A passive synthetic aperture method and system for underwater acoustics based on compressed sensing

Abstract

This invention discloses a method and system for passive synthetic aperture in underwater acoustics based on compressed sensing. The method includes: selecting an angle θ and a phase correction factor ψ of a uniform linear array to be searched; constructing a dictionary matrix to select J+1 segments of samples for synthetic aperture; and traversing every two consecutive sample segments x. all Based on the dictionary matrix, the sparse Bayes algorithm is used to obtain the corresponding two consecutive sample segments x. all Phase correction factor estimation; based on the phase correction factor estimation, the array manifold matrix A of the synthetic aperture is... w Compensation is performed using samples from segment J+1 and A. w High-resolution azimuth estimation of target signals is achieved through the SBL-Robust algorithm or other high-resolution DOA algorithms. This invention can effectively perform aperture expansion, achieving higher azimuth resolution performance compared to conventional beamforming and sparse Bayesian methods before expansion. Compared to traditional ETAM-type methods, it exhibits high azimuth resolution and direction-finding accuracy even when array motion does not overlap, and demonstrates robustness under low signal-to-noise ratio conditions.

Description

Technical Field

[0001] This invention belongs to the field of underwater acoustic signal processing, and specifically relates to a passive synthetic aperture method and system for underwater acoustics based on compressed sensing. Background Technology

[0002] Sonar's azimuth resolution and direction-finding accuracy are often important performance indicators for estimating the location of a target. To obtain higher azimuth resolution, arrays with larger physical apertures are often required. However, the application of large-aperture arrays is often limited in practice. For example, in underwater unmanned autonomous vehicles, due to platform size limitations, only small-aperture arrays can be carried for target detection.

[0003] To achieve better orientation resolution under small aperture conditions, high-resolution DOA algorithms such as MVDR and MUSIC were proposed in the 20th century. In recent years, deconvolution-based methods have also been proposed for orientation estimation. Compressed sensing theory can be used for sparse signal reconstruction, mathematically involving solving an underdetermined system of equations with sparse constraints. Currently, various algorithms exist for reconstructing sparse signals using compressed sensing, such as greedy algorithms, convex optimization algorithms, and Sparse Bayesian Learning (SBL). Sparse Bayesian Learning (SBL) is a compressed sensing method that assigns a prior distribution to unknown parameters and uses a Bayesian framework to obtain their corresponding maximum a posteriori distribution. Compared to traditional compressed sensing methods (such as L1-SVD), it offers advantages such as high computational efficiency, high robustness, and no need to set regularization parameters. It has been applied in areas such as orientation estimation, channel estimation, normal mode separation, target localization, and multipath arrival delay estimation. Besides high-resolution DOA algorithms, passive synthetic aperture technology can process signals received by moving small-aperture arrays to obtain virtual aperture arrays larger than the actual physical apertures, thereby achieving higher azimuth resolution, direction-finding accuracy, and array gain. Common passive synthetic aperture methods include the Yen and Carey method, the FFTSA method, the ML method, and the ETAM method. Among them, the ETAM method shows better performance in terms of robustness, direction-finding accuracy, and computational cost.

[0004] Many improved algorithms have emerged in the current ETAM method, but these ETAM-based algorithms still require array element overlap processing to achieve aperture expansion. When there are errors in the array displacement information between two adjacent measurements, it can easily cause a large deviation in the phase factor estimation of the virtual array, thus affecting the accuracy of azimuth estimation. Summary of the Invention

[0005] Traditional ETAM-based passive synthetic aperture methods suffer from inaccurate phase correction factor estimations for multiple targets during continuous array measurements when element overlap is not satisfied, ultimately leading to aperture expansion failure. The purpose of this invention is to overcome these shortcomings of the prior art and propose a compressed sensing-based underwater acoustic passive synthetic aperture method.

[0006] To achieve the above objectives, this invention proposes a passive synthetic aperture method for underwater acoustics based on compression sensing, the method comprising:

[0007] Step 1) Select the angle θ to be searched in the uniform linear array and the phase correction factor ψ, and construct the dictionary matrix.

[0008] Step 2) Select the J+1 segment of the sample with the synthetic aperture, and iterate through every two consecutive sample segments x all Based on dictionary matrix The sparse Bayesian algorithm is used to obtain the corresponding two consecutive sample segments x. all Phase correction factor estimation for each target;

[0009] Step 3) Estimate the array manifold matrix A for the synthetic aperture based on the phase correction factor from Step 2). w Compensation is performed using samples from segment J+1 and A. w High-resolution orientation estimation of target signals can be achieved using the SBL-Robust algorithm or other high-resolution DOA algorithms.

[0010] As an improvement to the above method, before step 1), there are K target signals with frequency f respectively at angle θ. k Incident on a uniform linear array.

[0011] As an improvement to the above method, the uniform linear array in step 1) is N elements with an element spacing of d, and moves at a constant linear velocity v.

