Active sonar echo enhancement method based on compressed sensing

Abstract

The invention relates to the technical field of underwater acoustic signal processing, in particular to an active sonar echo enhancement method based on compressed sensing, which comprises the following steps of: (1) converting an active sonar receiving signal into a time-frequency domain through a high-resolution time-frequency analysis method represented by short-time fractional Fourier transform; (2) converting into a compressed sensing problem through subspace projection processing according to a separation model of interference and target echoes; and (3) realizing interference suppression and outputting an echo enhancement result by solving a compressed sensing problem, converting the problem of suppressing interference in a time-frequency domain and enhancing a target echo into a classical noise-containing compressed sensing problem through subspace projection, improving the robustness of non-correlation interference in the process of recursively updating the subspace, and improving the robustness of the non-correlation interference in the process of recursively updating the subspace. And interference is effectively suppressed, and target echoes are enhanced.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic signal processing technology, specifically to an active sonar echo enhancement method based on compressed sensing. Background Technology

[0002] Sonar can be divided into two types: active sonar and passive sonar. Active sonar works by actively emitting sound waves and then receiving the echoes from underwater targets, while passive sonar works by receiving the radiated noise of targets. Strong stealth is one of the main advantages of passive sonar; however, with the rapid development of acoustic stealth technology, the radiated noise level of underwater targets has decreased rapidly, posing a significant challenge to passive sonar technology. Under this trend, active sonar technology has become increasingly important. Effectively enhancing the target echoes from active sonar is key to improving its performance.

[0003] Current research on suppressing active sonar interference and enhancing echo signals can be mainly divided into four categories: echo enhancement methods based on waveform design, echo enhancement methods based on spatial processing, echo enhancement methods based on subspace processing, and echo enhancement methods based on pre-whitening processing. However, the main interference in active sonar is reverberation. Reverberation not only has a waveform similar to the target echo in the time domain but also highly overlaps with the echo in the frequency domain, making it difficult to suppress active sonar interference solely from the time or frequency domain. From this perspective, time-frequency analysis methods can simultaneously obtain three-dimensional information about the target echo's time, frequency, and energy, becoming a powerful tool for suppressing active sonar interference.

[0004] Current research on target echo enhancement in the time-frequency domain has made some progress. Notably, researchers have proposed an echo enhancement method based on principal component tracking (PCT). This method leverages the different correlations between the target echo and interference in the time-frequency domain, using PCT to separate the target echo from the interference and thus enhance the target echo. This research provides a new approach to time-frequency domain echo enhancement. However, this research is based on the assumption that the columns of the interference's time-frequency matrix are strongly correlated, neglecting the energy of uncorrelated interference, which is a factor affecting the performance of the echo enhancement method. Summary of the Invention

[0005] In view of the shortcomings of the existing technology, the purpose of this invention is to provide an active sonar echo enhancement method based on compressed sensing.

[0006] To achieve the above objectives, the present invention provides the following technical solution: an active sonar echo enhancement method based on compressed sensing, the steps of which are as follows:

[0007] (1) The active sonar received signal is converted to the time-frequency domain by using a high-resolution time-frequency analysis method represented by the short-time fractional Fourier transform;

[0008] (2) Based on the separation model of interference and target echo, the problem is transformed into a compressed sensing problem through subspace projection processing;

[0009] (3) By solving the compressed sensing problem, interference is suppressed and the echo enhancement result is output.

[0010] In some embodiments, step (1) is specifically implemented as follows:

[0011] First, a short-time fractional Fourier transform is performed on the active sonar received signal to obtain the time-frequency matrix. The expression for the short-time fractional Fourier transform is as follows:

[0012]

[0013]

[0014] in, In order to transmit signals, For the window function, the Gaussian window function is used uniformly in this method. The angle is the fractional Fourier transform. Let be the impulse function;

[0015] Then the time-frequency matrix of the active sonar received signal Represented as a low-rank matrix and a sparse matrix sum:

[0016]

[0017] in, The low-rank matrix is ​​mainly composed of the energy of the disturbance. The sparse matrix is ​​mainly composed of the energy of the target echo.

