A method for processing single Ping shallow sea reverberation signals

Abstract

This application belongs to the technical field of marine acoustic signal processing, and provides a method for processing single-Ping shallow sea reverberation signals, including the following operations: obtaining the original time-frequency spectrum matrix of the single-Ping shallow sea reverberation signal and performing an interference structure enhancement operation based on local similarity on it. The interference structure enhancement operation based on local similarity includes the following steps: based on the local similarity of the interference structure of shallow sea reverberation, performing a matrix expansion operation on the original time-frequency spectrum matrix to obtain an expanded matrix of the original time-frequency spectrum matrix; performing a robust principal component analysis operation on the expanded matrix to obtain a low-rank approximation matrix of the expanded matrix; performing a matrix inverse expansion operation based on sliding window averaging on the low-rank approximation matrix to obtain a first enhanced matrix of the original time-frequency spectrum matrix. The method provided by this application utilizes the inherent characteristics of shallow sea reverberation to enhance the features of the time-frequency spectrum, and significant interference structure features can be obtained without multi-Ping data.

Description

Technical Field

[0001] The present application belongs to the technical field of ocean acoustic signal processing, and specifically relates to a method for processing a single Ping shallow sea reverberation signal. Background Art

[0002] Shallow sea reverberation is mainly caused by the scattering of sound waves by the sea surface, seabed and inhomogeneous bodies inside the seawater medium. In the shallow sea environment, due to the mutual interference of sound waves of different modes when propagating in the seawater, the shallow sea reverberation signal shows a specific interference structure pattern (reverberation interference fringes) in the time-frequency domain or the distance-frequency domain. The existence of the interference structure plays an important role in the signal processing and target detection of the sonar system. For example, it can be used to estimate the reverberation level of active sonar, or detect and track shallow sea underwater targets. However, due to the influence of factors such as random scattering on the seabed, the time-varying environment of the ocean and noise, the time-frequency spectrum of the original shallow sea reverberation signal has problems such as high noise level and insufficient clarity, making it difficult to obtain a significant interference fringe structure from it.

[0003] At present, there are many methods for interferometrically strengthening the shallow sea reverberation signal, for example, processing the reverberation signal from the wavelet domain and the fractional Fourier domain, performing singular value decomposition, modal decomposition and principal component analysis on the signals at different stages of the processing, etc.; for example, the Chinese invention patent CN117250604A previously applied for by the applicant uses multiple echo signals to construct an echo signal spectrum enhancement matrix to enhance the low-rank characteristics of the echo signal.

[0004] The above existing shallow sea reverberation signal processing methods all adopt the method of processing with the joint Ping signal to ensure the requirement of the data volume carrying the reverberation interference structure information. However, considering the influence of the shallow sea time-varying environment on the underwater acoustic signal during the propagation process, it is difficult to ensure the consistency of the interference structure information in each Ping signal, making it difficult to ensure the stability and clarity of the reverberation interference structure separated from multiple Ping signals. Therefore, there is an urgent need for a shallow sea reverberation signal processing method that can obtain significant interference structure characteristics through a single Ping signal. Summary of the invention

[0005] The purpose of this application is to provide a processing method for a single Ping shallow sea reverberation signal. The method utilizes the interference structure distribution characteristics of the shallow sea reverberation to perform structural enhancement processing on the Ping signal, effectively improving the accuracy of signal separation and feature extraction, and obtaining significant reverberation interference structure characteristics using only the Ping signal.

[0006] The embodiments of the present application can be implemented through the following technical solutions:

[0007] A method for processing single-Ping shallow sea reverberation signals includes the following operations: obtaining the original time-frequency spectrum matrix of the single-Ping shallow sea reverberation signal, and performing an interference structure enhancement operation based on local similarity on the original time-frequency spectrum matrix, where the interference structure enhancement operation based on local similarity includes steps A1 to A3:

[0008] Step A1, based on the local similarity of the interference structure of shallow sea reverberation, perform a matrix expansion operation on the original time-frequency spectrum matrix to obtain an expanded matrix of the original time-frequency spectrum matrix;

[0009] Step A2, perform a robust principal component analysis operation on the expanded matrix to obtain a low-rank approximation matrix of the expanded matrix;

[0010] Step A3, perform a matrix inverse expansion operation based on sliding window averaging on the low-rank approximation matrix to obtain a first enhanced matrix of the original time-frequency spectrum matrix.

[0011] Further, the local similarity of the interference structure is specifically: in the time-frequency spectrum of the shallow sea reverberation signal, the locally similar regions are located on both sides of the diagonal of the time-frequency spectrum and can be mapped to each other by translation.