[0012] As an improvement to the above method, step 1) dictionary matrix Satisfy the following formula:

[0013]

[0014] a(θ u ,ψ w )=[1,...,exp(-j2πf(N-1)dcosθ u / c),

[0015] exp(jψ w ),exp(jψ w )exp(-j2πf(N-1)dcosθ u / c)]T

[0016] Wherein, the phase correction factor is θ=[θ1,...,θ u ,...,θ U ] T Let ψ be the azimuth angle to be searched, ψ = [ψ1,...,ψ2]. w ,...,ψ W ] T Let be the phase correction factor to be searched, with a value range of [-π, π]. The number of target signals K << UW, where U represents the number of azimuth angles to be searched, W represents the number of phase correction factors to be searched, and a(θ) u ,ψ w ) represents the azimuth angle θ in the dictionary matrix. u The phase correction factor is ψ w c represents the speed of sound, j represents the imaginary part, and the superscript T indicates transpose.

[0017] As an improvement to the above method, in step 2), every two consecutive sample segments x all for:

[0018] x all =[x T (t i ),x T (t i +τ)] T

[0019] Where x(t) i ) and x(t i +τ) are respectively t i Time and t i The signal received by the uniform linear array at time +τ; the superscript T indicates transpose.

[0020] As an improvement to the above method, step 2) includes:

[0021] Set the sound source signal for all scanning positions It follows a complex Gaussian distribution with mean 0 and covariance matrix Γ, satisfying the following equation:

[0022]

[0023] In the formula, Γ=diag(γ) is a diagonal matrix, and the diagonal elements γ=[γ 1,1 ,…,γ 1,W ,…,γ U,1 ,…,γ U,W ] T The signal energy of each scan grid;

[0024] Setting noise e allIt follows a pattern with a mean of 0 and a covariance of σ. 2 Complex Gaussian distribution of I Then x all Follow the mean The variance is σ 2 The complex Gaussian distribution of I satisfies the following equation:

[0025]

[0026] Therefore, x is obtained. all Regarding γ and σ 2 The joint likelihood function is:

[0027]

[0028] In the formula, Let H represent the ideal received data covariance matrix, where the superscript H indicates the conjugate transpose; I represents the 2N×2N identity matrix.

[0029] For the joint likelihood function p(x) all |γ,σ 2 To obtain an estimate of the hyperparameter γ, maximize the logarithm.

[0030]

[0031] By differentiating γ and setting it to 0, we obtain the iterative update formula for γ:

[0032]

[0033] in, These are the hyperparameters γ before and after the current iteration, respectively.

[0034] σ is obtained from the following formula. 2 The estimated value

[0035]

[0036] in, For γ new The set of K positions corresponding to non-zero elements. It is the corresponding set of steering vectors, the corresponding positions of the K peaks in γ, which serve as the phase correction factor estimate and the pre-estimate of the target azimuth angle for each array expansion;

[0037] Repeat the above steps to process the J+1 consecutive samples J times, and obtain a total of JK phase correction factor estimates for K targets.

[0038] As an improvement to the above method, step 3) includes:

[0039] The array manifold matrix A for the synthetic aperture is estimated based on the phase correction factor. w Compensation is performed, and then combined with the J+1 segment samples, the k-th column vector a k Represented as:

[0040]

[0041] The phase correction factor ψ obtained from all estimates for each target k =[ψ k,1 ,ψ k,2 ,…,ψ k,J ] T Substitute a k Achieve aperture expansion; when errors occur in array motion, the ψ corresponding to each signal will be... k Substitute a k ;

[0042] For the synthesized array manifold matrix A w Perform phase compensation;

[0043] Direction estimation can be performed using the SBL-Robust algorithm or other high-resolution DOA algorithms.

[0044] On the other hand, the present invention proposes a compression sensing-based underwater acoustic passive synthetic aperture system, the system comprising:

[0045] The dictionary matrix construction module is used to select the angle θ and phase correction factor ψ of the uniform linear array to be searched, and construct the dictionary matrix.

[0046] The phase correction factor estimation module is used to select the J+1 segment of the synthetic aperture sample and iterate through every two consecutive sample segments x. all Based on dictionary matrix The sparse Bayesian algorithm is used to obtain the corresponding two consecutive sample segments x. all Phase correction factor estimation; and

[0047] The azimuth estimation module is used to estimate the array manifold matrix A for the synthetic aperture based on the phase correction factor from the phase correction factor estimation module. w Compensation is performed, and the high-resolution orientation of the target signal is estimated using the SBL-Robust algorithm or other high-resolution DOA algorithms.

[0048] Compared with the prior art, the advantages of the present invention are:

[0049] This method can effectively expand the aperture and achieve higher azimuth resolution compared to conventional beamforming and pre-expansion sparse Bayesian methods. Compared to traditional ETAM-type methods, this method has high azimuth resolution and direction finding accuracy when the array motion does not overlap, and its performance is robust under low signal-to-noise ratio conditions. Attached Figure Description

[0050] Figure 1 This is a flowchart of the underwater acoustic passive synthetic aperture method based on compression sensing of the present invention;

[0051] Figure 2 shows the phase correction factor estimation for SBL-PSA, where Figure 2(a) shows the phase correction factor between the first and second segments, and Figure 2(b) shows the phase correction factor between the second and third segments.

