Sparse-driven minimum kernel risk sensitive loss line spectrum enhancement method under non-Gaussian noise

Abstract

The invention relates to a sparse-driven minimum kernel risk sensitive loss line spectrum enhancement method under non-Gaussian noise, and belongs to the technical field of sonar detection. The invention aims to solve the problems that the existing adaptive line spectrum enhancement method cannot effectively suppress non-Gaussian noise and the existing method cannot be applied to real-time processing due to large calculated amount. The method comprises the following steps of: 1, acquiring a frequency domain input signal of the ALE, and setting a frequency domain self-adaptive weight initial value; 2, multiplying the frequency domain input signal by the frequency domain adaptive weight to obtain an output signal of the ALE, and subtracting the input signal from the output signal to obtain an estimation error; 3, carrying out adaptive weight updating iteration; 4, repeating the steps 2 to 3 until the frequency domain adaptive weight converges, and obtaining an optimal frequency domain adaptive weight; and 5, multiplying the frequency domain input signal by the optimal frequency domain adaptive weight to obtain an output signal of the ALE, wherein the output signal is an enhanced signal.

Description

Technical Field

[0001] The invention relates to a sparse driven minimum nuclear risk sensitive loss line spectrum enhancement method, belonging to the technical field of sonar detection. Background Art

[0002] The radiation noise of underwater targets is the main detection object of passive sonar. The power spectrum of target radiation noise is mainly composed of broadband continuous spectrum and narrowband line spectrum. Compared with broadband continuous spectrum, line spectrum shows better stability and higher intensity per unit bandwidth. Therefore, the extraction of line spectrum is of great significance for passive sonar detection.

[0003] With the development of stealth technology, the intensity of the line spectrum radiated by underwater targets has gradually decreased, while the background noise has remained relatively high. Therefore, passive sonar systems usually work in a low signal-to-noise ratio environment, which poses a challenge to line spectrum detection. In order to improve the signal-to-noise ratio of the line spectrum, the adaptive line enhancer (ALE) is widely used as a preprocessor for passive sonar systems.

[0004] Conventional ALE (CALE) is widely used due to its simple principle, good performance and low computational complexity. The essence of CALE is to use the characteristic that the correlation radius of the line spectrum is much larger than the correlation radius of the broadband noise to time delay the input signal of ALE so that the line spectrum in the original signal and the delayed signal remains correlated, while the broadband noise is decorrelated. CALE constructs the second-order statistics of the error and performs adaptive filtering iteration based on the minimum mean square error criterion, which can suppress broadband noise while retaining the line spectrum. However, the minimum mean square error criterion introduces random noise components in the weight vector, resulting in the misalignment of the ALE output signal, thereby limiting the ALE output signal-to-noise ratio gain. To address this problem, a series of sparse-driven ALE (Sparsity-based ALE, SALE) have been proposed. Based on CALE, SALE converts the adaptive iterative process from the time domain to the frequency domain, uses the sparsity of the line spectrum in the frequency domain, and introduces a sparsity penalty function in the frequency domain cost function to suppress the weight noise and obtain a higher signal-to-noise ratio gain. When applying the above ALE, it is usually assumed that the background noise follows a Gaussian distribution. However, due to the influence of various natural phenomena and human interference, underwater background noise usually contains high-intensity transient pulses and outliers, which is particularly evident in offshore waters affected by industrial noise and ship noise and in polar waters affected by ice melting noise. These transient pulse noises and outliers make the background noise non-Gaussian. In the background of non-Gaussian noise, the second-order statistics are divergent, resulting in a significant decrease in the performance of CALE and SALE designed based on the second-order statistics of errors under non-Gaussian noise.

[0005] In order to improve the performance in the background of non-Gaussian noise, some improved ALE have been proposed. A singular spectrum analysis-based ALE (SSA-ALE) uses the full eigenspectrum of the embedded matrix to replace the second-order error statistics, which is feasible in non-Gaussian noise. However, SSA-ALE requires the period of the signal to be known a priori, which is not suitable for passive sonar detection scenarios. A Shannon entropy-improved ALE (Shannon-ALE) uses the difference in disorder between periodic line spectrum signals and random noise in time series, introduces Shannon entropy that can measure time disorder into the cost function, and improves CALE based on the minimum Shannon entropy criterion. However, affected by the smoothing parameter and window length, Shannon entropy will broaden the pulse to varying degrees, which will have an adverse effect on subsequent line spectrum detection. A least mean p-power based ALE (PALE) uses the p-order statistics of the error instead of the second-order statistics as the cost function, making it more robust in the presence of impulse noise and outlier interference. A sparse-driven PALE (SPALE) further improves PALE by using the sparsity of the line spectrum in the frequency domain, achieving better performance. However, the computational cost of SPALE is very high, which poses a challenge to real-time processing. Therefore, it is necessary to improve ALE to further improve its performance in the background of non-Gaussian noise. Summary of the invention