[0012] Further, analyze and determine the local similarity of the interference structure through the following steps:

[0013] Establish a shallow sea reverberation model;

[0014] Based on the shallow sea reverberation model, determine the ideal time-frequency spectrum matrix of the single-Ping shallow sea reverberation signal;

[0015] Extract the locally similar regions with similar interference structures from the ideal time-frequency spectrum matrix and determine their local similarity of the interference structure.

[0016] Further, obtain the expanded matrix through the following steps:

[0017] Step A11, according to the size of the original time-frequency spectrum matrix of the single-Ping shallow sea reverberation signal determine a sliding window with a size of where and are the minimum and maximum frequency sampling points respectively, and are the minimum and maximum time sampling points respectively, and are the number of rows and columns of the sliding window respectively;

[0018] Step A12, make the sliding window take a step size of 1 and move within Traverse and slide in the order of rows first and columns second, and sequentially intercept the elements within the window to obtain the following as shown in the formula sub-matrices :

[0019] ,

[0020] wherein is row column two-dimensional matrix, , are respectively the serial numbers of the frequency sampling points and time sampling points in the original time-frequency spectrum matrix;

[0021] Step A13, in accordance with the window sliding order, sequentially reshape each sub-matrix into a one-dimensional column vector with a length of as follows :

[0022] ,

[0023] wherein () means extracting all elements in a two-dimensional matrix in the order of rows first and columns second and arranging them as a column vector;

[0024] Step A14, arrange each in rows to obtain the extended matrix as shown in the following formula :

[0025] ,

[0026] wherein is row column two-dimensional matrix.

[0027] Furthermore, step A2 includes the following steps:

[0028] Step A21, initialize the low-rank matrix , sparse matrix and set , , wherein , have the same size as , is the expected value of the rank of, is the number of non-zero terms in;

[0029] Step A22: Iteratively execute steps A221 to A222 until the number of iterations reaches a preset upper limit or the result of robust principal component analysis reaches a preset convergence target:

[0030] Step A221, perform a low-rank approximation on the difference between and with rank and update the low-rank matrix according to the low-rank approximation result; ;

[0031] Step A222, retain the elements with the largest absolute values in the residual matrix and set the remaining elements to zero, thereby obtaining the updated sparse matrix ;

[0032] Step A23, use the low-rank matrix at the end of the iteration as the low-rank approximation matrix of the extended matrix .

[0033] Furthermore, step A3 includes the following steps:

[0034] Step A31, split each column of the low-rank approximation matrix and number them in the same order as in step A14 to obtain the following column vectors:

[0035] ;

[0036] Step A32, for each column vector , convert by converting each of its elements into a row vector in groups of elements, and convert it into a sub-matrix with rows and columns;

[0037] Step A33, place each sub-matrix in the same window sliding order as in step A12, perform an operation of superimposing the elements in the same position and taking the average value, and finally obtain a first enhanced matrix of the original time-frequency spectrum matrix.

[0038] Preferably, when is odd, is the rounded value of , and when is even, is ; when is odd, for The rounded value of When is an even number, for .

[0039] Preferably, the method for processing a single Ping shallow sea reverberation signal further comprises performing an interference structure enhancement operation based on a waveguide invariant on the primary enhancement matrix.

[0040] Further, performing an interference structure enhancement operation based on a waveguide invariant on the primary enhancement matrix comprises the following steps:

[0041] Step B1, a primary enhancement matrix of the original time spectrum Each grid point Slope Path interpolation to obtain the values at several interpolation points ,in, , , , are the frequency resolution and time resolution, respectively. is the preset waveguide invariant, is the interpolation point;

[0042] Step B2, The window is drawn around :

[0043] ,

[0044] in, is the window size parameter;

[0045] Step B3, determining the secondary enhancement matrix of the original time-frequency spectrum matrix based on the following formula:

[0046] ,

[0047] in, For the secondary reinforcement matrix The value at is a counting function.

[0048] Preferably, the preset waveguide invariant has multiple candidate values; after using each candidate value to perform interference structure enhancement operation based on the waveguide invariant, the operation with the most obvious enhancement effect is selected from each operation result, and its result is used as the secondary enhancement matrix of the original time-frequency spectrum matrix.