[0052] Figure 3 shows the azimuth spectrum comparison of CBF, SBL and SBL-PSA at a signal-to-noise ratio of 10dB, where Figure 3(a) is a 10-element array and Figure 3(b) is a 30-element array.

[0053] Figure 4 shows the azimuth spectrum comparison of different displacement errors under single-target conditions, where Figure 4(a) shows no displacement error and Figure 4(b) shows a displacement error of 60%.

[0054] Figure 5 shows the orientation spectrum comparison under multi-target conditions with different displacement errors, where Figure 5(a) shows no displacement error and Figure 5(b) shows a displacement error of 60%.

[0055] Figure 6 shows the phase correction factor estimation of SBL-PSA with array motion error in the case of multiple targets. Figure 6(a) shows the phase correction factor between the first and second segments, Figure 6(b) shows the phase correction factor between the second and third segments, Figure 6(c) shows the phase correction factor between the third and fourth segments, and Figure 6(d) shows the phase correction factor between the fourth and fifth segments.

[0056] Figure 7 shows the relationship between azimuth estimation performance and array displacement error, where Figure 7(a) is the root mean square error and Figure 7(b) is the success probability.

[0057] Figure 8 shows the relationship between the azimuth estimation performance, the phase correction factor estimation performance, and the signal-to-noise ratio. Figure 8(a) shows the root mean square error of the azimuth estimation, and Figure 8(b) shows the root mean square error of the phase estimation.

[0058] Figure 9 shows the orientation history of the single-target experimental data, where Figure 9(a) is CBF, Figure 9(b) is SBL, Figure 9(c) is ETAM, and Figure 9(d) is SBL-PSA.

[0059] Figure 10 This is a diagram showing the orientation history of SBL-PSA when the array elements do not overlap;

[0060] Figure 11 is a map of the orientation history of multi-target experimental data, where Figure 11(a) is CBF, Figure 11(b) is SBL, Figure 11(c) is ETAM, and Figure 11(d) is SBL-PSA. Detailed Implementation

[0061] The method of the present invention is a passive synthetic aperture method applicable to the case of non-overlapping motion of towed arrays. It estimates the phase correction factor and angle of each target through a sparse Bayesian learning algorithm, and then performs phase compensation on each target on the manifold matrix of the synthetic array to achieve aperture expansion and azimuth estimation.

[0062] The following is a detailed description and derivation of the method of the present invention.

[0063] Array Received Signal Model

[0064] Consider an N-element uniform linear array with element spacing d moving at a constant velocity v. K target signals with frequency f are emitted at angles θ. k Incident on the array, t i The signal model received by the time array can be represented as:

[0065] x(t i )=As(t i )+e(t i (1)

[0066] In the formula Let A be an array manifold matrix, and each element a... nk =exp[-j2πf(n-1)dcosθ k / c]. s(t i )=[s1(t i ),…,s K (t i )] T For t i The sound source signal at time t, e(t) i )=[e1(t i ),…,e N (t i )] T For t i The received noise at time t. i The signal model received by the array at time +τ can be expressed as:

[0067] x(t i +τ)=A τ s(t i )+e(t i +τ) (2)

[0068] Where A τEach element a τ,nk =exp(jφ)exp[-j2πf((n-1)d+vτ)cosθ k / c], φ=2πfτ is the phase correction factor of the target signal between these two consecutive measurements. A joint reception model for the two consecutive measurements can be constructed from equations (1) and (2):

[0069] x all =A all s+e all (3)

[0070] Where x all =[x T (t i ),x T (t i +τ)] T A all =[A(t) i ); A(t) i +τ)],e all =[e T (t i ),e T (t i +τ)] T The above model can be extended as follows:

[0071]

[0072] in θ=[θ1,...,θ U ] T Represents the orientation of all scans, ψ = [ψ1,...,ψ] W ] T This represents the phase correction factor for all scans. Let K represent the sound source signals at all scan positions. Typically, the number of sound sources K << UW, meaning that only a small number of elements on the scan grid have non-zero numbers, given the received signal x. all and extended joint array manifold matrix In this case, compressed sensing can be used to... Solve the problem.

