A method and device for reverberation suppression of an active sonar underwater
By using the RPCA method and dynamic step size adjustment under the ADMM framework, the problem of reverberation interference in shallow water areas of UUV active sonar was solved, achieving effective reverberation suppression and signal-to-noise ratio improvement, and adapting to different underwater acoustic environments.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- INST OF ACOUSTICS CHINESE ACAD OF SCI
- Filing Date
- 2026-03-24
- Publication Date
- 2026-06-23
Smart Images
Figure CN122260291A_ABST
Abstract
Description
Technical Field
[0001] This specification relates to the field of sonar technology in one or more embodiments, and in particular to a method and apparatus for suppressing reverberation in underwater active sonar. Background Technology
[0002] Reverberation suppression has become a research hotspot, addressing the severe reverberation interference experienced by active sonar on unmanned underwater vehicles (UUVs) in shallow water. Reverberation is formed by the superposition of echoes from numerous scattering bodies. Suppression methods mainly include: reducing the scattering area by improving directivity in the spatial domain (limited by UUV installation space); designing anti-reverberation pulse signals, such as LFM and HFM, in the signal parameter domain (limited by operating bandwidth); and utilizing the statistical difference between the target and reverberation for signal processing in the statistical domain, such as AR models, PCI, FrFT, and BSS. However, statistical domain methods rely on overly idealistic model assumptions. In environments with strong reverberation and low signal-to-mixing ratios, the essential differences between the target and reverberation are easily masked, leading to method failure or instability. Summary of the Invention
[0003] This application describes a method and apparatus for suppressing reverberation in underwater active sonar, which can solve the above-mentioned technical problems.
[0004] According to the first aspect, a method for suppressing reverberation in underwater active sonar is provided, comprising:
[0005] Active sonar is used to detect underwater moving targets and receive echo signals. An original multi-frame data matrix is constructed based on the echo signals. The elements in the original multi-frame data matrix represent the echo amplitude and phase of the spatial unit at each time.
[0006] The original multi-frame data matrix is offset-compensated to obtain the offset-compensated matrix;
[0007] The offset-compensated matrix is decomposed into a low-rank matrix and a sparse matrix as constraints. The objective function is minimized using the low-rank matrix and the sparse matrix to obtain the principal component analysis optimization model. The low-rank matrix represents the reverberation component in the echo signal, and the sparse matrix represents the target echo component in the echo signal.
[0008] The principal component analysis optimization model is iteratively solved, and the target echo component in the echo signal is obtained after the iteration converges.
[0009] In some embodiments, constructing an original multi-frame data matrix based on the echo signals includes:
[0010] The data frame matrix is obtained in the i-th working cycle. Vectorize into column vectors ;
[0011] The column vector obtained from the matrix of N consecutive data frames By splicing, the multi-frame data matrix is obtained. ,Right now ;
[0012] Among them, the data frame matrix It is the range-azimuth matrix obtained after beamforming the received echo signal. It is a complex field. and These represent the discretized distance and angular dimensions, respectively.
[0013] In some embodiments, the offset-compensated matrix is obtained by offset compensation of the original multi-frame data matrix, including:
[0014] Introducing the offset matrix The offset-compensated matrix is obtained. ,in,
[0015]
[0016] Where α>0 is a constant. It is a matrix of all 1s.
[0017] In some embodiments, the principal component analysis optimization model is obtained by using the decomposition of the offset-compensated matrix into a low-rank matrix and a sparse matrix as constraints, and constructing a minimization objective function with the low-rank matrix and the sparse matrix, including:
[0018] Establishing a robust principal component analysis (RPCA) optimization problem:
[0019]
[0020]
[0021] in It is a low-rank matrix that represents the reverberation component in the echo signal. It is a sparse matrix that represents the target echo component in the echo signal; Represents the rank of the matrix, serving as a low-rank constraint; Representing a matrix Norms, as sparsity constraints; It is a trade-off parameter between C and I, which controls the strength of sparsity.
[0022] In some more specific embodiments, the step of iteratively solving the principal component analysis optimization model includes:
[0023] Initialize sparse matrix , Lagrange multipliers , The iteration counter k, k=0;
[0024] Step 51: Calculate the low-rank matrix
[0025] For matrix Perform Singular Value Decomposition (SVD):
[0026]
[0027] For singular value matrices Applying the soft threshold operator, the threshold is The updated singular values are obtained. ;in, and It is a unitary matrix. yes The conjugate matrix;
[0028] Reconstructing the low-rank matrix ;
[0029] Step 52: Calculate the sparse matrix
[0030] For matrix Applying the soft threshold operator, the threshold is :
[0031]
[0032] Step 53: Update the Lagrange multipliers
[0033]
[0034] Step 54: Check termination conditions
[0035] Calculate the original residuals ;
[0036] Calculate dual residuals ;
[0037] Calculate the first condition Second condition ,in, and These are the preset convergence thresholds for the original residual and the dual residual, respectively. and All are positive numbers;
[0038] Otherwise, continue;
[0039] Step 54: Update penalty parameters
[0040] Calculated based on dynamic adjustment strategy Then set k = k + 1 and return to step 51.