[0049] An embodiment of the present application provides a method for processing a single Ping shallow - sea reverberation signal. By making full use of the inherent characteristic of the local similarity of the interference structure existing in the spectrum during shallow - sea reverberation, operations of expanding the effective information carried by the single Ping signal and strengthening the interference structure are performed, and significant interference structure features can be extracted from the single Ping shallow - sea reverberation signal. Compared with the existing method for processing shallow - sea reverberation signals that requires combining multiple Ping signals to extract the interference structure, the calculation amount is small, and it is not necessary to consider the influence of the time - varying characteristics of the ocean environment on multiple Ping signals, so it has stronger anti - noise ability and adaptability in a complex ocean environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a schematic flowchart of a method for processing a single Ping shallow - sea reverberation signal provided according to some embodiments of the present application;

[0051] Figure 2 It is a schematic diagram of the original time - frequency spectrum matrix of a specific single Ping shallow - sea reverberation signal;

[0052] Figure 3 It is a schematic diagram of the propagation principle of a shallow - sea reverberation model and a shallow - sea reverberation signal;

[0053] Figure 4 It is a schematic diagram of the ideal time - frequency spectrum matrix of a single Ping shallow - sea reverberation signal obtained according to the shallow - sea reverberation model;

[0054] Figure 5 It is a schematic diagram of performing a matrix expansion operation on the original time - frequency spectrum matrix in a specific embodiment;

[0055] Figure 6 It is a schematic diagram of the region with local similarity in the expanded matrix in a specific embodiment;

[0056] Figure 7 It is a flowchart of performing robust principal component analysis on the expanded matrix in a specific embodiment;

[0057] Figure 8 For Figure 2 It is a schematic diagram of the first - stage enhanced matrix of the original time - frequency spectrum matrix shown;

[0058] Figure 9 It is a schematic diagram of the original time - frequency spectrum matrix of another specific single Ping shallow - sea reverberation signal;

[0059] Figure 10 For Figure 9 It is a schematic diagram of the first - stage enhanced matrix of the original time - frequency spectrum matrix shown;

[0060] Figure 11Schematic flow chart of a method for processing single Ping shallow sea reverberation signals provided according to some embodiments of the present application;

[0061] Figure 12 Schematic diagram of the principle of performing waveguide invariant-based interference structure enhancement operation on a primary enhancement matrix in a specific embodiment;

[0062] Figure 13 For Figure 9 Schematic diagram of the secondary enhancement matrix of the original time-frequency spectrum matrix shown; Detailed implementation manners

[0063] Hereinafter, the present application will be further described based on preferred implementation manners with reference to the accompanying drawings.

[0064] Figure 1 Flow chart of a method for processing single Ping shallow sea reverberation signals provided according to some embodiments of the present application. Referring to Figure 1 , the method includes the following operations:

[0065] Operation 1: Obtain the original time-frequency spectrum matrix of the single Ping shallow sea reverberation signal;

[0066] Operation 2: Perform a local similarity-based interference structure enhancement operation on the original time-frequency spectrum matrix.

[0067] Specifically, Operation 1 can be implemented in a manner known to those skilled in the art. For example, the single Ping shallow sea reverberation signal (in the time domain) can be processed by short-time Fourier transform to obtain its original time-frequency spectrum matrix , where , are the minimum and maximum frequency sampling points respectively, , are the minimum and maximum time sampling points respectively. Obviously, the original time-frequency spectrum matrix is rows columns of a matrix, and the elements of each grid point are the sound pressure or sound intensity of the reverberation signal corresponding to each sampling time and sampling frequency.

[0068] Figure 2 Shows the two-dimensional color map of the original time-frequency spectrum matrix obtained after performing the above processing on a specific single Ping shallow sea reverberation signal. This Ping signal comes from the measured data set of a shallow sea sound field propagation experiment. The water depth of the shallow sea where the experiment is located is 88 meters, the sound source is an explosion sound source with a depth of 50 meters, the receiver depth is 65 meters, the distance between the sound source and the receiver is 200 meters, and a total of 31 Ping shallow sea reverberation signals are collected. Figure 2It is the processing result of the shallow - sea reverberation signal of the first Ping. The size of its original time - frequency spectrum matrix is 256×46, that is, it includes 256 frequency sampling points and 46 time sampling points in total. Among them, in this time - frequency spectrum matrix and the related time - frequency spectrum matrices described later, the values of each grid point have been normalized.

[0069] By Figure 2 It can be seen that the original time - frequency spectrum matrix of the single - Ping shallow - sea reverberation signal contains a large amount of noise interference, and it is difficult to obtain significant interference structure features from it. Therefore, in the embodiments of the present application, the interference structure of the original time - frequency spectrum matrix is enhanced through Operation 2 to suppress noise, so that the interference fringes are significantly enhanced in the processed time - frequency spectrum matrix.