[0073] Phase correction factor estimation based on sparse Bayes

[0074] Assumption It follows a complex Gaussian distribution with mean 0 and covariance matrix Γ, that is:

[0075]

[0076] In the formula, Γ=diag(γ) is a diagonal matrix, and the diagonal elements γ=[γ1,1 ,…,γ 1,W ,…,γ U,1 ,…,γ U,W ] T Let e ​​be the signal energy of each scan grid. Assume the noise is e. all It follows a pattern with a mean of 0 and a covariance of σ. 2 Complex Gaussian distribution of I Then the received signal x all Follow the mean The variance is σ 2 The complex Gaussian distribution of I, i.e. Therefore, x all Regarding γ and σ 2 The joint likelihood function is:

[0077]

[0078] In the formula Let represent the ideal received data covariance matrix. We estimate γ by maximizing the logarithm of the joint likelihood function in equation (6):

[0079]

[0080] Differentiating equation (6) and setting it to 0, we obtain the iterative update formula for γ:

[0081]

[0082] Noise σ 2 The estimate is obtained from the following formula:

[0083]

[0084] in For γ new The set of K positions corresponding to non-zero elements. This is the set of its corresponding steering vectors. The corresponding positions of the K peaks in γ can be used as a phase correction factor and a pre-estimate of the target azimuth angle for each array expansion. In practical use, it is first necessary to determine the values ​​of γ and σ. 2 Initialize with K, and then use equations (8) and (9) to set γ and σ. 2 Iterative updates are performed until the γ obtained from two consecutive iterations converges to a preset threshold.

[0085] When an error occurs in the displacement measured by the array in each consecutive measurement, i.e., v′τ ≠ vτ, where v′τ is the actual displacement and vτ is the preset displacement, let v′ = v + Δv, that is, v′τ = vτ + Δvτ, then t i The array manifold A at time +τ′ τ′ The elements in the middle are:

[0086] a τ′,nk =exp(jφ)exp(-j2πfΔvτcosθ k / c)exp[-j2πf((n-1)d+vτ)cosθ k / c] (10)

[0087] In the formula, exp(-j2πfΔvτcosθ k / c) represents the error term caused by the array displacement error Δvτ. Let Δr = Δvτ, and consider this term as the phase error caused by the array displacement error. Then the actual phase correction factor ψ k ′ should be:

[0088]

[0089] ψ k ′ and the azimuth angle θ of each target k This is relevant. When using a preset displacement as the manifold matrix and estimating it via SBL, Δr can compensate for the phase correction factor of each target, preventing errors in phase factor estimation caused by array displacement perturbations. By processing J+1 consecutive samples J times, J phase correction factors can be obtained for each of the K targets.

[0090] The received signal X(t) of consecutive J+1 segments of samples i This can be represented as:

[0091] X(t i ) = A w s(t i )+E(t i (12)

[0092] In the formula X(t) i )=[x T (t i ),x T (t i +τ1),…,x T (t i +τ J )] T ,

[0093] E(t i )=[e T (t i ),e T (t i +τ1),…,e T (t i +τ j )] T , For the synthetic aperture manifold matrix, its k-th column vector a k It can be represented as:

[0094]

[0095] The phase correction factor ψ obtained from all estimates for each target k =[ψ k,1 ,ψ k,2 ,…,ψ k,J ] T Substitute a k This is used to achieve aperture expansion. When there are no errors in the array motion, the phase correction factor for each target is the same, i.e., ψ1=ψ2…=ψ K When errors occur in the array motion, it is necessary to adjust the ψ corresponding to each signal. k Substitute a k Phase compensation is performed on each target to achieve aperture expansion. The synthetic array manifold matrix A... w After phase compensation, CBF or other high-resolution DOA algorithms can be used to achieve more accurate azimuth estimation of the target. This invention employs the SBL-Robust method, applicable to array perturbations, to achieve azimuth estimation. This proposed method is abbreviated as SBL-PSA.

[0096] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0097] Example 1

[0098] Embodiment 1 of the present invention proposes a passive synthetic aperture method for underwater acoustics based on compression sensing, the method comprising:

[0099] A passive synthetic aperture method for underwater acoustics based on compressed sensing, the method comprising:

[0100] Step 1) Select the angle θ to be searched in the uniform linear array and the phase correction factor ψ, and construct the dictionary matrix.

[0101] Specifically: The following formula is used to establish the two consecutive received signals x all Corresponding dictionary matrix

[0102]

[0103] a(θ u ,ψ w )=[1,...,exp(-j2πf(N-1)dcosθ u / c),

[0104] exp(jψ w),exp(jψ w )exp(-j2πf(N-1)dcosθ u / c) T

[0105] Where θ = [θ1,...,θ] U ] T Let ψ be the azimuth angle to be scanned, ψ = [ψ1,...,ψ2]. W ] T This is the phase correction factor to be scanned, which is generally set to [-π, π].

[0106] Step 2) Select the J+1 segment of the sample with the synthetic aperture, and iterate through every two consecutive sample segments x all Based on dictionary matrix The sparse Bayesian algorithm is used to obtain the corresponding two consecutive sample segments x. all Phase correction factor estimation for each target;

[0107] Specifically: based on dictionary matrix and the narrowband signal x received in every two consecutive transactions all The sparse Bayesian algorithm is used to estimate the hyperparameter γ of the sparse vector s. The non-zero elements in γ correspond to the pre-estimates of the phase correction factor and azimuth angle. J+1 consecutive samples require J processing steps, resulting in a total of JK phase correction factors.