[0006] The purpose of the present invention is to solve the problem that the existing adaptive line spectrum enhancement method cannot effectively suppress non-Gaussian noise, and the existing method has a large amount of calculation and cannot be applied to real-time processing, and proposes a sparse driven minimum kernel risk sensitive loss line spectrum enhancement method under non-Gaussian noise.

[0007] The specific process of the sparse driven minimum kernel risk sensitive loss line spectrum enhancement method under non-Gaussian noise is as follows:

[0008] Step 1: Obtain the frequency domain input signal of ALE and set the initial value of frequency domain adaptive weight;

[0009] The ALE is an adaptive line spectrum enhancer;

[0010] Step 2: Multiply the frequency domain input signal by the frequency domain adaptive weight to obtain the ALE output signal, and subtract the output signal from the input signal to obtain the estimated error;

[0011] Step 3: According to the frequency domain adaptive weight iteration formula, perform adaptive weight update iteration;

[0012] Step 4: Repeat steps 2 to 3 until the frequency domain adaptive weights converge and obtain the optimal frequency domain adaptive weights;

[0013] Step 5: Multiply the frequency domain input signal by the optimal frequency domain adaptive weight to obtain the ALE output signal, which is the enhanced signal.

[0014] Preferably, in step 1, the frequency domain input signal of ALE is obtained and the initial value of frequency domain adaptive weight is set; the specific process is:

[0015] Step 1: Sample the sonar received data to obtain the original signal snapshot x(i), and perform decorrelation and delay on the original signal snapshot x(i) to obtain the time domain input signal X(i) of ALE, which can be expressed as

[0016] X(i)=[x(i-Δ),x(i-Δ-1),L,x(i-Δ-L+1)] T (1)

[0017] Where L represents the filter length, Δ represents the delay, i represents the i-th moment, and the superscript T represents the transposition.

[0018] Step 1 and 2: Perform discrete Fourier transform on the time domain input signal X(i) to obtain the frequency domain input signal

[0019] Step 13: Frequency domain adaptive weights Initialized to the zero vector.

[0020] Preferably, in the steps one and two, a discrete Fourier transform is performed on the time domain input signal X(i) to obtain a frequency domain input signal The expression is:

[0021]

[0022] in, Represents the normalized discrete Fourier transform matrix.

[0023] Preferably, the normalized discrete Fourier transform matrix It is expressed as:

[0024]

[0025] Where j represents the imaginary unit, j 2 =-1.

[0026] Preferably, in step 2, the frequency domain input signal is multiplied by the frequency domain adaptive weight to obtain the output signal of the ALE, and the output signal is subtracted from the input signal to obtain the estimation error; the specific process is:

[0027] Step 21: Input the frequency domain signal Frequency Domain Adaptive Weight Multiply to get the output signal of ALE;

[0028] Step 22: Subtract the original signal snapshot x(i) from the output signal y(i) to obtain the estimated error e(i).

[0029] Preferably, in step 21, the frequency domain input signal Frequency Domain Adaptive Weight The output signal of ALE is obtained by multiplication; it is expressed as:

[0030]

[0031] in, represents the frequency domain adaptive weight vector; the superscript H indicates conjugation; W(i) represents the time domain adaptive weight vector.

[0032] Preferably, in step 22, the original signal snapshot x(i) is subtracted from the output signal y(i) to obtain the estimated error e(i); expressed as

[0033] e(i)=x(i)-y(i) (4).

[0034] Preferably, in step 3, adaptive weight update iteration is performed according to the frequency domain adaptive weight iteration formula; the specific process is:

[0035]

[0036] Among them, η is the step size, λ is the risk sensitive parameter, and κ σ (·) represents the kernel function, σ represents the kernel width, ρ represents the zero attraction coefficient, represents a zero attractor.

[0037] Preferably, the zero attraction term It is expressed as:

[0038]

[0039] Among them, β represents the threshold parameter of the weight, and |·| represents the modulo operation;

[0040] sgn(·) is a sign operator.

