Line spectrum enhancement method based on frequency domain moving sliding window
The target line spectrum and interference are separated by frequency domain moving sliding window and alternating direction multiplier method (ADMM), which solves the problem of low signal-drying ratio in water acoustic detection, and achieves enhanced line spectrum and interference suppression, improving detection effect.
Patent Information
- Application Number
- CN202510364449.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-26
- Publication Date
- 2025-07-18
AI Technical Summary
The prior art faces the problem of low signal-to-dry ratio in water acoustic detection, which makes it difficult to effectively enhance the linear spectrum signal and affect the detection performance.
The frequency domain moving sliding window method is adopted to perform frequency domain smoothing and sliding window interception through a one-dimensional Kalman filter, and the target line spectrum and interference are separated by an alternating direction multiplier method (ADMM) to achieve line spectrum enhancement.
It effectively improves the recognizable and detection performance of linear spectrum in low signal-to-distance environments, and has good engineering application prospects.
Smart Images
Figure CN120334889A_ABST
Abstract
Description
Technical Field:
[0001] The present invention belongs to the technical field of underwater acoustic signal processing, and particularly relates to a line spectrum enhancement method based on a frequency-domain moving sliding window. Background Art:
[0002] The detection of narrowband line spectra is one of the main means of underwater acoustic detection. Both theory and experiments have proven that the radiated noise signals of underwater targets contain rich line spectrum components and can propagate over long distances. For example, Russian scientist Burenkov et al. conducted experimental research on the propagation distance of a line spectrum signal with a frequency of 228 Hz. The experimental results showed that the propagation distance of the measured line spectrum signal could reach 9000 km and had a stable phase. Therefore, in the field of passive sonar detection, the detection technology for narrowband line spectrum components occupies an important position. In the field of active sonar detection, a single-frequency signal is usually transmitted at the transmitting end. By means of the Doppler effect generated by the target movement, in the frequency domain of the active sonar received signal, the target echo is separated from the reverberation limit and enters the noise limit, thereby greatly improving the performance of the active sonar. Therefore, in the field of active sonar detection, the detection technology for narrowband line spectrum components is also one of the important research directions. However, both active detection and passive detection face the common problem of low signal-to-interference ratio, and there is an urgent need for line spectrum enhancement and improvement of the signal-to-interference ratio to enhance the detection effect. In recent years, a series of line spectrum enhancement technologies such as adaptive line spectrum enhancement, coherent cumulative line spectrum enhancement, and line spectrum enhancement based on deep learning have emerged. However, the performance of adaptive line spectrum enhancement is very sensitive to the change of iterative noise and is not good at low signal-to-noise ratio; the performance of coherent cumulative line spectrum enhancement depends on the input of prior information, and the actual application performance is limited; the line spectrum enhancement based on deep learning requires a large amount of sample data training, and the engineering application is difficult. Summary of the Invention:
[0003] The technical problem to be solved by the present invention is to provide a line spectrum enhancement method based on a frequency-domain moving sliding window. This method adopts the method of frequency-domain moving sliding window and multi-segment joint processing, and separates the target line spectrum and interference through a one-dimensional Kalman filter and the alternating multiplier method, realizing line spectrum enhancement.
[0004] The technical solution of the present invention is to provide a line spectrum enhancement method based on a frequency-domain moving sliding window, including the following steps:
[0005] Step 1: Perform a fast Fourier transform (FFT) on the received signal containing line spectra received by the sonar receiving end and take the amplitude spectrum to obtain the frequency-domain data of the received signal;
[0006] Step 2: Realize frequency-domain smoothing of the frequency-domain data through a one-dimensional Kalman filter;
[0007] Step 3: Perform sliding window truncation on the smoothed frequency domain data, and arrange the truncated data in sequence to form a matrix \(B\in R\) m×n , where \(m\) is the window length and \(n\) is the number of truncated segments;
[0008] Step 4: Separate the line spectrum and interference in matrix \(B\) by the alternating direction method of multipliers, and output a sparse matrix;
[0009] Step 5: Rearrange the columns of the sparse matrix and output the line spectrum enhancement result.