[0041] In some more specific embodiments, the update penalty parameter includes:
[0042] Define two relative distance metrics:
[0043] The relative distance of the first condition The relative distance of the second condition ;
[0044] The penalty parameters are dynamically updated based on the comparison between the relative distances under the first condition and the relative distances under the second condition. :
[0045]
[0046] in,
[0047] When the original residual decreases too slowly ;
[0048] When the dual residual decreases too slowly ;
[0049] When the two are in balance = .
[0050] In some more specific embodiments, it also includes:
[0051] After the iteration is complete, from the final low-rank matrix Subtract offset compensation amount The reverberation component is obtained. :
[0052]
[0053] The final sparse matrix This is the target echo component.
[0054] According to a second aspect, an underwater active sonar reverberation suppression device is provided, comprising:
[0055] The first processing unit is used to detect underwater moving targets using active sonar, receive echo signals, and construct an original multi-frame data matrix based on the echo signals, wherein the elements in the original multi-frame data matrix represent the echo amplitude and phase of the spatial unit at each time.
[0056] The second processing unit is used to perform offset compensation on the original multi-frame data matrix to obtain an offset-compensated matrix.
[0057] The third processing unit is used to decompose the offset-compensated matrix into a low-rank matrix and a sparse matrix as constraints, and construct a minimization objective function using the low-rank matrix and the sparse matrix to obtain a principal component analysis optimization model. The low-rank matrix represents the reverberation component in the echo signal, and the sparse matrix represents the target echo component in the echo signal.
[0058] The fourth processing unit is used to iteratively solve the principal component analysis optimization model and obtain the target echo component in the echo signal after the iteration converges.
[0059] In some embodiments, the first processing unit is used for
[0060] The data frame matrix is obtained in the i-th working cycle. Vectorize into column vectors ;
[0061] The column vector obtained from the matrix of N consecutive data frames By splicing, the multi-frame data matrix is obtained. ,Right now ;
[0062] Among them, the data frame matrix It is the range-azimuth matrix obtained after beamforming the received echo signal. It is a complex field. and These represent the discretized distance and angular dimensions, respectively.
[0063] In some embodiments, the second processing unit is used to introduce an offset matrix. The offset-compensated matrix is obtained. ,in,
[0064]
[0065] Where α>0 is a constant. It is a matrix of all 1s.
[0066] In some embodiments, the third processing unit is used to establish a robust principal component analysis (RPCA) optimization problem:
[0067]
[0068]
[0069] in It is a low-rank matrix that represents the reverberation component in the echo signal. It is a sparse matrix that represents the target echo component in the echo signal; Represents the rank of the matrix, serving as a low-rank constraint; Representing a matrix Norms, as sparsity constraints; It is a trade-off parameter between C and I, which controls the strength of sparsity.
[0070] In some more specific embodiments, the fourth processing unit is used for
[0071] Initialize sparse matrix , Lagrange multipliers , The iteration counter k, k=0;
[0072] Step 51: Calculate the low-rank matrix
[0073] For matrix Perform Singular Value Decomposition (SVD):
[0074]
[0075] For singular value matrices Applying the soft threshold operator, the threshold is The updated singular values are obtained. ;in, and It is a unitary matrix. yes The conjugate matrix;
[0076] Reconstructing the low-rank matrix ;
[0077] Step 52: Calculate the sparse matrix
[0078] For matrix Applying the soft threshold operator, the threshold is :
[0079]
[0080] Step 53: Update the Lagrange multipliers
[0081]
[0082] Step 54: Check termination conditions
[0083] Calculate the original residuals ;
[0084] Calculate dual residuals ;
[0085] Calculate the first condition Second condition ,in, and These are the preset convergence thresholds for the original residual and the dual residual, respectively. and All are positive numbers;
[0086] like and If the iteration terminates, then the iteration ends.
[0087] Otherwise, continue;
[0088] Step 54: Update penalty parameters
[0089] Calculated based on dynamic adjustment strategy Then set k = k + 1 and return to step 51.
[0090] In some more specific embodiments, the fourth processing unit is used for
[0091] Define two relative distance metrics:
[0092] The relative distance of the first condition The relative distance of the second condition ;
[0093] The penalty parameters are dynamically updated based on the comparison between the relative distances under the first condition and the relative distances under the second condition. :
[0094]
[0095] in,
[0096] When the original residual decreases too slowly ;
[0097] When the dual residual decreases too slowly ;
[0098] When the two are in balance = .
[0099] In some more specific embodiments, it also includes:
[0100] After the iteration is complete, from the final low-rank matrix Subtract offset compensation amount The reverberation component is obtained. :
[0101]
[0102] The final sparse matrix This is the target echo component.
[0103] According to a third aspect, a computer storage medium is provided, on which a computer program is stored, which, when executed by one or more processors, implements the underwater active sonar reverberation suppression method as described in any of the above embodiments.
[0104] According to a fourth aspect, an electronic device is provided, including a memory and one or more processors, wherein the memory stores a computer program that, when executed by the one or more processors, implements the underwater active sonar reverberation suppression method as described in any of the above embodiments.