[0108] Step 3) Estimate the array manifold matrix A for the synthetic aperture based on the phase correction factor from Step 2). w Compensation is performed using samples from segment J+1 and A. w High-resolution orientation estimation of target signals can be achieved using the SBL-Robust algorithm or other high-resolution DOA algorithms.

[0109] Example 2

[0110] Embodiment 2 of the present invention proposes a passive synthetic aperture system for underwater acoustics based on compression sensing, implemented based on the method of Embodiment 1. The system includes:

[0111] The dictionary matrix construction module is used to select the angle θ and phase correction factor ψ of the uniform linear array to be searched, and construct the dictionary matrix.

[0112] The phase correction factor estimation module is used to select the J+1 segment of the synthetic aperture sample and iterate through every two consecutive sample segments x. all Based on dictionary matrix The sparse Bayesian algorithm is used to obtain the corresponding two consecutive sample segments x. all Phase correction factor estimation;

[0113] The azimuth estimation module is used to estimate the array manifold matrix A for the synthetic aperture based on the phase correction factor from the phase correction factor estimation module. w Compensation is performed, and the high-resolution orientation of the target signal is estimated using the SBL-Robust algorithm or other high-resolution DOA algorithms.

[0114] The following numerical simulations compare this method with traditional ETAM-type methods and the pre-extension SBL method to further illustrate the advantages of this method.

[0115] Simulation 1: Comparison of the improved method with the CBF and SBL methods without array expansion.

[0116] The target signal is set as a far-field plane wave, with a source frequency of 300Hz, a stationary source, and incident azimuths of 70° and 73°. The reference sound velocity is 1500m / s, and the receiving array is a 10-element uniform horizontal towed array with a spacing of 1.5m and a tow speed of 3.25m / s. The sampling frequency is 4096Hz, the array movement distance between each measurement is set to 13.5m, i.e., 10 array elements are expanded each time, and the number of measurements is 3. The phase correction factor between every two consecutive measurements is set to 0.966, and the value range of the phase correction factor is [-π, π]. The original 10-element array can be expanded into a 30-element virtual array using the SBL-PSA method. Unless otherwise specified, the following simulations use the source frequency, sound velocity, number of receiving array elements and element spacing, sampling frequency, and tow speed described above.

[0117] Compare the azimuth estimation accuracy of CBF, SBL, and SBL-PSA before and after aperture expansion. Add Gaussian white noise with a signal-to-noise ratio of 10dB to the target signal. The signal-to-noise ratio is defined as the ratio of signal power to noise power. Figures 2(a) and 2(b) show the phase correction factor estimates obtained through SBL-PSA. Because there are three measurement segments, the array needs to be extended twice. The white boxes indicate the actual phase deviation and azimuth of the target. As shown in Figure 2, the phase factor estimation between the first and second segments yields a rough DOA estimate near the target location due to the close proximity of the targets. Since the array has no motion error, the phase correction factors for the two targets are equal, and the estimated phase correction factor is around 0.966. Phase compensation synthetic aperture is applied to the target, and the azimuth spectrum is calculated. Figure 3(a) shows the comparison of the azimuth spectra of the CBF, SBL, and SBL-PSA after two extensions at a signal-to-noise ratio of 10dB. Figure 3(b) shows the comparison of the azimuth spectra of the CBF and SBL with 30 elements and the SBL-PSA after two extensions. As shown in Figure 3, at a signal-to-noise ratio of 10 dB, the main lobes of the 10-element CBF and the 30-element CBF are wide, and the side lobes are high, making it impossible to distinguish between two targets. Although the SBL before aperture expansion has a high azimuth resolution, it is still unable to distinguish between two targets due to the limitation of the small physical aperture. However, the SBL-PSA with a third aperture expansion can accurately estimate the azimuth of two targets, and its azimuth resolution performance is close to that of the 30-element SBL, thus distinguishing between these two relatively close targets. Therefore, the method proposed in this invention can effectively synthesize apertures and has higher azimuth estimation accuracy compared to the CBF and SBL before aperture expansion.

[0118] Simulation 2. Improved method compared with ETAM and BD-ETAM

[0119] To compare SBL-PSA with ETAM-like methods, the array movement distance between two consecutive measurements was set to 7.5m. This means there are 5 overlapping array elements between each measurement segment. Traditional ETAM and BD-ETAM methods were introduced for comparison. Five consecutive measurement segments were used, representing four aperture expansion cycles.