[0018] In some embodiments, step (2) is specifically performed as follows:

[0019] For time-frequency matrix Perform principal component analysis to obtain its principal component matrix. ,use Indicates the principal component matrix in time The estimate, using express Orthogonal complement, low-rank matrix It has a relationship with the principal component matrix:

[0020]

[0021] in, express The set of eigenvalues, express Support set.

[0022] In some of these embodiments, by and , time-frequency matrix Written as

[0023] .

[0024] in, = yes In subspace Projection on yes In subspace The projection on the surface.

[0025] In some embodiments, the data matrix Projected onto by In the constructed subspace, a low-rank matrix is ​​constructed to minimize interference. The impact, received

[0026]

[0027]

[0028] if ,So Therefore, there is

[0029]

[0030] at this time If it is considered a minor disturbance, then from the projection data Searching for sparse data The problem then becomes the problem of traditional noisy sparse compressed sensing.

[0031] In some embodiments, step (3) is specifically implemented as follows:

[0032] By data matrix Projected onto by In the constructed subspace, the low-rank part is constructed to eliminate interference. ,recover The problem can be transformed into the following form:

[0033]

[0034] in The size is proportional to the magnitude of the error in the subspace estimation, and it is adaptively set to... , Describing the L1 norm, Let I denote the L2 norm, and I be the identity matrix;

[0035] Solve using the least squares method .

[0036] In some embodiments, through formula renew ,

[0037] Updated using recursive principal component analysis. ;

[0038] The calculation is repeated iteratively until the maximum number of iterations is reached or convergence is achieved, at which point the time-frequency matrix composed of the target echoes is output. .

[0039] Compared with the prior art, the beneficial effects of the present invention are: by subspace projection, the problem of suppressing interference and enhancing target echo in the time and frequency domain is transformed into a classic noisy compressed sensing problem, and in the process of recursively updating the subspace, the robustness to unrelated interference is improved, effectively suppressing interference and enhancing target echo.

[0040] Details of one or more embodiments of this application are set forth in the following drawings and description to make other features, objects and advantages of this application more readily apparent. The embodiments of this application will provide a detailed description and understanding of the application. Attached Figure Description

[0041] Figure 1 The flowchart shows the active sonar echo enhancement method based on compressed sensing.

[0042] Figure 2 The target model diagram for simulation;

[0043] Figure 3 The results are the echo enhancement results in the simulation, where (a) is the result after performing a short-time Fourier transform on the received signal; (b) is the result after performing a short-time fractional Fourier transform on the received signal; (c) is the echo enhancement result obtained by using the existing principal component tracking method based on (b); and (d) is the result after processing with the present invention based on (b).

[0044] Figure 4 The experimental results of processing real target echoes are shown in the figure, where (a) is the result of short-time Fourier transform and (b) is the result after processing according to the present invention. Detailed Implementation

[0045] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0046] Please see Figure 1 This invention provides a technical solution: an active sonar target echo enhancement method based on compressed sensing. Based on the difference between target echo and interference in the time-frequency domain, the method separates the echo and interference through subspace projection, transforming it into a traditional compressed sensing problem. By solving this problem, interference suppression and echo enhancement are achieved. Specifically, the method includes the following steps:

[0047] First, the time-frequency domain distribution of the active sonar echo signal is obtained through short-time fractional Fourier transform. When the transmitted signal is a linear frequency modulated signal, the target echo appears as several finite-length oblique line segments in the time-frequency domain, exhibiting strong sparsity. However, when reverberation is the main component of active sonar interference, studies have shown that it exhibits strong low-rank characteristics within the frequency band of the active sonar signal. Therefore, the problem of separating the target echo from the interference in the time-frequency domain is transformed into a mathematical problem of low-rank sparse decomposition.