[0105] In the methods and systems provided in the embodiments of this specification, robust principal component analysis (RPCA) framework based on alternating direction multiplier method (ADMM) is used for reverberation suppression, and this framework has been optimized. By introducing a more suitable dynamic step size adjustment mechanism, the robustness and convergence speed of the algorithm are effectively improved. Experimental results show that, under appropriate parameter configuration, this method can effectively suppress reverberation, significantly improve the signal-to-mixing ratio, and simultaneously improve the algorithm's operating efficiency, exhibiting good environmental adaptability and parameter adjustability. Attached Figure Description
[0106] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0107] Figure 1 This diagram illustrates a flow chart of an underwater active sonar reverberation suppression method provided in an embodiment of this specification.
[0108] Figure 2a This diagram illustrates the distance-azimuth map corresponding to one frame of the original data matrix provided in the embodiments of this specification.
[0109] Figure 2b A schematic diagram of the decomposed sparse matrix provided in the embodiments of this specification is shown;
[0110] Figure 2c A schematic diagram of the decomposed low-rank matrix provided in the embodiments of this specification is shown;
[0111] Figure 3a This diagram illustrates the signal amplitude distribution of the original data.
[0112] Figure 3b This diagram illustrates the signal amplitude distribution of the sparse matrix after ADMM.
[0113] Figure 4a The graph shows the decreasing curves of log(sp) and log(sd) when ρ=0.005;
[0114] Figure 4b The graph shows the decreasing curves of log(sp) and log(sd) when ρ=0.05;
[0115] Figure 4c The graph shows the decreasing curves of log(sp) and log(sd) when ρ=0.5;
[0116] Figure 5 This diagram illustrates a module schematic of an underwater active sonar reverberation suppression device provided in an embodiment of this specification. Detailed Implementation
[0117] The solution provided in this specification will now be described with reference to the accompanying drawings.
[0118] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions in the embodiments of this application will be described below with reference to the accompanying drawings.
[0119] In the description of the embodiments of this application, the words "exemplary," "for example," or "for instance" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as "exemplary," "for example," or "for instance" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of the words "exemplary," "for example," or "for instance" is intended to present the relevant concepts in a specific manner.
[0120] In the description of the embodiments of this application, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, B existing alone, and A and B existing simultaneously. Furthermore, unless otherwise stated, the term "multiple" means two or more.
[0121] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. The terms "comprising," "including," "having," and their variations all mean "including but not limited to," unless otherwise specifically emphasized.
[0122] With the rapid development of marine engineering technology, unmanned underwater vehicles (UUVs) are playing an increasingly important role in deep-sea exploration, seabed topography mapping, and underwater target identification. Active sonar, as the core sensing device of UUVs, undertakes key tasks such as collision avoidance, search and detection, and environmental perception. However, underwater sound propagation is affected by scattering from water bodies and boundaries, resulting in significant reverberation effects. Especially when operating in shallow water, reverberation can severely interfere with the target detection performance of active sonar. Addressing this technical challenge, reverberation suppression has always been a research hotspot in the field of underwater active sonar.
[0123] Reverberation is formed by the superposition of echoes from numerous scatterers in space. Suppressing reverberation hinges on reducing the number of scatterer echoes within the irradiated area. In the spatial domain, improving the array's spatial directivity can reduce the scattering area, thereby increasing the signal-to-reverberation ratio (RRR). However, this approach is limited by the installation space constraints of UUV platforms, limiting its practical application. In the signal parameter domain, adjusting bandwidth and pulse length is another way to optimize sonar performance. Currently, reverberation suppression is addressed by designing more reverberation-resistant pulse signals, such as linear frequency modulation (LFM) and hyperbolic frequency modulation (HFM) signals. However, these methods are also limited by the sonar's operating bandwidth and other technical constraints. Once the sonar array configuration and operating bandwidth are determined, further enhancing reverberation suppression in the statistical domain through signal processing methods becomes a highly practical research direction. Examples include pre-whitening algorithms based on autoregressive (AR) models, principal component inversion (PCI) based on subspace decomposition, methods based on fractional Fourier transform (FrFT), and reverberation suppression methods based on blind source separation (BSS). These methods primarily utilize the statistical difference between the target echo and reverberation to suppress reverberation through signal processing. The core of these methods lies in leveraging the difference between the target echo and reverberation in a certain transform domain or statistical characteristic. However, they rely on overly idealistic model assumptions. In environments with strong reverberation or low signal-to-mixing ratios, the essential difference between the target and reverberation is masked, leading to method failure or instability.
[0124] To address the shortcomings of existing statistical domain reverberation suppression methods in environments with strong reverberation and low signal-to-mixing ratio (SMR) and their parameter sensitivity, this invention proposes a reverberation suppression method for underwater active sonar. This method, based on a robust principal component analysis (RPCA) framework using the alternating direction multiplier method (ADMM), introduces a dynamic step-size adjustment mechanism to enhance the algorithm's robustness and convergence speed. Experimental results show that, with appropriate parameter configuration, the proposed method effectively suppresses reverberation, significantly improves the SMR, and enhances algorithm efficiency, demonstrating good environmental adaptability and parameter adjustability.
[0125] like Figure 1 As shown, the flowchart of an underwater active sonar reverberation suppression method proposed in this invention specifically includes:
[0126] Step 110: Use active sonar to detect moving targets, receive echo signals, and use the echo signals to obtain the original multi-frame data matrix.