[0120] First, the impact of array displacement error on passive synthetic aperture azimuth estimation was simulated under single-target conditions. The signal-to-noise ratio was 10 dB, and the target was located at 70°. Without array error, azimuth spectra were obtained using four methods: CBF, ETAM, BD-ETAM, and SBL-PSA. The comparison results are shown in Figure 4(a). Figure 4(a) shows that under single-target conditions, the azimuth estimates obtained by CBF, ETAM, BD-ETAM, and SBL-PSA are consistent with the true values. The main lobe widths of ETAM and BD-ETAM are basically the same, and their main lobes are narrower and their side lobes are lower than those of CBF, resulting in higher azimuth resolution. SBL-PSA uses compressed sensing and has even higher azimuth resolution. A 60% displacement error was added to each segment of array motion, and azimuth spectra were obtained using the four methods: CBF, ETAM, BD-ETAM, and SBL-PSA. The comparison results are shown in Figure 4(b). As can be seen from Figure 4(b), even when there are errors in the array motion, ETAM and BD-ETAM can still accurately estimate the azimuth of a single target.

[0121] Next, the impact of array displacement error on various passive synthetic aperture methods under multi-target conditions is compared. Two sound sources are set at 70° and 90° respectively, with an input signal-to-noise ratio of 10dB. The azimuth spectra are obtained using four methods—CBF, ETAM, BD-ETAM, and SBL-PSA—under two conditions: no array error and an array displacement error of 60%. The azimuth estimation results are shown in Figure 5. Figure 5(a) shows the comparison results of the azimuth spectra without array error, and Figure 5(b) shows the comparison results of the azimuth spectra with an array error of 60%. As can be seen from Figure 5(a), when there is no array displacement error, ETAM and BD-ETAM can still accurately estimate the DOA for multiple targets. However, when there is an array displacement error, the azimuth estimation of ETAM and BD-ETAM is biased, and accurate estimation for one of the targets cannot be achieved. SBL-PSA, on the other hand, can accurately estimate two targets under both error-free and error-prone conditions. Figure 5(a) shows no displacement error; Figure 5(b) shows a displacement error of 60%. There are a total of four sets of adjacent measurements. Each set of phase factor estimates shows two targets, each corresponding to a different phase correction factor. The white boxes represent the actual phase difference and azimuth position of the targets. The phase correction factor ψ corresponding to each target is determined separately. k .

[0122] Next, to demonstrate the performance of the proposed method under different array displacement errors and signal-to-noise ratios, SBL-PSA is compared with ETAM and BD-ETAM. The success probability of azimuth estimation is defined as the ratio of the number of successful estimations to the total number of trials. An estimation error less than 1° is considered a successful estimation. The root mean square error (RMSE) is defined as:

[0123]

[0124] K is the number of sound sources, set to 2, N mc The number of Monte Carlo simulation experiments is set to 200. θ i,k Let θ be the actual location of the k-th sound source in the i-th Monte Carlo simulation experiment. i,k The estimated azimuth of the k-th sound source in the i-th Monte Carlo simulation experiment is shown in Figure 6. The two sound sources are located at 70° and 90° respectively. The simulation results are shown in Figure 6. The relative standard deviation of the array displacement in the simulation ranges from 0 to 0.6. Figure 6(a) shows the phase correction factor between the first and second segments, Figure 6(b) shows the phase correction factor between the second and third segments, Figure 6(c) shows the phase correction factor between the third and fourth segments, and Figure 6(d) shows the phase correction factor between the fourth and fifth segments. As can be seen from Figures 7(a) and 7(b), the root mean square error increases with the increase of the relative standard deviation of the array displacement. The root mean square error of ETAM is the largest. When the relative standard deviation of the displacement is between 0 and 0.15, the root mean square errors of BD-ETAM and SBL-PSA are relatively close. When the relative standard deviation of the displacement is greater than 0.15, the root mean square error of SBL-PSA is lower than that of BD-ETAM. The estimation success probability of ETAM, BD-ETAM, and SBL-PSA decreases with increasing relative standard deviation of array displacement. When the relative standard deviation of displacement offset is greater than 0.15, the success probability of SBL-PSA is higher than that of ETAM and BD-ETAM. Examining these three algorithms based on root mean square error and success probability, when the displacement deviation is small, BD-ETAM has higher estimation accuracy and resolution success probability than SBL-PSA. When the displacement deviation is large, SBL-PSA maintains better aperture expansion performance.

[0125] Next, the impact of different signal-to-noise ratios (SNRs) on the performance of SBL-PSA phase correction factor estimation and azimuth estimation is presented. Since ETAM and BD-ETAM cannot estimate the phase correction factor for multiple targets separately, a single-target Monte Carlo simulation was conducted with 200 simulations. The target was set to 70°, and the phase correction factor between consecutive measurements was 1.933. The input SNR in the simulation ranged from 10dB to -5dB, with no array displacement error. The results are shown in Figure 8. Figure 8(a) shows the root mean square error (RMSE), and Figure 8(b) shows the success probability. As shown in Figure 8, when the SNR is greater than 0dB, the RMSEs of BD-ETAM and SBL-PSA for azimuth estimation are low and relatively similar, with ETAM exhibiting the worst azimuth estimation performance. When the SNR is less than 0dB, the performance of both BD-ETAM and SBL-PSA deteriorates sharply, with SBL-PSA showing more robust performance compared to BD-ETAM. The phase factor estimation error increases as the signal-to-noise ratio (SNR) decreases. ETAM exhibits the worst phase factor estimation performance. When the SNR is greater than 3 dB, the phase factor estimation errors of BD-ETAM and SBL-PSA are relatively low and close. When the SNR is less than 3 dB, SBL-PSA's phase estimation performance is slightly better than BD-ETAM. Therefore, in the single-target scenario, SBL-PSA does not estimate the phase correction factor through cross-correlation. Under high SNR conditions, its azimuth estimation and phase correction factor estimation performance are close to that of BD-ETAM. Under low SNR conditions, its robustness is better than both BD-ETAM and ETAM, and its accuracy in azimuth and phase factor estimation is higher.