[0041] Preferably, in step 5, the frequency domain input signal is multiplied by the optimal frequency domain adaptive weight to obtain the output signal of ALE, and the output signal is the enhanced signal; the specific process is:

[0042] Input the frequency domain signal and the optimal frequency domain adaptive weight The output signal of ALE is obtained by multiplication; it is expressed as:

[0043]

[0044] The beneficial effects of the present invention are:

[0045] In view of the problem that the existing ALE performance is not ideal under the background of non-Gaussian noise, the present invention proposes a sparsely driven minimum kernel risk sensitive loss line spectrum enhancement SMKRSL-ALE (Sparsity-based Minimum Kernel Risk-Sensitive Loss Criterion-basedALE) method to effectively suppress non-Gaussian noise and improve the performance of ALE under the background of non-Gaussian noise.

[0046] The present invention constructs a new adaptive line spectrum enhancer suitable for non-Gaussian noise background, which can effectively suppress non-Gaussian noise and has good performance while having moderate calculation amount.

[0047] The present invention relates to an adaptive line spectrum enhancement method suitable for non-Gaussian noise background. The method can effectively suppress non-Gaussian noise while retaining line spectrum components, improve the output signal-to-noise ratio of ALE, and obtain good performance under non-Gaussian background. At the same time, the method has moderate computational complexity and can meet the needs of real-time processing.

[0048] The present invention discloses an adaptive line spectrum enhancement method suitable for non-Gaussian noise background. The present invention mainly introduces nuclear risk sensitivity loss into the cost function of the adaptive line spectrum enhancer, and adopts the criterion of minimizing nuclear risk sensitivity loss to perform adaptive weight iterative update, thereby realizing effective suppression of non-Gaussian noise. In addition, a pseudo-L0 norm sparse penalty function is introduced into the cost function to realize effective suppression of weight noise, further improve the output signal-to-noise ratio of the line spectrum enhancer, and improve performance. The present invention can effectively suppress non-Gaussian background noise and realize effective enhancement of target line spectrum under non-Gaussian noise background. The present invention belongs to a passive sonar line spectrum signal processing method, which can be used as a preprocessor for pre-processing of passive sonar target line spectrum detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 The principle block diagram of SMKRSL-ALE proposed in the present invention;

[0050] Figure 2 LOFAR spectrum of the ALE input signal in the implementation example of the present invention, Frequency / Hz is frequency / Hertz;

[0051] Figure 3These are the LOFAR spectra of the ALE output signals in the implementation examples of the present invention, where (a) is the LOFAR spectrum of the CALE output signal, (b) is the LOFAR spectrum of the SALE output signal, (c) is the LOFAR spectrum of the PALE output signal, (d) is the LOFAR spectrum of the SPALE output signal, and (e) is the LOFAR spectrum of the SMKRSL-ALE output signal. DETAILED DESCRIPTION

[0052] Specific implementation method 1: The specific process of the sparse driven minimum nuclear risk sensitive loss line spectrum enhancement method under non-Gaussian noise in this implementation method is as follows:

[0053] Step 1: Obtain the frequency domain input signal of ALE and set the initial value of frequency domain adaptive weight;

[0054] The ALE is an adaptive line spectrum enhancer;

[0055] Step 2: Multiply the frequency domain input signal by the frequency domain adaptive weight to obtain the ALE output signal, and subtract the output signal from the input signal to obtain the estimation error;

[0056] Step 3: According to the frequency domain adaptive weight iteration formula, perform adaptive weight update iteration;

[0057] Step 4: Repeat steps 2 to 3 until the frequency domain adaptive weights converge and obtain the optimal frequency domain adaptive weights;

[0058] Step 5: Multiply the frequency domain input signal by the optimal frequency domain adaptive weight to obtain the ALE output signal, which is the enhanced signal.

[0059] Specific implementation method 2: This implementation method is different from the specific implementation method 1 in that in step 1, the frequency domain input signal of ALE is obtained and the initial value of frequency domain adaptive weight is set; the specific process is:

[0060] Step 1: Sample the sonar received data to obtain the original signal snapshot x(i), and perform decorrelation and delay on the original signal snapshot x(i) to obtain the time domain input signal X(i) of ALE, which can be expressed as

[0061] X(i)=[x(i-Δ),x(i-Δ-1),L,x(i-Δ-L+1)] T (1)

[0062] Where L represents the filter length, Δ represents the delay, i represents the i-th moment, and the superscript T represents the transposition.