[0127] In this embodiment of the application, a low-speed vehicle equipped with active sonar detects moving targets, assuming that the underwater environment is stable for a short period of time and that the main disturbance is reverberation.
[0128] Active sonar periodically transmits pulses and receives echo signals, which are then beamformed to obtain data frames. , representing the distance-orientation matrix.
[0129] The data frame is obtained in the i-th working cycle. ,in It is a complex field. and These represent the discretized distance and angular dimensions, respectively.
[0130] To utilize the correlation between multiple frames of data, each frame matrix is... Vectorize into column vectors And concatenate N consecutive frames of data into a multi-frame data matrix. ,Right now ;
[0131] According to low-rank and sparsity theory, the original data matrix M can be decomposed into a low-rank matrix. and a sparse matrix ,Right now ;
[0132] in Represents the reverberation component (steady-state background). Represents the target echo.
[0133] right The i-th column is inversely vectorized to obtain the detection result of the i-th frame. .
[0134] Step 120: Perform offset compensation on the original multi-frame data matrix to obtain the offset-compensated matrix.
[0135] The offset-compensated matrix represents the matrix resulting from the superposition of the real echo and the virtual background.
[0136] In this embodiment, the sparse decomposition method is based on the rank-sparseness principle, which requires ensuring... Non-low rank and Non-sparse. However, in underwater acoustic environments, certain conditions can cause the low-rank matrix to exhibit high sparsity. To avoid this problem, an offset matrix is introduced:
[0137]
[0138] Where α>0 is a constant. It is a matrix of all 1s. The offset matrix makes... The zero elements in the rank are made non-zero to prevent the low-rank part from being too sparse.
[0139] It is a virtual, uniform background scattering layer. Because Since it is a low-rank matrix, the offset will be automatically classified as a low-rank matrix during the ADMM solution process. In this process, the separation of sparse components is not affected.
[0140] Step 130: Decompose the offset-compensated matrix into a low-rank matrix and a sparse matrix as constraints, construct the minimization objective function using the low-rank matrix and the sparse matrix, and obtain the principal component analysis optimization model. The low-rank matrix represents the reverberation component in the echo signal, and the sparse matrix represents the target echo component in the echo signal.
[0141] Decompose the matrix into low-rank matrices. sparse matrix , making The low-rank matrix Characterizing reverberation components, sparse matrix Characterize the target echo components.
[0142] Specifically, in the embodiments of this application, a robust principal component analysis (RPCA) optimization problem is established:
[0143]
[0144]
[0145] in, Represents the rank of the matrix, serving as a low-rank constraint; Representing a matrix Norms, as sparsity constraints; It is a trade-off parameter between C and I, which controls the strength of sparsity.
[0146] Because of this and Since the norm is non-convex and non-smooth, this optimization problem is NP-hard. Therefore, the kernel norm is used instead of the approximate rank. Norm substitution approximation The norm is used to relax the original problem. The relaxed convex optimization form is as follows:
[0147]
[0148]
[0149] in, It is the nuclear norm of the matrix. It is a matrix Norm.
[0150] Step 140: Iteratively solve the principal component analysis optimization model using the alternating direction multiplier method, and output the target echo component, which is a sparse matrix obtained after iterative convergence.
[0151] The derivation of the Alternating Direction Method of Multipliers (ADMM) is as follows:
[0152] Define the Lagrange function as
[0153]
[0154] in It is the Frobenius norm of the matrix. Represents the inner product of two matrices. It is a Lagrange multiplier.
[0155] The update steps for C, I, and Y are as follows:
[0156]
[0157]
[0158] and The solutions are respectively
[0159]
[0160] in, , It is the singular value decomposition of a matrix. It is a soft threshold function, and the calculation formula is as follows:
[0161]
[0162] Where ε is a constant. It is the element in the i-th row and j-th column of matrix X.
[0163] Termination conditions can be determined based on the original feasibility and dual feasibility.
[0164] The original feasibility of ADMM is
[0165] (1)
[0166] in, and Let C and I be the values for the optimal solution, respectively. Considering the KKT conditions, the dual feasibility is...
[0167] (2)
[0168] (3)
[0169] in, Y is the optimal solution.
[0170] According to duality theory, equations (1), (2), and (3) above are: , and This is a necessary and sufficient condition for the optimal solution to the problem.
[0171] Based on the optimality condition, the difference between the iteration point and the optimality is used as the termination condition. Define the original residual:
[0172] (4)
[0173] Define dual residuals:
[0174] (5)
[0175] Based on the original residual and dual residual defined by equations (4) and (5), the termination condition is defined as follows:
[0176]
[0177]
[0178] in and They are all relatively small normal numbers.
[0179] Finally, by iteratively solving the principal component analysis optimization model using the alternating direction multiplier method, the target echo was obtained. .
[0180] The following is the pseudocode for ADMM used in sparse decomposition:
[0181] Inputs: M,λ,
[0182] Initialization:
[0183] , , k=0
[0184] while(1)
[0185]
[0186]
[0187]
[0188]
[0189] If stopping criteria are satisfied, break;
[0190] compute using Eq.