[0126] Experiment 1: Comparison of the improved method with other methods under single-objective conditions

[0127] Data from a towed array passive detection sea trial conducted in the South China Sea was selected. The experiment involved a dual-ship operation, with the receiving ship traveling at 5 knots. A 30-element towed array with an element spacing of 1.5m was used to receive the signal. The experimental ship remained stationary and transmitted a 100Hz single-frequency signal with a signal sampling rate f. s=12000Hz. The receiving ship processed the sea trial data using CBF, SBL, ETAM, and SBL-PSA. Each passive synthetic aperture algorithm used 15 overlapping array elements. Through four consecutive measurements, the physical aperture of 30 elements was expanded into a virtual array of 75 elements. The azimuth history is shown in Figure 9. As can be seen in Figure 9(a), the physical aperture CBF has a small physical aperture, a large main lobe width, and poor azimuth resolution, as shown in Figure 9(b). Although the main lobe width and azimuth resolution can be improved by the high-resolution DOA algorithm, after 40s, the physical aperture DOA algorithm struggles to detect the target signal from 40s to 60s. This may be due to the low signal-to-noise ratio of the received signal. Comparing Figure 9(b) and Figure 9(d), the target azimuth history trajectory from 40s to 60s in Figure 9(d) is continuous and clear. This shows that passive synthetic aperture can effectively expand the aperture and achieve a higher detection signal-to-noise ratio than the original short array. Comparing Figure 9(c) and Figure 9(d), the improved algorithm in Figure 9(d) is significantly better than ETAM in terms of azimuth estimation accuracy within the range of 20s to 60s.

[0128] Unlike the ETAM method, SBL-PSA can be applied to cases where array elements do not overlap. The preset displacement for two consecutive measurements is set to 43.5m, which is the length of the array itself. Through four consecutive measurements, the physical aperture of a 30-element array is expanded to a virtual array of 120 elements. Figure 9(a) shows CBF, Figure 9(b) shows SBL, Figure 9(c) shows ETAM, and Figure 9(d) shows SBL-PSA. Figure 10 As shown, even though there is no overlap between array elements, SBL-PSA can still effectively achieve aperture expansion.

[0129] Experiment 2: Comparison of the improved method with other methods under multi-objective conditions

[0130] The sea trial data for the two targets are constructed using the following formula. The target bearing θ1 is derived from the estimation results of SBL-PSA, and the target bearing θ2 is set to 75°.

[0131]

[0132] s n (t)=s n,1 (t)+s n,2 (t) (16)

[0133] s n (t), s n,1 (t) and s n,2(t) represents the multi-target data, raw data, and target 2 data received at time t, respectively. The azimuth history diagram is shown in Figure 11. As shown in Figure 11, the azimuth spectrum estimation of ETAM in the first 30 seconds is unstable, and the peak value differs from the actual target position. This may be due to the error between the preset displacement and the actual displacement, while the target estimation result of SBL-PSA is more accurate and stable. This result shows that when there is an error in the array displacement, SBL-PSA is more accurate than ETAM in estimating the phase correction factor and the target azimuth. Figure 11 is the azimuth history diagram of multi-target experimental data, where Figure 11(a) is CBF, Figure 11(b) is SBL, Figure 11(c) is ETAM, and Figure 11(d) is SBL-PSA.

[0134] Overview

[0135] This invention proposes a passive synthetic aperture method for underwater acoustics based on compressed sensing. It establishes a dictionary matrix related to azimuth and phase correction factors using SBL (Synthetic Boolean), processes continuously measured underwater acoustic signals to obtain phase factor estimates and angle pre-estimates for each target, and then performs phase compensation on each target in the synthetic array manifold matrix to achieve aperture expansion. Compared to ETAM and BD-ETAM, this method can effectively expand the aperture when there are errors in array motion, significantly improving direction finding accuracy and azimuth resolution. Under low signal-to-noise ratio conditions, the phase correction factor estimation performance of this method is improved compared to BD-ETAM and ETAM, demonstrating better robustness.