[0048] Secondly, based on the low-rank structure of the interference in the time-frequency matrix of the active sonar received signal, the principal component matrix is ​​obtained through principal component analysis. Under the guidance of the recursive projection compressed sensing algorithm, the principal component matrix is ​​projected onto its orthogonal complement space to eliminate most of the energy of the interference time-frequency matrix. The problem of target echo enhancement in the time-frequency domain is transformed into a sparse matrix estimation problem under small interference. The problem is solved through compressed sensing theory, and the obtained sparse matrix is ​​the result after echo enhancement.

[0049] Based on the above steps, the specific implementation plan is as follows:

[0050] 1. First, perform a short-time fractional Fourier transform on the active sonar received signal to obtain the time-frequency matrix. The expression for the short-time fractional Fourier transform is:

[0051]

[0052]

[0053] in, In order to transmit signals, For the window function, the Gaussian window function is used uniformly in this method. The angle is the fractional Fourier transform. Let be the impulse function.

[0054] 2. First, the obtained time-frequency matrix... Represented as

[0055]

[0056] in, The low-rank matrix is ​​mainly composed of the energy of the disturbance. The sparse matrix is ​​mainly composed of the energy of the target echo.

[0057] 3. For the time-frequency matrix Perform principal component analysis to obtain its principal component matrix. ,use Indicates the principal component matrix in time The estimate, using express Orthogonal complement, low-rank matrix It has a relationship with the principal component matrix:

[0058]

[0059] in, express The set of eigenvalues, express Support set.

[0060] 4. Through and The time-frequency matrix can be Written as

[0061] .

[0062] in, = yes In subspace Projection on yes In subspace The projection on the surface.

[0063] 5. Transform the data matrix Projected onto by In the constructed subspace, a low-rank matrix is ​​constructed to minimize interference. The impact, received

[0064]

[0065]

[0066] 6. If ,So Therefore, there is

[0067]

[0068] at this time This can be considered a minor disturbance. Therefore, based on the projection data... Searching for sparse data The problem then becomes the problem of traditional noisy sparse compressed sensing. This noisy sparse compressed sensing describes the situation where errors occur... Lower estimate The process.

[0069] 7. Restore The problem can be transformed into the following form:

[0070]

[0071] in The size is proportional to the magnitude of the error in the subspace estimation, and it can be adaptively set to... , Describing the L1 norm, Let L2 norm be denoted by and I be the identity matrix. Solve using the least squares method. .

[0072] 8. Through renew .

[0073] 9. Update using recursive principal component analysis. The recursive principal component analysis process will not be elaborated further.

[0074] 10. Iterate through the calculations until the maximum number of iterations is reached or convergence is achieved, then output the time-frequency matrix composed of the target echoes.

[0075] The technical solution of this application is verified using simulation test data:

[0076] Appendix Figure 2 The target model for simulation is a rigid cylinder with one end being a hemisphere and the other end being a frustum.

[0077] Appendix Figure 3 This is the result of echo enhancement in the simulation. Figure 3 (a) shows the result of performing a short-time Fourier transform on the received signal; Figure 3 (b) shows the result of performing a short-time fractional Fourier transform on the received signal; Figure 3 (c) represents the middle (c) Figure 3 The echo enhancement results obtained by using the existing principal component tracking method based on (b); Figure 3 (d) is in Figure 3The results are shown in Figure (b) after processing with this method. In the simulation, the transmitted signal was a linear frequency modulated signal of 20kHz-40kHz, the sound wave was incident along the normal direction of a hemispherical shape, the signal-to-interference ratio of the received signal was 0dB, and the interference energy was mainly reverberation, generated by the unit scattering model. As can be seen from the results, this method improves performance compared to existing echo enhancement methods based on principal component tracking, significantly reducing residual interference energy and verifying the effectiveness of this method.