[0070] Obviously, due to the limited amount of information carried by the single - Ping shallow - sea reverberation signal, it is impossible to use multiple independent signals for noise suppression and feature enhancement like the multi - Ping joint processing scheme. Therefore, only by strengthening the effective information in a targeted manner according to the inherent characteristics of the shallow - sea reverberation signal can the effect of the single - Ping signal processing method be ensured. For this purpose, it is necessary to first analyze the mechanism and characteristics of the shallow - sea reverberation interference structure to select an appropriate matrix enhancement operation.

[0071] In some preferred embodiments, the local similarity characteristics of the interference structure of the shallow - sea reverberation can be analyzed and determined through the following steps:

[0072] The first step is to establish a shallow - sea reverberation model.

[0073] Specifically, Figure 3 shows a specific shallow - sea bistatic reverberation model. From Figure 3 it can be known that the bistatic reverberation at a certain moment can be explained as the sum of the echo signals of scatterers with a fixed sum of the distances from the sound source and the receiver, that is, the echo signals generated by an elliptical ring with the sound source and the receiver as foci, where is the sound - source position, is the receiver position, is the distance between the sound source and the receiver, is the distance from the sound source to the scatterer, is the distance from the scatterer to the receiver, is the scattering micro - element on the elliptical ring.

[0074] The second step is to determine the ideal time - frequency spectrum matrix of the single - Ping shallow - sea reverberation signal based on the shallow - sea reverberation model.

[0075] The ideal time-frequency spectrum matrix is the result obtained by only considering the ideal propagation of underwater acoustic signals in the shallow sea channel and seabed scattering. Since it does not alias various noises in the actual propagation process, it can clearly show the interference fringes in the time-frequency spectrum, which is conducive to analyzing the similarity of the interference structure.

[0076] The ideal time-frequency spectrum matrix of the single Ping shallow sea reverberation signal can be established by means known to those skilled in the art. For example, in some alternative embodiments, reference can be made to the Chinese invention patent CN117250604A previously applied by the applicant to establish the reverberation sound pressure spectrum or the ideal expression of the reverberation sound intensity spectrum , where and are continuous frequency variables and time variables respectively. The above-mentioned ideal expression of the reverberation sound pressure spectrum or the ideal expression of the reverberation sound intensity spectrum can both be used as the ideal time-frequency spectrum of the single Ping shallow sea reverberation signal. By performing discrete sampling on it, the ideal time-frequency spectrum matrix can be obtained.

[0077] Alternatively, in some other alternative embodiments, the Helmholtz equation can also be solved using the method of separating variables. The far-field sound pressure of the one-way propagation of the sound source is expressed as the sum of a series of normal modes, and then the sound pressure expression of the reverberation is obtained using the principle of acoustic field reciprocity. The time-domain echo signal of a single scatterer is calculated using the inverse Fourier transform, and then integrated over all scatterers to obtain the time-domain expression of the single Ping reverberation signal. By performing a short-time Fourier transform on the time-domain expression, the ideal time-frequency spectrum matrix of the single Ping reverberation signal can also be obtained (similarly, the values of each element in the matrix can be sound pressure or sound intensity).

[0078] In the third step, local regions with similar interference structures are extracted from the ideal time-frequency spectrum matrix, and their local similarity of the interference structure is determined.

[0079] Figure 4 shows a schematic diagram of the ideal time-frequency spectrum matrix of the single Ping reverberation signal generated through the above steps in a specific embodiment. The environmental parameter settings are similar to those of the actual shallow sea acoustic field propagation experiment, with a water depth of 88.75 m, the sound speed, density, and absorption coefficient of the sediment being 1664 m / s, 1.9 g / cm 3 and 0.2 dB / , the sound source depth is 50 m, the receiver depth is 65 m, the distance between the sound source and the receiver is 200 m, the reverberation time is 2 - 6 s, the frequency range is 300 - 555 Hz, and the seabed scattering adopts the Lambert scattering model.

[0080] As Figure 4As shown, since the ideal time-frequency spectrum matrix does not contain the contamination of various noises, it presents obvious interference fringe structural characteristics. Searching and extracting regions with similar interference structure distribution characteristics of pixel values in the ideal time-frequency spectrum matrix, local similarity regions as shown by the red and black boxes in the figure can be obtained. As shown in the figure, these two similar regions are located on both sides of the diagonal of the ideal time-frequency spectrum matrix and can be mapped to each other by translation.