[0063] Step 1 and 2: Perform discrete Fourier transform on the time domain input signal X(i) to obtain the frequency domain input signal

[0064] Step 13: Frequency domain adaptive weights Initialized to the zero vector.

[0065] The other steps and parameters are the same as those in the first embodiment.

[0066] Specific implementation method three: This implementation method is different from specific implementation methods one or two in that in steps one and two, a discrete Fourier transform is performed on the time domain input signal X(i) to obtain a frequency domain input signal The expression is:

[0067]

[0068] in, Represents the normalized discrete Fourier transform matrix.

[0069] The other steps and parameters are the same as those in the first or second embodiment.

[0070] Specific implementation method 4: This implementation method is different from any one of the specific implementation methods 1 to 3 in that the normalized discrete Fourier transform matrix It is expressed as:

[0071]

[0072] Where j represents the imaginary unit, j 2 =-1.

[0073] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0074] Specific implementation method five: This implementation method is different from any one of specific implementation methods one to four in that in step two, the frequency domain input signal is multiplied by the frequency domain adaptive weight to obtain the output signal of the ALE, and the output signal is subtracted from the input signal to obtain the estimated error; the specific process is:

[0075] Step 21: Input the frequency domain signal Frequency Domain Adaptive Weight Multiply to get the output signal of ALE;

[0076] Step 22: Subtract the original signal snapshot x(i) from the output signal y(i) to obtain the estimated error e(i).

[0077] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0078] Specific implementation method 6: This implementation method is different from the specific implementation methods 1 to 5 in that the frequency domain input signal is Frequency Domain Adaptive Weight The output signal of ALE is obtained by multiplication; it is expressed as:

[0079]

[0080] in, represents the frequency domain adaptive weight vector; the superscript H indicates conjugation; W(i) represents the time domain adaptive weight vector.

[0081] The other steps and parameters are the same as those in Specific Implementation Methods 1 to 5.

[0082] Specific implementation method 7: This implementation method is different from the specific implementation methods 1 to 6 in that in step 22, the original signal snapshot x(i) is subtracted from the output signal y(i) to obtain the estimated error e(i); it is expressed as

[0083] e(i)=x(i)-y(i) (4).

[0084] The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

[0085] Specific implementation eight: This implementation differs from any one of specific implementations one to seven in that in step three, adaptive weight update iteration is performed according to the frequency domain adaptive weight iteration formula; the specific process is:

[0086] The cost function of ALE is constructed based on the criterion of simultaneously minimizing the kernel risk-sensitive loss KRSL (Kernel Risk-Sensitive Loss) and the pseudo-L0 norm sparse penalty function, which is expressed as

[0087]

[0088] in,

[0089] J SMKRSL (i) represents the cost function;

[0090] The first term on the right side of the equal sign It represents the nuclear risk sensitive loss KRSL;

[0091] The second term on the right side of the equal sign represents the pseudo-L0 norm sparse penalty function;

[0092] λ>0 indicates risk-sensitive parameter, κ σ (·) represents the kernel function, ζ represents the balance parameter between minimizing the kernel risk sensitive loss (KRSL) and minimizing the pseudo L0 norm, L represents the total length or total order of the filter, l represents the filter order number, β represents the threshold parameter of the weight, represents the weight of the l-th order filter at time i;

[0093] Among them, the kernel width σ>0, the kernel function uses the commonly used Gaussian kernel function, κ σ (xy) = exp(-(xy) 2 / 2σ 2 ), σ>0 represents the kernel width, x represents the input signal, and y represents the output signal;

[0094] Through the cost function J SMKRSL (i) Frequency domain adaptive weight vector Conjugation Find the partial derivative and get the gradient vector of the cost function, expressed as

[0095]

[0096] Based on the gradient vector of the cost function and frequency domain input signal Iterate and update along the negative direction of the gradient vector to obtain the frequency domain weight iteration formula;

[0097] The frequency domain weight iteration formula is expressed as:

[0098]

[0099] Among them, μ is the step size, η is the step length, η=μ / σ 2 , ρ is the zero attraction coefficient, ρ = μζ;

[0100] In order to reduce the computational complexity, the exponential term It can be approximated as a first-order Taylor expansion, expressed as

[0101]

[0102]

[0103] Among them, η is the step size, λ is the risk sensitive parameter, and κ σ (·) represents the kernel function, σ represents the kernel width, ρ represents the zero attraction coefficient, represents a zero attractor.