[0191] k=k+1
[0192] end
[0193] ,
[0194] Output:
[0195] The following is an explanation of the pseudocode above:
[0196] Input: Original multi-frame data matrix M, tradeoff parameter λ, initial penalty parameter
[0197] initialization:
[0198] Offset compensation for the input matrix ,in, k=0
[0199] Initialize sparse matrix , Lagrange multipliers , Iteration counter k, k=0
[0200] Iterative process (running in a loop until the termination condition is met):
[0201] 1. Calculate the low-rank matrix :
[0202] For matrix Perform Singular Value Decomposition (SVD):
[0203]
[0204] For singular value matrices Applying the soft threshold operator, the threshold is The updated singular values are obtained.
[0205] Reconstructing the low-rank matrix:
[0206] 2. Calculate the sparse matrix :
[0207] For matrix Applying the soft threshold operator, the threshold is :
[0208]
[0209] 3. Update the Lagrange multipliers :
[0210]
[0211] 4. Check termination conditions:
[0212] Calculate the original residuals
[0213] Dual residuals
[0214] Calculate the normalized residual:
[0215]
[0216]
[0217] in and They are all relatively small normal numbers.
[0218] and If the iteration fails, the iteration terminates; otherwise, it continues.
[0219] 5. Update penalty parameters :
[0220] Calculated based on dynamic adjustment strategy Then set k = k + 1 and return to step 1.
[0221] Post-processing and output:
[0222] After the iteration ends, the offset compensation is subtracted from the final low-rank matrix to obtain the true reverberation estimate. :
[0223]
[0224] Sparse matrix That is, the target echo component
[0225] Output sparse matrix This serves as the target detection result after reverberation suppression.
[0226] Among them, the soft threshold function It is a soft threshold function, and the calculation formula is as follows:
[0227]
[0228] Specifically, in step 5, the dynamic adjustment strategy method includes:
[0229] 1. Define the basis for adjustment
[0230] Based on the original residual during the iteration process and dual residuals Given the logarithmic approximate linear decreasing property, two relative distance indices are defined:
[0231] Relative distance of original residuals:
[0232] Dual residual relative distance: ,
[0233] in and These are the preset convergence thresholds for the original residual and the dual residual, respectively.
[0234] 2. Establish comparison criteria
[0235] By comparison and The relative magnitude of the values is used to judge the balance of the residual decrease:
[0236] like This indicates that the original residual decreased too slowly (the dual residual decreased too quickly).
[0237] like This indicates that the dual residual decreases too slowly (the original residual decreases too quickly).
[0238] Otherwise, it is assumed that the two decrease at roughly the same rate.
[0239] 3. Formulate adjustment rules
[0240] The penalty parameters are dynamically updated based on the comparison results. :
[0241]
[0242] in,
[0243] When the original residual decreases too slowly ;
[0244] When the dual residual decreases too slowly ;
[0245] When the two are in balance = (Unchanged).
[0246] In this way, by monitoring the residual descent rate in real time and dynamically adjusting the penalty parameter... This ensures that the original residual and the dual residual decrease in a coordinated manner, thereby improving the convergence speed and stability of the algorithm.
[0247] In summary, the proposed method based on the relative distance between the original residual and the dual residual... The dynamic adjustment strategy has good universality and robustness, and can effectively accelerate the convergence of the algorithm under different initial conditions without compromising the reverberation suppression performance.
[0248] To more clearly illustrate the technical solution proposed in this invention, the following description is provided in conjunction with the accompanying drawings and specific embodiments. The specific parameters and steps in the embodiments are merely examples and do not constitute a limitation on the scope of protection of the claims. A T-array sonar system was used to detect moving targets equipped with corner reflectors and buoys. During the experiment, the target was towed by a ship within the detection range, and echo data was recorded at a range of 150 m.
[0249] During sparse decomposition, 10 consecutive frames of data are processed at a time. Each frame is a range-azimuth matrix with 66,000 sampling points along the range axis (corresponding to approximately 192 m) and 41 beam directions along the azimuth axis (covering -40° to +40°, with a 2° step). To balance computational efficiency and reverberation suppression, the range axis is downsampled at 1 / 6 of its sampling rate, reducing the number of range sampling points to 11,000.
[0250] First, offset compensation is performed on the obtained original data matrix to obtain the offset-compensated matrix.
[0251] Next, the offset-compensated matrix is decomposed into a low-rank matrix and a sparse matrix as constraints. The objective function is minimized using the low-rank matrix and the sparse matrix to obtain the principal component analysis optimization model. Finally, the principal component analysis optimization model is solved iteratively. After the iteration converges, the sparse matrix and the low-rank matrix are obtained.
[0252] The experimental data and processing results are shown in Figure 2. Figure 2(a) shows a frame from the original data, with white circles marking the target location, yellow circles marking unidentified interference, and the remaining bright areas representing reverberation and noise. Figures 2(b) and 2(c) show the sparse matrix and low-rank matrix obtained after sparse decomposition using the algorithm presented in this paper (with parameter λ=0.01), respectively, with white circles still marking the target location. The results show that most of the interference in the original data has been effectively eliminated, and the target is clearly identifiable.