[0081] Figure 4 The presented interference structure characteristics and their local similarity are the result of the periodic strengthening and cancellation during the superposition of each mode normal wave in the shallow sea sound field propagation, and are the inherent characteristics of shallow sea reverberation. Obviously, this local similarity of the interference structure also exists in the time-frequency spectrum of the measured shallow sea reverberation signal. Therefore, in Operation 2, this characteristic can be utilized to strengthen the characteristics of the original time-frequency spectrum matrix, so as to achieve the purpose of suppressing noise and highlighting the interference structure characteristics.

[0082] Specifically, as Figure 1 shown, Operation 2 further includes the following three steps:

[0083] Step A1: Based on the local similarity of the interference structure of shallow sea reverberation, perform a matrix expansion operation on the original time-frequency spectrum matrix to obtain an expanded matrix of the original time-frequency spectrum matrix;

[0084] Step A2: Perform a robust principal component analysis operation on the expanded matrix to obtain a low-rank approximation matrix of the expanded matrix;

[0085] Step A3: Perform a matrix inverse expansion operation based on the sliding window average on the low-rank approximation matrix to obtain a primary strengthened matrix of the original time-frequency spectrum matrix.

[0086] Among them, Step A1 utilizes the local similarity of the interference structure of shallow sea reverberation obtained above to perform a matrix expansion operation on the original time-frequency spectrum matrix of the single Ping reverberation signal to enhance the effective information content of the expanded matrix. Then, in Step A2, the principal components are extracted from the strengthened matrix through the principal component analysis operation. Finally, in Step A3, through the matrix inverse expansion operation, it is ensured that the primary strengthened matrix obtained after processing has the same matrix structure.

[0087] The following combines the accompanying drawings to detail the specific implementation manners of Steps A1 - A3 of Operation 2.

[0088] In some specific embodiments, the matrix expansion operation of Step A1 includes the following steps:

[0089] Step A11: Determine a sliding window of size according to the size of the original time-frequency spectrum matrix of the single Ping shallow sea reverberation signal, where are the minimum and maximum frequency sampling points respectively, and are the minimum and maximum time sampling points respectively, and and are the number of rows and columns of the sliding window respectively. and are the number of rows and columns of the sliding window respectively. When

[0090] is odd, preferably take the rounded value of as , and when is even, preferably take as ; when is odd, preferably take the rounded value of as , and when is even, preferably take as ; Through the above settings, the local similarity information of the interference structure carried in the original time-frequency spectrum matrix can be utilized to the greatest extent, thereby improving the effect of strengthening the matrix interference structure. Step A12: Let the sliding window slide traversally in the order of first row and then column on

[0091] with a step size of 1, and successively intercept the elements within the window to obtain the following sub-matrices shown as follows: :

[0092] ,

[0093] where is a two-dimensional matrix with rows and columns, and and are the serial numbers of the frequency sampling points and time sampling points in the original time-frequency spectrum matrix respectively;

[0094] Step A13: According to the window sliding order, successively reshape each sub-matrix into a one-dimensional column vector of length as follows:

[0095] ,

[0096] Among them, () means extracting all elements in a two-dimensional matrix in the order of row first and column second and arranging them as a column vector;

[0097] Step A14, arrange each in row order to obtain an extended matrix as shown in the following formula :

[0098] ,

[0099] Among them, is a two-dimensional matrix of rows and

[0100] Figure 5 Taking a matrix as an example, it shows the specific implementation results of each step of the matrix expansion operation. One dimension of this matrix is used to represent time (or distance), and the other dimension is used to represent frequency. Obviously, for matrix, , , that is it can be expressed as:

[0101] .

[0102] In order to maximize the utilization of the effective information in , the size of the sliding window can be set to , that is , , and slide this sliding window with a step size of 1 in the above order of row first and column second and intercept the elements therein to construct sub-matrices until all interceptable positions are traversed. Finally, sub-matrices can be obtained, and in the intercept order, they are respectively: , , , , , , , , , among which, each sub-matrix contains elements.

[0103] Furthermore, convert the 3 row vectors in each sub-matrix into column vectors in turn, and then arrange and splice them in order to obtain 9 column vectors: , , , , , , , , , and finally, arrange these 9 column vectors by rows to obtain an extended matrix of 9 rows and 9 columns as shown in Figure 6 , and its expression is as shown in the following formula: , and its expression is as follows:

[0104] .

[0105] Through Figure 6 , it can be seen that during the process of expanding the original time-frequency spectrum matrix based on the local similarity of the interference structure, regions with the same element distribution (as shown by the two 1×3 box regions and the two 2×3 box regions in the figure) are placed on both sides of the matrix diagonal in a translatable mapping manner. Therefore, the local similarity of the original time-frequency spectrum matrix is further enhanced.