[0010] The present invention first performs a fast Fourier transform (FFT) on the received signal at the sonar receiving end and takes the amplitude spectrum to obtain the frequency domain data of the received signal. The frequency domain data is smoothed in the frequency domain through a one-dimensional Kalman filter, then sliding window truncation is performed on the smoothed data, and the truncated data is arranged in sequence to form a matrix \(B\in R\) m×n , where \(m\) is the window length and \(n\) is the number of truncated segments. The line spectrum appears as an impulse function in the frequency domain. After performing moving sliding window and multi-segment joint processing, the positions where the line spectrum appears in each column of matrix \(B\) are different. Therefore, the line spectrum energy shows strong sparsity in matrix \(B\). The spectrum of noise is relatively stable compared with the line spectrum, and its frequency domain amplitude matrix shows low rank compared with the line spectrum frequency domain amplitude matrix, and the low rank property of the data is also enhanced after smoothing through a one-dimensional Kalman filter. Through the above processing, the frequency domain line spectrum enhancement problem is transformed into a mathematical problem of low rank and sparse decomposition. The alternating direction method of multipliers (ADMM) is applied to complete matrix decomposition, realize the separation of the line spectrum and interference, and obtain the result after line spectrum enhancement. The experimental processing results show that this method can enhance the line spectrum, suppress interference, effectively improve the identifiability and detection performance of the line spectrum in a low signal-to-interference ratio environment, and has good engineering application prospects.
[0011] Preferably, in step 2, the one-dimensional Kalman filter obtains the estimated value at this moment through the estimated value at the previous moment and the measured value at this moment, and the estimation equation is
[0012]
[0013] where \(\alpha\) is the Kalman gain, is the estimated value at time \(k\), and \(Z\) k is the measured value at time \(k\).
[0014] Preferably, the Kalman gain \(\alpha\) can be adaptively changed according to the data, or can be set as a fixed constant for the sake of simplifying the calculation amount.
[0015] Preferably, in step 4, based on the augmented Lagrangian multiplier method, the alternating direction method of multipliers completes the solution through the alternating calculation of two variables, and the expression of the augmented Lagrangian multiplier method is
[0016]
[0017] Among them, L is a low-rank matrix, S is a sparse matrix, Λ is a Lagrange multiplier, <·> is the inner product of matrices, and β > 0 is a penalty coefficient.
[0018] Compared with the prior art, the present invention has the following advantages:
[0019] This method can enhance the line spectrum, suppress interference, effectively improve the recognizability and detection performance of the line spectrum in a low signal-to-interference ratio environment, and has good engineering application prospects. Description of the drawings:
[0020] Figure 1 It is a flowchart of a line spectrum enhancement method based on a frequency-domain moving sliding window.
[0021] Figure 2 It is a comparison diagram before and after processing the simulation frequency-domain sliding window amplitude matrix.
[0022] Figure 3 It is a comparison diagram before and after simulation line spectrum enhancement.
[0023] Figure 4 It is a comparison diagram before and after processing the experimental frequency-domain sliding window amplitude matrix.
[0024] Figure 5 It is a comparison diagram before and after experimental line spectrum enhancement. Specific implementation manner:
[0025] The following further describes the present invention in conjunction with the drawings for the specific implementation manner:
[0026] A line spectrum enhancement method based on a frequency-domain moving sliding window, as Figure 1 shown, specifically includes the following steps,
[0027] (1) First, perform a fast Fourier transform on the received signal containing the line spectrum and take the amplitude spectrum.
[0028] (2) Implement frequency-domain smoothing through the estimation equation of the one-dimensional Kalman filter where α is the Kalman gain, is the estimated value at time k, and Z k is the measured value at time k.
[0029] (3) Use a window function to perform sliding interception on the smoothed frequency-domain amplitude spectrum.
[0030] (4) Arrange the slid-intercepted spectra in sequence to form a matrix B ∈ R m×n , where m is the window length and n is the number of intercepted segments;
[0031] (5) The problem of separating the line spectrum energy from the interference in the amplitude matrix B is modeled as the following convex optimization problem
[0032]
[0033] where L is a low-rank matrix, S is a sparse matrix, ||S||0 represents the zero norm of matrix s, that is, the number of non-zero elements, and λ is a trade-off parameter.
[0034] (6) The above equation is convex-relaxed to obtain the following convex optimization problem.
[0035]
[0036] where ||L|| * represents the nuclear norm of matrix L, that is, the sum of its singular values; ||S||1 represents the 1-norm of the vectorized matrix S, that is, the sum of the absolute values of all its elements.
[0037] (7) The above equation is transformed into
[0038]
[0039] by the augmented Lagrangian multiplier method, where Λ is the Lagrangian multiplier; <·> is the matrix inner product; and β > 0 is the penalty coefficient.
[0040] (8) The above equation is solved by ADMM. Fix S to minimize L, fix L to minimize S, and after alternating solutions converge, matrix decomposition is achieved. The above minimization process can be directly solved by setting the derivative to 0, which will not be elaborated here.
[0041] (9) Rearrange the columns of matrix S and output the line spectrum enhancement result.
