, due to the selected frequency band not meeting the Nyquist sampling rate, multiple grating lobes appear in the results, and the side lobes are relatively high.

[0157] Based on the proposed IRD-FDSBL algorithm, the initial spectrum obtained by the FDSBL method is iteratively updated to obtain the azimuth estimation result, as shown below. Figure 16 , 17 As shown, the initial number of vectors in the dictionary matrix is ​​721. Figure 16 (a)~(d) and Figure 17 (e)~(f) show the results for setting the number of remaining entries in the dictionary matrix at the time of stopping iteration to 10, 20, 50, 100, 150, and 200, respectively. Figure 16 and Figure 17 It can be seen that the clarity of the azimuth spectrum trajectory is significantly improved after iterative updates. Sidelobes caused by spurious peaks are almost eliminated, the overall background is lower, the main lobe is narrower, and the azimuth resolution is higher. When Q is set to 10 and 20, the left target trajectory is not very continuous from the 20th to the 40th minute. As the number of remaining entries Q in the dictionary matrix increases, the continuity of the target trajectory improves slightly. When the number of remaining entries Q in the dictionary matrix increases to 50, the two target trajectories are relatively clear and have almost no sidelobe influence, while also showing a significant suppression effect on mirror targets. When the number of remaining entries Q in the dictionary matrix increases to 200, both target trajectories are clearer and more coherent. Comparing the results of different Q values, it can be seen that when Q is set smaller, the number of sidelobes affecting the observation in the azimuth map is less, but there may be discontinuities in the target trajectory at some locations. When Q is set larger, the target trajectory is more continuous and the azimuth estimation result is better, but the influence of sidelobes and spurious peaks increases accordingly. Therefore, when the signal-to-noise ratio is low or the number of targets is large, it is necessary to set appropriate stopping iteration conditions.

[0158] This disclosed technical solution applies the sparse Bayesian learning algorithm to the FD sparse signal reconstruction problem, and proposes a multi-shot frequency difference sparse Bayesian learning algorithm (FDSBL), which improves the robustness and resolution of orientation estimation compared with the traditional FDB method.

[0159] Furthermore, an iteratively refined dictionary matrix (IRD-FDSBL) method is proposed. This method optimizes the dictionary matrix by quantifying the stability of the FDSBL azimuth spectrum peaks between different frequency pairs and removing elements corresponding to unstable components from the dictionary matrix. The dictionary matrix is ​​then iteratively updated multiple times to remove spurious peaks.

[0160] Numerical simulation and experimental data results both demonstrate that the proposed method can effectively remove spurious peaks in frequency difference processing, improve the detection capability of weak targets, and thus improve the accuracy of target azimuth estimation. At the same time, the technical solution disclosed in this paper has high computational efficiency and good applicability.

[0161] Any changes made to the above embodiments by those skilled in the art without departing from the true spirit and scope of this disclosure should be included within the scope of protection covered by the claims. The scope of protection claimed by this invention is limited only by the claims.

Claims

1. A method for estimating azimuth relative to spurious peaks using sparse Bayesian learning, characterized in that, include: The array of elements collects acoustic signals to obtain multi-shot array signals; L reference high-frequency points are selected in the high signal-to-noise ratio band of the acoustic signal and the difference frequency value is set to obtain L frequency pairs; where L is a positive integer greater than 1. For each reference high-frequency point, a dictionary matrix characterizing the complex amplitude response of each element to the acoustic signal in each grid direction is constructed based on the element position and orientation search parameters of the array element array; wherein, the orientation search parameters include a preset scanning angle domain and the number of grid points; the grid direction refers to the direction obtained by discretizing the preset scanning angle domain according to the preset number of grid points; Based on the multi-snap array signal, the L frequency pairs and the dictionary matrix, frequency difference sparse signal reconstruction is performed based on sparse Bayesian learning to construct a joint spectrum matrix characterizing the signal intensity of each reference high-frequency acoustic signal in each grid direction. By quantifying the stability of the signal strength as it changes with the reference high frequency point, spurious signal strengths generated by frequency difference cross terms in the joint spectrum matrix are identified and removed, resulting in an optimized joint spectrum matrix. The optimized joint spectrum matrix is ​​averaged in the frequency domain to obtain the azimuth spectrum, and then the azimuth estimation result is obtained.

2. The method according to claim 1, characterized in that, The construction and optimization of the joint spectral matrix, wherein the construction of the joint spectral matrix includes: For each frequency pair, a differential feature matrix is ​​constructed based on the multi-shot array signals of its corresponding two frequency points; Initialize the sparse Bayesian hyperparameters for each reference high-frequency point, including signal strength hyperparameters and noise estimation hyperparameters; For each of the reference high-frequency points, a cross-covariance matrix is ​​constructed based on its dictionary matrix and the current sparse Bayesian hyperparameters; Using the evidence maximization framework based on sparse Bayesian learning, the hyperparameter iterative formula derived from the likelihood function is maximized using a fixed-point iterative method, and the signal strength hyperparameter and noise estimation hyperparameter are iteratively estimated up to a preset number of times. The joint spectrum matrix is ​​constructed based on the signal strength hyperparameters iterated to a preset number of times.

3. The method according to claim 1 or 2, characterized in that, Optimization of the joint spectral matrix, wherein quantifying the stability of the signal intensity as a function of the reference high-frequency point includes: Set a hard threshold, set the elements in the joint spectrum matrix that are greater than or equal to the hard threshold to 1, and keep the original values ​​of the remaining elements to obtain a partially binarized joint spectrum matrix; For the grid column vectors in the partially binarized joint spectrum matrix, at least one of the remaining grid column vectors is randomly selected, and the elements are multiplied one by one and the average of the results is taken to obtain the updated partially binarized joint spectrum matrix. The updated partially binarized joint spectrum matrix is ​​summed in the frequency domain to obtain the pseudospectrum; The stability threshold is calculated based on the pseudospectrum, thereby quantifying the stability.

4. The method according to claim 3, characterized in that, The number of the remaining grid column vectors selected randomly is equal to L.

5. The method according to claim 4, characterized in that, Optimization of the joint spectral matrix, wherein identifying and removing spurious signal intensities in the joint spectral matrix due to frequency difference cross terms, includes: Based on the quantization of stability, remove the grid column vectors corresponding to the false signal strength from the current dictionary matrix to obtain the updated dictionary matrix; Based on the updated dictionary matrix, the sparse Bayesian hyperparameters corresponding to the true signal strength in the current joint spectrum matrix are estimated once, and the signal strength hyperparameters corresponding to the false signal strength are assigned to a minimum value to obtain the updated joint spectrum matrix. Using the updated joint spectrum matrix, the stability quantization, dictionary matrix update, and joint spectrum matrix update are performed again. When the column vectors of the dictionary matrix grid are less than or equal to the preset number of vectors, the current joint spectrum matrix is ​​the optimized joint spectrum matrix.

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