[0253] The following is an evaluation of the results. The Signal Reverberation Ratio (SRR) is used as the evaluation metric to measure the detectability of the target signal against interference and noise backgrounds. The SRR is defined as the ratio of effective signal power to the power of interference (reverberation) plus noise, and its mathematical expression is:
[0254]
[0255] in, For the target echo signal power, This represents the total power of reverberation and noise. A higher SRR value indicates a stronger ability of the system to extract the target signal in complex environments.
[0256] To quantitatively evaluate the reverberation suppression effect, data from the azimuth angle of the target (22nd beam) were selected, the approximate range of the target was manually marked, and the signal-to-mixing ratio (SRR) of the original data and the processed sparse matrix were calculated. The signal amplitude distribution of the original data is shown in Figure 3(a) (the target signal is marked in red), and its calculated SRR is 18.93 dB. The signal amplitude distribution of the processed sparse matrix is shown in Figure 3(b), and its calculated SRR is increased to 49.48 dB, with a SRR gain ΔΔ reaching 30.55 dB.
[0257] Experimental results show that the present invention can significantly improve the signal-to-mixing ratio and effectively suppress reverberation interference, verifying the effectiveness and reliability of the method in actual underwater acoustic environments.
[0258] Furthermore, it should be noted that all experiments in this invention were run on the following platform: Intel Core i7-11800H CPU @ 2.30 GHz, with Windows 10 + Visual Studio 2019 as the software environment. The reverberation suppression algorithm was implemented using the C++17 standard. To achieve efficient and stable matrix operations, the Eigen template library (version 3.3.9) was selected as the core computational tool, and economical singular value decomposition was employed during the ADMM iteration process to improve efficiency. To further accelerate computation, the Intel Math Kernel Library (MKL) was introduced for optimization.
[0259] The following is the experimental verification process of the influence and selection of parameter λ.
[0260] In the reverberation suppression algorithm based on sparse decomposition, the convergence and performance of ADMM are highly dependent on the selection of the trade-off parameter λ and the penalty parameter ρ. λ controls the balance between the decomposition of the low-rank matrix and the sparse matrix, directly affecting the signal-to-mixing ratio of the result; while ρ determines the convergence speed and iterative stability of the algorithm.
[0261] When λ is too large, the sparsity weight is too high, and the optimal solution tends to... ;
[0262] When λ is too small, the low-rank weights are too high, and the optimal solution tends to... .
[0263] In other words, both excessively large and excessively small λ values will cause ADMM decomposition to fail. In the experiment, considering both the signal-to-mixing ratio and the visual clarity of the target echo, λ = 0.012 was selected.
[0264] First, the ρ-value adjustment sequence is tested using existing methods:
[0265]
[0266] Among them, parameters , , , Set as suggested , , and take the initial value. Tests show that the adjusted sequence converges slowly.
[0267] By observing the decreasing trend of the termination condition variables sp and sd during the iteration process, it was found that og(sp) and log(sd) decreased approximately linearly. To investigate the effect of ρ, experiments were first conducted with a fixed ρ, and the decreasing curves of log(sp) and log(sd) were plotted with different ρ values.
[0268] As shown in Figures 4(a), 4(b), and 4(c), the results indicate that sp decreases faster when ρ is larger, and sd decreases faster when ρ is smaller. Based on this, 0.05 was initially selected as the initial value. .
[0269] Using log(sp) and log(sd) as the basis for updating ρ, consider log(sp) and log(sd) respectively with... and When the difference between the two is large, ρ should be updated to balance the descent rate.
[0270] Therefore, a new ρ value adjustment sequence is proposed:
[0271]
[0272] To verify the effectiveness of the proposed dynamic adjustment strategy, we tested different initial penalty parameters. Below, a comparison was made between fixed... With dynamic updates The number of iterations for the two strategies.
[0273] In the experiment, k=2 was chosen. Test each =0.005, =0.05、 The results for the three scenarios are shown in Table 1.
[0274] ρ strategy 0.005 0.05 0.5 Fixed ρ 76 15 142 Update ρ 27 15 23
[0275] Table 1 Different initial values Number of iterations when different strategies are adopted
[0276] As can be seen from Table 1:
[0277] when When the value is too small (0.005) or too large (0.5), the fixed strategy requires a large number of iterations to converge (76 and 142, respectively), while the proposed dynamic update strategy significantly reduces the number of iterations (to 27 and 23, respectively).
[0278] when When the value is appropriate (0.05), the number of iterations of the dynamic update strategy is the same as that of the fixed strategy (15 times), indicating that the strategy will not increase unnecessary iterations due to excessive intervention.
[0279] Furthermore, experiments show that in the trade-off of parameters Under fixed conditions, The change in [value] has little effect on the signal-to-mixing ratio (SRR), indicating that the proposed strategy can maintain a good SRR while improving the convergence speed. In practical engineering applications, [the following is selected] , The proposed dynamic update strategy was adopted, and the average processing time for ten frames of data (matrix dimension approximately 11000×4111000×41) was approximately 8 seconds, which meets the requirements for real-time processing.
[0280] Figure 5 This is a schematic diagram of a module for an underwater active sonar reverberation suppression device. (Example) Figure 5 As shown, the underwater active sonar reverberation suppression device includes:
[0281] The first processing unit is used to detect underwater moving targets using active sonar, receive echo signals, and construct an original multi-frame data matrix based on the echo signals, wherein the elements in the original multi-frame data matrix represent the echo amplitude and phase of the spatial unit at each time.