[0106] After obtaining the extended matrix through step A1, perform robust principal component analysis on it in step A2 to obtain a low-rank approximation matrix. In the embodiments of the present application, those skilled in the art can use various robust principal component analysis methods they have mastered to implement step A2. For example, the process shown in Figure 7 can be adopted to perform robust principal component analysis on the extended matrix through the following steps:

[0107] Step A21, initialize the low-rank matrix , the sparse matrix and set , , where , have the same size as , is the expected value of the rank of , and is the number of non-zero terms in .

[0108] Step A22: Iteratively execute steps A221 to A222 until the number of iterations reaches the preset upper limit or the result of the robust principal component analysis reaches the preset convergence target:

[0109] Step A221, perform the best low-rank approximation processing of rank on the difference between and , and update the low-rank matrix according to the processing result;

[0110] Step A222, retain the elements with the largest absolute values from the residual matrix , and set the remaining elements to zero, thereby obtaining an updated sparse matrix ; ;

[0111] Step A23, use the low-rank matrix at the end of the iteration as the low-rank approximation matrix of the extended matrix .

[0112] In each of the above steps, , and the upper limit of the number of iterations can be set to a more appropriate value according to the processing accuracy. The convergence target can adopt a form such as , where represents the Frobenius norm, and is a preset convergence threshold. In addition, the present application does not limit the best low-rank approximation processing method in Step A221. Those skilled in the art can use various methods including but not limited to singular value decomposition (SVD), QR decomposition, etc. to achieve the best low-rank approximation processing according to the prior art.

[0113] The low-rank approximation matrix reflects the "structure" or "background" in the extended matrix . However, since has changed the time-frequency distribution of the original time-frequency spectrum matrix , therefore, it is necessary to reconstruct the low-rank approximation matrix through Step A3 so that it can be restored to have the same structure as , thereby ensuring that the subsequent interference structure analysis can be performed in the correct time-frequency domain.

[0114] In some specific embodiments, Step A3 includes the following steps:

[0115] Step A31, split each column of the low-rank approximation matrix and number them in the same order as in Step A14, obtaining the following column vectors:

[0116] ;

[0117] Step A32, for each column vector , by converting the elements therein into row vectors in groups of elements, convert into a -row -column sub-matrix ;

[0118] Step A33, placing each sub-matrix in the same window sliding order as in step A12 , the elements at the same position are superimposed and averaged, and finally a primary enhancement matrix of the original time-frequency spectrum matrix is obtained .

[0119] Obviously, the above steps are Figure 5 The reverse operation of the matrix expansion operation shown in the figure, wherein, since during the matrix expansion operation, when elements are intercepted in the window sliding order, elements at some positions may appear in multiple sub-matrices, correspondingly, during the inverse matrix expansion operation, multiple elements may be superimposed at a certain position. Therefore, when multiple elements are superimposed at the same position, it is necessary to perform an averaging operation on the superimposed results.

[0120] Figure 8 Shows the Figure 2 The original time-frequency spectrum matrix in After performing the matrix enhancement operations from step A1 to step A3, the primary enhancement matrix .pass Figure 8 It can be seen that after the interference structure enhancement operation based on local similarity, the time-frequency spectrum of the single Ping reverberation signal has shown obvious interference fringe structure characteristics, which proves that the method provided in the present application can effectively extract the reverberation interference fringe structure from the single Ping reverberation signal without the support of multi-Ping data, providing a more reliable method for reverberation suppression and target detection in complex marine environments, and has significant advantages in practical engineering applications.

[0121] Figure 9 Schematic diagram of the original time-frequency spectrum matrix of another single Ping shallow sea reverberation signal. Figure 2 From the same dataset, its number is 9. Figure 10 A schematic diagram of a primary enhancement matrix of the original time-frequency spectrum matrix obtained after performing an interference structure enhancement operation based on local similarity is shown. Figure 10 It can be seen that the Ping shallow sea reverberation signal has only undergone one enhancement operation, and its interference structure characteristics have not been significantly improved. It can be seen that due to the complexity and variability of the marine environment, the various types of noise superimposed on the signals emitted at different times in the same experiment have different degrees of influence on the effective information. Even after one enhancement operation, some Ping signals may still not show a significant interference structure. Therefore, it is necessary to further enhance the structural characteristics of some of the one-time enhancement matrices. Obviously, a different mechanism from the first enhancement operation should be used at this time to have a more significant impact on the signal that has not been significantly improved after the first enhancement operation.