[0136] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A passive synthetic aperture method for underwater acoustics based on compressed sensing, the method comprising: Step 1) Select the angle θ to be searched in the uniform linear array and the phase correction factor ψ, and construct the dictionary matrix. Step 2) Select the J+1 segment of the sample with the synthetic aperture, and iterate through every two consecutive sample segments x all Based on dictionary matrix The sparse Bayesian algorithm is used to obtain the corresponding two consecutive sample segments x. all Phase correction factor estimation for each target; Step 3) Estimate the array manifold matrix A for the synthetic aperture based on the phase correction factor from Step 2). w Compensation is performed using samples from segment J+1 and A. w High-resolution orientation estimation of target signals can be achieved using the SBL-Robust algorithm or other high-resolution DOA algorithms. Before step 1), the method further includes: having K target signals with frequency f respectively at angle θ k Incident on a uniform linear array; The uniform linear array in step 1) has N elements and the element spacing is d. It moves at a constant linear speed v. Step 1) Dictionary matrix Satisfy the following formula: a(θ u ,ψ w )=[1,...,exp(-j2πf(N-1)dcosθ u / c), exp(jψ w ),exp(jψ w )exp(-j2πf(N-1)dcosθ u / c)] Τ Among them, the phase correction factor is θ = [θ1,..., θ u ,..., θ U Τ is the azimuth angle to be searched, ψ = [ψ1,..., ψ w ,..., ψ W Τ is the phase correction factor to be searched, and its value range is [-π, π]. The number of target signals K << UW, where U represents the number of azimuth angles to be searched, W represents the number of phase correction factors to be searched. a(θ u , ψ w ) represents the dictionary matrix with the azimuth angle θ u and the phase correction factor ψ w . c represents the speed of sound, j represents the imaginary part, and the superscript T represents the transpose;​​ Step 2) includes: Set the sound source signal for all scanning positions It follows a complex Gaussian distribution with mean 0 and covariance matrix Γ, satisfying the following equation: In the formula, Γ=diag(γ) is a diagonal matrix, and the diagonal elements γ=[γ 1,1 ,…,γ 1,W ,…,γ U,W ] Τ The signal energy of each scan grid; Setting noise e all It follows a pattern with a mean of 0 and a covariance of σ. 2 Complex Gaussian distribution of I Then x all Follow the mean The variance is σ 2 The complex Gaussian distribution of I satisfies the following equation: Therefore, x is obtained. all Regarding γ and σ 2 The joint likelihood function is: In the formula, Let H represent the ideal received data covariance matrix, where the superscript H indicates the conjugate transpose; I represents the 2N×2N identity matrix. For the joint likelihood function p(x) all |γ,σ 2 To obtain an estimate of the hyperparameter γ, maximize the logarithm. By differentiating γ and setting it to 0, we obtain the iterative update formula for γ: in, These are the hyperparameters γ before and after the current iteration, respectively. σ is obtained from the following formula. 2 The estimated value in, For γ new The set of K positions corresponding to non-zero elements. It is the corresponding set of steering vectors, the corresponding positions of the K peaks in γ, which serve as the phase correction factor estimate and the pre-estimate of the target azimuth angle for each array expansion; Repeat the above steps to process the J+1 consecutive samples J times, and obtain a total of JK phase correction factor estimates for K targets; Step 3) includes: The array manifold matrix A for the synthetic aperture is estimated based on the phase correction factor. w Compensation is performed, and then combined with the J+1 segment samples, the k-th column vector a k Represented as: The phase correction factor ψ obtained from all estimates for each target k =[ψ k,1 ,ψ k,2 ,…,ψ k,J ] Τ Substitute a k Achieve aperture expansion; when errors occur in array motion, the ψ corresponding to each signal will be... k Substitute a k ; For the synthesized array manifold matrix A w Perform phase compensation; Direction estimation can be performed using the SBL-Robust algorithm or other high-resolution DOA algorithms.

2. The underwater acoustic passive synthetic aperture method based on compression sensing according to claim 1, characterized in that, In step 2), each two consecutive sample segments x all for: x all =[x Τ (t i ),x Τ (t i +τ)] Τ Where x(t) i ) and x(t i +τ) are respectively t i Time and t i The signal received by the uniform linear array at time +τ; the superscript T indicates transpose.

3. A system based on the compression sensing-based passive synthetic aperture method for underwater acoustics as described in claim 1, characterized in that, The system includes: The dictionary matrix construction module is used to select the angle θ and phase correction factor ψ of the uniform linear array to be searched, and construct the dictionary matrix. The phase correction factor estimation module is used to select the J+1 segment of the synthetic aperture sample and iterate through every two consecutive sample segments x. all Based on dictionary matrix The sparse Bayesian algorithm is used to obtain the corresponding two consecutive sample segments x. all Phase correction factor estimation; and The azimuth estimation module is used to estimate the array manifold matrix A for the synthetic aperture based on the phase correction factor from the phase correction factor estimation module. w Compensation is performed, and the high-resolution orientation of the target signal is estimated using the SBL-Robust algorithm or other high-resolution DOA algorithms.

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