[0282] The second processing unit is used to perform offset compensation on the original multi-frame data matrix to obtain an offset-compensated matrix.
[0283] The third processing unit is used to decompose the offset-compensated matrix into a low-rank matrix and a sparse matrix as constraints, and construct a minimization objective function using the low-rank matrix and the sparse matrix to obtain a principal component analysis optimization model. The low-rank matrix represents the reverberation component in the echo signal, and the sparse matrix represents the target echo component in the echo signal.
[0284] The fourth processing unit is used to iteratively solve the principal component analysis optimization model and obtain the target echo component in the echo signal after the iteration converges.
[0285] In some embodiments, the first processing unit is used for
[0286] The data frame matrix is obtained in the i-th working cycle. Vectorize into column vectors ;
[0287] The column vector obtained from the matrix of N consecutive data frames By splicing, the multi-frame data matrix is obtained. ,Right now ;
[0288] Among them, the data frame matrix It is the range-azimuth matrix obtained after beamforming the received echo signal. It is a complex field. and These represent the discretized distance and angular dimensions, respectively.
[0289] In some embodiments, the second processing unit is used to introduce an offset matrix. The offset-compensated matrix is obtained. ,in,
[0290]
[0291] Where α>0 is a constant. It is a matrix of all 1s.
[0292] In some embodiments, the third processing unit is used to establish a robust principal component analysis (RPCA) optimization problem:
[0293]
[0294]
[0295] in It is a low-rank matrix that represents the reverberation component in the echo signal. It is a sparse matrix that represents the target echo component in the echo signal; Represents the rank of the matrix, serving as a low-rank constraint; Representing a matrix Norms, as sparsity constraints; It is a trade-off parameter between C and I, which controls the strength of sparsity.
[0296] In some more specific embodiments, the fourth processing unit is used for
[0297] Initialize sparse matrix , Lagrange multipliers , The iteration counter k, k=0;
[0298] Step 51: Calculate the low-rank matrix
[0299] For matrix Perform Singular Value Decomposition (SVD):
[0300]
[0301] For singular value matrices Applying the soft threshold operator, the threshold is The updated singular values are obtained. ;in, and It is a unitary matrix. yes The conjugate matrix;
[0302] Reconstructing the low-rank matrix ;
[0303] Step 52: Calculate the sparse matrix
[0304] For matrix Applying the soft threshold operator, the threshold is :
[0305]
[0306] Step 53: Update the Lagrange multipliers
[0307]
[0308] Step 54: Check termination conditions
[0309] Calculate the original residuals ;
[0310] Calculate dual residuals ;
[0311] Calculate the first condition Second condition ,in, and These are the preset convergence thresholds for the original residual and the dual residual, respectively. and All are positive numbers;
[0312] like and If the iteration terminates, then the iteration ends.
[0313] Otherwise, continue;
[0314] Step 55: Update penalty parameters
[0315] Calculated based on dynamic adjustment strategy Then set k = k + 1 and return to step 51.
[0316] In some more specific embodiments, the fourth processing unit is used for
[0317] Based on the original residual during the iteration process and dual residuals Given the logarithmic approximate linear decreasing property, two relative distance indices are defined:
[0318] The relative distance of the first condition The relative distance of the second condition ;
[0319] The penalty parameters are dynamically updated based on the comparison between the relative distances under the first condition and the relative distances under the second condition. :
[0320] By comparison and The relative magnitude of the values is used to judge the balance of the residual decrease:
[0321] like This indicates that the original residual decreased too slowly;
[0322] like This indicates that the dual residual decreases too slowly;
[0323] Otherwise, it is assumed that the two decrease at roughly the same rate.
[0324] The penalty parameters are dynamically updated based on the comparison results. :
[0325]
[0326] in,
[0327] When the original residual decreases too slowly ;
[0328] When the dual residual decreases too slowly ;
[0329] When the two are in balance = .
[0330] In some more specific embodiments, it also includes:
[0331] After the iteration is complete, from the final low-rank matrix Subtract offset compensation amount The reverberation component is obtained. :
[0332]
[0333] The final sparse matrix This is the target echo component.
[0334] In summary, this application employs a robust principal component analysis (RPCA) framework based on the alternating direction multiplier method (ADMM) for reverberation suppression, and optimizes it. By introducing a more suitable dynamic step size adjustment mechanism, the robustness and convergence speed of the algorithm are effectively improved. Experimental results show that, under appropriate parameter configuration, this method can effectively suppress reverberation, significantly improve the signal-to-mixing ratio (SMR), and simultaneously increase the algorithm's operating efficiency, demonstrating good environmental adaptability and parameter adjustability.
[0335] According to another embodiment, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and running on the processor, wherein when the processor executes the program, it implements the underwater active sonar reverberation suppression method as described above.
[0336] According to another embodiment, a computer-readable storage medium is also provided, on which a computer program is stored, which, when executed in a computer, causes the computer to perform an underwater active sonar reverberation suppression method.