[0042] The simulation of this embodiment is described as follows:
[0043] Figure 2 This is the comparison diagram of the frequency-domain sliding window amplitude matrix before and after processing in the simulation of this embodiment. Among them, Figure 2 (a) is the matrix before processing, Figure 2 (b) is the matrix after processing. In the simulation, the line spectrum frequency is 500 Hz, the pulse width is 0.4 s, there are 0.8 s of zeros at both the beginning and the end of the line spectrum, the total signal length is 2 s, and the sampling rate is 3000 Hz. Add full-bandwidth Gaussian white noise to it so that the signal-to-noise ratio is -10 dB. For easy comparison, the matrix is energy-normalized. It can be seen from the simulation results that this method can effectively suppress interference and significantly improve the clarity and recognizability of the line spectrum.
[0044] Figure 3 This is the comparison diagram of the line spectrum before and after enhancement in the simulation of this embodiment. Among them, Figure 3(a) is the line spectrum before processing. Figure 3 (b) is the line spectrum after being processed by this method. It can be found from the data processing results that before processing, the spectral energy of the interference is relatively strong, which has a great interference on the target line spectrum. At this time, the signal-to-interference ratio is about 8.7 dB. After processing, the energy of the interference is significantly suppressed. At this time, the signal-to-interference ratio is about 21 dB, and the processing gain is about 12.3 dB.
[0045] Figure 4 This is the comparison diagram before and after the processing of the test frequency-domain sliding window amplitude matrix in this embodiment. Among them, Figure 4 (a) is the matrix before processing. Figure 4 (b) is the matrix after processing. In the experiment, a single-frequency signal of 1 kHz is transmitted to the target through an omnidirectional transmitting transducer. The target moves in an irregular curve. The receiving end uses a 96-element linear array to receive, and the received signal is processed for down-converting to baseband. It can be seen from the test results that for real data, this method can still effectively suppress interference and enhance the line spectrum.
[0046] Figure 5 This is the comparison diagram of the test line spectrum before and after enhancement in this embodiment. Figure 5 (a) is the line spectrum before processing. Figure 5 (b) is the line spectrum after being processed by this method. It can be seen from the result diagram that this method can suppress the interference in the frequency domain. The signal-to-interference ratio before processing is about 9.8 dB, and the signal-to-interference ratio after processing is about 16.5 dB. The processing gain is about 6.7 dB.
[0047] It can be seen that the present invention transforms the problem of enhancing the frequency-domain line spectrum into a mathematical problem of low-rank and sparse decomposition through the above processing. The alternating direction method of multipliers (ADMM) is applied to complete the matrix decomposition, realizing the separation of the line spectrum and the interference, and obtaining the result after the line spectrum is enhanced. The experimental processing results show that this method can enhance the line spectrum, suppress the interference, effectively improve the identifiability and detection performance of the line spectrum in a low signal-to-interference ratio environment, and has good engineering application prospects.
[0048] The above is only an illustration of the preferred embodiments of the present invention, but it should not be construed as a limitation to the claims. All equivalent process transformations made using the specification of the present invention are included in the scope of the patent protection of the present invention.
Claims
1. A line spectrum enhancement method based on a frequency-domain moving sliding window, characterized in that: including the following steps, Step 1: Perform a fast Fourier transform on the received signal containing line spectra and take the magnitude spectrum to obtain the frequency-domain data of the received signal; Step 2: Achieve frequency-domain smoothing of the frequency-domain data through a one-dimensional Kalman filter; Step 3: Perform sliding window truncation on the smoothed frequency domain data, and arrange the truncated data in sequence to form a matrix B ∈ R m×n , where m is the window length and n is the number of truncated segments; Step 4: Separate the line spectra from the interference in matrix B by the alternating direction method of multipliers and output a sparse matrix; Step 5: Rearrange the columns of the sparse matrix and output the result of line spectrum enhancement.
2. The method for line spectrum enhancement based on a frequency domain moving sliding window according to claim 1, wherein: In Step 2, the one-dimensional Kalman filter obtains the estimated value at this moment through the estimated value at the previous moment and the measured value at this moment, and the estimation equation is where α is the Kalman gain, is the estimated value at time k, and Z k is the measured value at time k.
3. The line spectrum enhancement method based on a frequency-domain moving sliding window according to claim 2, wherein: The Kalman gain α can be adaptively changed according to the data or set to a fixed constant.
4. The method for enhancing line spectrum based on frequency-domain moving sliding window according to claim 1, wherein: In Step 4, the alternating direction method of multipliers is based on the augmented Lagrangian multiplier method and completes the solution through the alternating calculation of two variables. The expression of the augmented Lagrangian multiplier method is where L is a low-rank matrix, S is a sparse matrix, Λ is a Lagrangian multiplier, <·> is the inner product of matrices, and β> is a penalty coefficient.