[0078] Appendix Figure 4 The experimental results of processing real target echoes are shown in the figure. Figure 4 In the middle (a), the result of the short-time Fourier transform is shown. Figure 4 Figure (b) shows the result after processing using the method presented in this paper. The data was obtained through a scaled-down experiment. The target in the experiment was a spherical crown-shaped body with a length of 24 cm and a radius of 3 cm, possessing a rigid outer shell, and transmitting a linear frequency modulated signal of 340 kHz to 440 kHz. As can be seen from the results, this method can suppress interference and enhance the target echo, verifying the effectiveness of this method based on the experimental data.

[0079] This method effectively suppresses interference-enhanced target echoes in the time-frequency domain, improving the detection performance of active sonar. Furthermore, compared to existing methods, the recursive estimation subspace structure of this method exhibits stronger robustness to uncorrelated components in the interference time-frequency matrix. Simulation results and experimental data demonstrate that this method effectively suppresses interference-enhanced target echoes and possesses outstanding detection performance.

[0080] The above embodiments merely illustrate several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

[0081] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for enhancing the echo of active sonar based on compressed sensing, characterized in that: The steps are as follows: (1) The active sonar received signal is converted to the time-frequency domain by using a high-resolution time-frequency analysis method represented by the short-time fractional Fourier transform; (2) Based on the separation model of interference and target echo, the problem is transformed into a compressed sensing problem through subspace projection processing; (3) By solving the compressed sensing problem, interference is suppressed and the echo enhancement result is output.

2. The active sonar echo enhancement method based on compressed sensing according to claim 1, characterized in that: According to step (1), the specific method is as follows: First, a short-time fractional Fourier transform is performed on the active sonar received signal to obtain the time-frequency matrix. The expression for the short-time fractional Fourier transform is as follows: in, In order to transmit signals, For the window function, the Gaussian window function is used uniformly in this method. The angle is the fractional Fourier transform. Let be the impulse function; Then the time-frequency matrix of the active sonar received signal Represented as a low-rank matrix and a sparse matrix sum: in, The low-rank matrix is ​​mainly composed of the energy of the disturbance. The sparse matrix is ​​mainly composed of the energy of the target echo.

3. The active sonar echo enhancement method based on compressed sensing according to claim 2, characterized in that: According to step (2), the specific method is as follows: For time-frequency matrix Perform principal component analysis to obtain its principal component matrix. ,use Indicates the principal component matrix in time The estimate, using express Orthogonal complement, low-rank matrix It has a relationship with the principal component matrix: in, express The set of eigenvalues, express Support set.

4. The active sonar echo enhancement method based on compressed sensing according to claim 3, characterized in that: pass and , time-frequency matrix Written as in, = yes In subspace Projection on yes In subspace The projection on the surface.

5. The active sonar echo enhancement method based on compressed sensing according to claim 4, characterized in that: Data matrix Projected onto by In the constructed subspace, a low-rank matrix is ​​constructed to minimize interference. The impact, received if ,So Therefore, there is at this time For minor interference, then from the projection data Searching for sparse data The problem has been transformed into the traditional problem of noisy sparse compressed sensing.

6. The active sonar echo enhancement method based on compressed sensing according to claim 5, characterized in that: According to step (3), the specific method is as follows: By data matrix Projected onto by In the constructed subspace, the low-rank part is constructed to eliminate interference. ,recover The problem can be transformed into the following form: in The size is proportional to the magnitude of the error in the subspace estimation, and it is adaptively set to... , Describing the L1 norm, Let I denote the L2 norm, and I be the identity matrix; Solve using the least squares method .

7. The active sonar echo enhancement method based on compressed sensing according to claim 6, characterized in that: Through formula renew , Updated using recursive principal component analysis. ; The calculation is repeated iteratively until the maximum number of iterations is reached or convergence is achieved, at which point the time-frequency matrix composed of the target echoes is output. .

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