[0122] observeFigure 4 It can be seen that the ideal time-frequency spectrum of the shallow sea reverberation signal (denoted by ) has regular interference fringes on the time-frequency plane, and these interference fringes satisfy the following waveguide invariant relationship:

[0123] ,

[0124] where is the waveguide invariant, which characterizes the slope of the interference fringes and is also determined by the inherent characteristics of the shallow sea environment. Therefore, this characteristic can be utilized to perform an interference structure enhancement operation on the primary enhancement matrix based on the waveguide invariant. Based on the above analysis, in some preferred embodiments of the present application, as Figure 11 shown, the method further includes Operation 3: performing an interference structure enhancement operation on the primary enhancement matrix of the original time-frequency spectrum matrix.

[0125] Specifically, performing an interference structure enhancement operation on the primary enhancement matrix of the original time-frequency spectrum matrix further includes the following steps:

[0126] Step B1, performing path interpolation along the slope at each grid point of the primary enhancement matrix of the original time-frequency spectrum to obtain the values at several interpolation points , where , , , , are the frequency resolution and time resolution respectively, is the preset waveguide invariant, and is the interpolation point;

[0127] Step B2, defining a window as shown in the following formula around : :

[0128] ,

[0129] where is the window size parameter;

[0130] Step B3, determining the secondary enhancement matrix of the original time-frequency spectrum matrix based on the following formula:

[0131] ,

[0132] where is the value of the secondary enhancement matrix at , and is the counting function.

[0133] Reference Figure 12 and perform an interference structure enhancement operation based on the waveguide invariant on . That is, in the time-frequency plane, interpolation is performed on each point along the direction defined by the waveguide invariant, and the original value of each point is replaced by the average value of several interpolation points. Obviously, through this operation, the parts with the same trend due to interference fringes on the slope can be superimposed and enhanced, while components such as random noise are cancelled out by accumulation, thereby realizing the enhancement operation of the interference structure.

[0134] The preset waveguide invariant can be set according to the measurement results of the shallow sea environment. In addition, in some preferred embodiments, multiple alternative values can be set for the waveguide invariant, and then after performing the interference structure enhancement operation using each alternative value, the operation with the most obvious enhancement effect (that is, the most significant characteristics of the alternating interference fringes after the operation) is selected from the results of each operation, and its result is used as the secondary enhancement matrix of the original time-frequency spectrum matrix. Since for each grid point in, only interpolation and superposition in the direction defined by its waveguide invariant will result in significant enhancement, so the value of the waveguide invariant can be obtained more accurately through the above steps.

[0135] Figure 13 shows the schematic diagram of the finally obtained secondary enhancement matrix after performing two enhancement operations on the original time-frequency spectrum matrix shown in Figure 9 . By comparing Figure 10 and Figure 13 , it can be seen that after further enhancing the single Ping signal using the waveguide invariant characteristics, the problem that the single enhancement operation has poor effects on some Ping signals can be effectively solved, and the accuracy and robustness of this method can be effectively improved.

[0136] The specific embodiments of the present application have been described in detail above. For those skilled in the art of this technology, without departing from the principle of the present application, several improvements and modifications can still be made to the present application, and these improvements and modifications also fall within the protection scope of the claims of the present application.

Claims

1. A method for processing a single Ping shallow sea reverberation signal, characterized in that Including the following operations: Obtain the original time-frequency spectrum matrix of the single Ping shallow sea reverberation signal, and perform an interference structure enhancement operation based on local similarity on the original time-frequency spectrum matrix. Among them, the interference structure enhancement operation based on local similarity includes steps A1 to A3: Step A1, based on the local similarity of the interference structure of the shallow sea reverberation, perform a matrix expansion operation on the original time-frequency spectrum matrix to obtain an expanded matrix of the original time-frequency spectrum matrix; Step A2, perform a robust principal component analysis operation on the expanded matrix to obtain a low-rank approximation matrix of the expanded matrix; Step A3, perform a matrix inverse expansion operation based on sliding window averaging on the low-rank approximation matrix to obtain a first enhanced matrix of the original time-frequency spectrum matrix.

2. The processing method of the single Ping shallow sea reverberation signal according to claim 1, wherein The local similarity of the interference structure is specifically: In the time-frequency spectrum of the shallow sea reverberation signal, the locally similar regions are located on both sides of the diagonal of the time-frequency spectrum and can be mapped to each other by translation.