[0337] Those skilled in the art will recognize that, in one or more of the examples above, the functions described in this invention can be implemented using hardware, software, firmware, or any combination thereof. When implemented in software, these functions can be stored in a computer-readable medium or transmitted as one or more instructions or code on a computer-readable medium.
[0338] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made on the basis of the technical solution of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for suppressing reverberation in underwater active sonar, characterized in that, include: Active sonar is used to detect underwater moving targets and receive echo signals. An original multi-frame data matrix is constructed based on the echo signals. The elements in the original multi-frame data matrix represent the echo amplitude and phase of the spatial unit at each time. The original multi-frame data matrix is offset-compensated to obtain the offset-compensated matrix; The offset-compensated matrix is decomposed into a low-rank matrix and a sparse matrix as constraints. The objective function is minimized using the low-rank matrix and the sparse matrix to obtain the principal component analysis optimization model. The low-rank matrix represents the reverberation component in the echo signal, and the sparse matrix represents the target echo component in the echo signal. The principal component analysis optimization model is iteratively solved, and the target echo component in the echo signal is obtained after the iteration converges.
2. The method according to claim 1, characterized in that, Based on the echo signal, an original multi-frame data matrix is constructed, including: The data frame matrix is obtained in the i-th working cycle. Vectorize into column vectors ; The column vector obtained from the matrix of N consecutive data frames By splicing, the multi-frame data matrix is obtained. ,Right now ; Among them, the data frame matrix It is the range-azimuth matrix obtained after beamforming the received echo signal. It is a complex field. and These represent the discretized distance and angular dimensions, respectively.
3. The method according to claim 1, characterized in that, By performing offset compensation on the original multi-frame data matrix, an offset-compensated matrix is obtained, including: Introducing the offset matrix The offset-compensated matrix is obtained. ,in, ; Where α>0 is a constant. It is a matrix of all 1s.
4. The method according to claim 1, characterized in that, Based on the constraint of decomposing the offset-compensated matrix into a low-rank matrix and a sparse matrix, a minimization objective function is constructed using the low-rank matrix and the sparse matrix to obtain the principal component analysis optimization model, including: Establishing a robust principal component analysis (RPCA) optimization problem: in It is a low-rank matrix that represents the reverberation component in the echo signal. It is a sparse matrix that represents the target echo component in the echo signal; Represents the rank of the matrix, serving as a low-rank constraint; Representing a matrix Norms, as sparsity constraints; yes and The trade-off parameters between them control the strength of sparsity.
5. The method according to claim 1, characterized in that, The step of iteratively solving the principal component analysis optimization model includes: Initialize sparse matrix , Lagrange multipliers , The iteration counter k, k=0; Step 51: Calculate the low-rank matrix For matrix Perform Singular Value Decomposition (SVD): For singular value matrices Applying the soft threshold operator, the threshold is The updated singular values are obtained. ;in, and It is a unitary matrix. yes The conjugate matrix; Reconstructing the low-rank matrix ; Step 52: Calculate the sparse matrix For matrix Applying the soft threshold operator, the threshold is : Step 53: Update the Lagrange multipliers Step 54: Check termination conditions Calculate the original residuals ; Calculate dual residuals ; Calculate the first condition Second condition ,in, and These are the preset convergence thresholds for the original residual and the dual residual, respectively. and All are positive numbers; like and If the iteration terminates, then the iteration ends. Otherwise, continue; Step 55: Update penalty parameters Calculated based on dynamic adjustment strategy Then set k = k + 1 and return to step 51.
6. The method according to claim 5, characterized in that, Based on the updated penalty parameters, including: Define two relative distance metrics: The relative distance of the first condition The relative distance of the second condition ; The penalty parameters are dynamically updated based on the comparison between the relative distances under the first condition and the relative distances under the second condition. : in, When the original residual decreases too slowly ; When the dual residual decreases too slowly ; When the two are in balance = .
7. The method according to claim 5, characterized in that, Also includes: After the iteration is complete, from the final low-rank matrix Subtract offset compensation amount The reverberation component is obtained. , ; The final sparse matrix This is the target echo component.
8. An underwater active sonar reverberation suppression device, characterized in that, include: The first processing unit is used to detect underwater moving targets using active sonar, receive echo signals, and construct an original multi-frame data matrix based on the echo signals, wherein the elements in the original multi-frame data matrix represent the echo amplitude and phase of the spatial unit at each time. The second processing unit is used to perform offset compensation on the original multi-frame data matrix to obtain an offset-compensated matrix. The third processing unit is used to decompose the offset-compensated matrix into a low-rank matrix and a sparse matrix as constraints, and construct a minimization objective function using the low-rank matrix and the sparse matrix to obtain a principal component analysis optimization model. The low-rank matrix represents the reverberation component in the echo signal, and the sparse matrix represents the target echo component in the echo signal. The fourth processing unit is used to iteratively solve the principal component analysis optimization model and obtain the target echo component in the echo signal after the iteration converges.
9. An electronic device, characterized in that, It includes a memory and one or more processors, the memory storing a computer program that, when executed by the one or more processors, implements the underwater active sonar reverberation suppression method as described in any one of claims 1 to 7.
10. A computer storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by one or more processors, implements the underwater active sonar reverberation suppression method as described in any one of claims 1 to 7.