3. The processing method of the single Ping shallow sea reverberation signal according to claim 2, wherein, Analyze and determine the local similarity of the interference structure through the following steps: Establish a shallow sea reverberation model; Based on the shallow sea reverberation model, determine the ideal time-frequency spectrum matrix of the single Ping shallow sea reverberation signal; Extract the locally similar regions with similar interference structures from the ideal time-frequency spectrum matrix and determine their local similarity of the interference structure.

4. The method for processing a single Ping shallow sea reverberation signal according to claim 1, wherein Obtain the expanded matrix through the following steps: Step A11, according to the original time-frequency spectrum matrix of the single Ping shallow sea reverberation signal , determine a sliding window with a size of , where and are the minimum and maximum frequency sampling points respectively, and are the minimum and maximum time sampling points respectively, and are the number of rows and columns of the sliding window respectively; Step A12, make the sliding window slide traversally in the order of first row and then column on with a step size of 1, and successively intercept the elements within the window to obtain the sub-matrices as shown in the following formula : ， Among them, is a two-dimensional matrix of rows and columns, where and are the sequence numbers of the frequency sampling points and time sampling points in the original time-frequency spectrum matrix, respectively; Step A13, in the order of window sliding, sequentially reshape each sub-matrix into a one-dimensional column vector with a length of according to the following formula : ， Among them, () means extracting all elements in a two-dimensional matrix in the order of row first and column second and arranging them as a column vector; Step A14, arrange each one in the window sliding order in row arrangement to obtain an extended matrix as shown in the following formula : ， Among them, is a two-dimensional matrix of [[number of rows]] rows and [[number of columns]] columns. It should be noted that the specific content of , and may need to be filled in according to the actual situation in the original text. Here, I assume they are some variables related to the number of rows and columns for a more complete translation expression. If they have specific meanings in the original text, please adjust the translation accordingly.

5. The processing method of the single Ping shallow sea reverberation signal according to claim 4, characterized in that Step A2 further includes the following steps: Step A21, initialize the low-rank matrix , the sparse matrix and set , , where , has the same size as ; is the expected value of the rank of ; is the number of non-zero terms in Step A22: Iteratively execute steps A221 to A222 until the number of iterations reaches the preset upper limit of the number of iterations, or the result of the robust principal component analysis reaches the preset convergence target: Step A221, perform the difference between and a low-rank approximation processing with a rank of , and update the low-rank matrix ; Step A222, retain the elements with the largest absolute values from the residual matrix and set the remaining elements to zero, thereby obtaining the updated sparse matrix ;​ Step A23, use the low-rank matrix at the end of iteration as the low-rank approximation matrix of the extended matrix .

6. The method for processing a single Ping shallow sea reverberation signal according to claim 5, wherein Step A3 further includes the following steps: Step A31: Split each column of the low-rank approximation matrix and number them in the same order as in Step A14, obtaining the following column vectors: ； Step A32, for each column vector , by converting each of its elements into a row vector in groups of elements, is converted into rows column sub-matrix ; Step A33: Place each sub-matrix in the same window sliding order as in Step A12 , perform an operation of superimposing elements at the same position and then calculating the average value, and finally obtain a first enhanced matrix of the original time-frequency spectrum matrix .

7. The processing method of the single Ping shallow sea reverberation signal according to any one of claims 4 to 6, characterized in that When is odd, is rounded value of, when is even, is ; When is odd, is the rounded value of, when is even, is .

8. The processing method of the single Ping shallow sea reverberation signal according to claim 6, characterized in that, It further includes: Perform an interference structure enhancement operation based on the waveguide invariant on the first enhanced matrix.

9. The method for processing a single Ping shallow sea reverberation signal according to claim 8, wherein Performing an interference structure enhancement operation based on the waveguide invariant on the first enhanced matrix further includes the following steps: Step B1, at each grid point of the primary enhancement matrix of the original time-frequency spectrum perform path interpolation along the slope to obtain the values at a number of interpolation points , where , , , are the frequency resolution and the time resolution respectively, is the preset waveguide invariant, is the interpolation point; Step B2, within surround, define a window as shown in the following formula : ， Among them, is the window size parameter; Step B3, determine the second enhanced matrix of the original time-frequency spectrum matrix based on the following formula: ， wherein, is the value of the secondary strengthening matrix at , is a counting function.

10. The processing method of the single Ping shallow sea reverberation signal according to claim 9, characterized in that There are multiple alternative values for the preset waveguide invariant; After performing the interference structure enhancement operation based on the waveguide invariant using each alternative value, select the operation with the most obvious enhancement effect from the results of each operation, and use its result as the second enhanced matrix of the original time-frequency spectrum matrix.

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