[0104] The adaptive weights are iteratively updated according to formula (5).

[0105] The other steps and parameters are the same as those in Specific Embodiments 1 to 7.

[0106] Specific implementation method 9: This implementation method is different from the specific implementation methods 1 to 8 in that the zero attraction item It is expressed as:

[0107]

[0108] Among them, β represents the threshold parameter of the weight, and |·| represents the modulo operation;

[0109] sgn(·) is a sign operator, which indicates the positive or negative sign of the value.

[0110] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0111] Specific implementation method ten: This implementation method is different from any one of specific implementation methods one to nine in that in step five, the frequency domain input signal is multiplied by the optimal frequency domain adaptive weight to obtain the output signal of the ALE, and the output signal is the enhanced signal; the specific process is:

[0112] Input the frequency domain signal and the optimal frequency domain adaptive weight The output signal of ALE is obtained by multiplication; it is expressed as:

[0113]

[0114] The other steps and parameters are the same as those in Specific Embodiments 1 to 9.

[0115] The present invention may also have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A sparse driven minimum kernel risk sensitive loss line spectrum enhancement method under non-Gaussian noise, characterized by: The specific process of the method is: Step 1: Obtain the frequency domain input signal of ALE and set the initial value of frequency domain adaptive weight; The ALE is an adaptive line spectrum enhancer; Step 2: Multiply the frequency domain input signal by the frequency domain adaptive weight to obtain the ALE output signal, and subtract the output signal from the input signal to obtain the estimation error; Step 3: According to the frequency domain adaptive weight iteration formula, perform adaptive weight update iteration; Step 4: Repeat steps 2 to 3 until the frequency domain adaptive weights converge and obtain the optimal frequency domain adaptive weights; Step 5: Multiply the frequency domain input signal by the optimal frequency domain adaptive weight to obtain the ALE output signal, which is the enhanced signal.

2. The sparse driven minimum kernel risk sensitive loss line spectrum enhancement method under non-Gaussian noise according to claim 1, characterized in that: In the step 1, the frequency domain input signal of ALE is obtained and the initial value of frequency domain adaptive weight is set; the specific process is: Step 1: Sample the sonar received data to obtain the original signal snapshot x(i), and perform decorrelation and delay on the original signal snapshot x(i) to obtain the ALE time domain input signal X(i), which is expressed as X(i)=[x(i-Δ),x(i-Δ-1),L,x(i-Δ-L+1)] T (1) Where L represents the filter length, Δ represents the delay, i represents the i-th moment, and the superscript T represents the transposition. Step 1 and 2: Perform discrete Fourier transform on the time domain input signal X(i) to obtain the frequency domain input signal Step 13: Frequency domain adaptive weights Initialized to the zero vector.

3. The sparse driven minimum kernel risk sensitive loss line spectrum enhancement method under non-Gaussian noise according to claim 2, characterized in that: In the steps 1 and 2, the time domain input signal X(i) is subjected to discrete Fourier transform to obtain the frequency domain input signal The expression is: in, Represents the normalized discrete Fourier transform matrix.

4. The sparse driven minimum kernel risk sensitive loss line spectrum enhancement method under non-Gaussian noise according to claim 3, characterized in that: The normalized discrete Fourier transform matrix It is expressed as: Where j represents the imaginary unit, j 2 =-1.

5. The sparse driven minimum kernel risk sensitive loss line spectrum enhancement method under non-Gaussian noise according to claim 4, characterized in that: In the step 2, the frequency domain input signal is multiplied by the frequency domain adaptive weight to obtain the output signal of the ALE, and the output signal is subtracted from the input signal to obtain the estimation error; the specific process is: Step 21: Input the frequency domain signal Frequency Domain Adaptive Weight Multiply to get the output signal of ALE; Step 22: Subtract the original signal snapshot x(i) from the output signal y(i) to obtain the estimated error e(i).

6. The sparse driven minimum kernel risk sensitive loss line spectrum enhancement method under non-Gaussian noise according to claim 5, characterized in that: In step 21, the frequency domain input signal Frequency Domain Adaptive Weight The output signal of ALE is obtained by multiplication; it is expressed as: in, represents the frequency domain adaptive weight vector; the superscript H indicates conjugation; W(i) represents the time domain adaptive weight vector.

7. The sparse driven minimum kernel risk sensitive loss line spectrum enhancement method under non-Gaussian noise according to claim 6, characterized in that: In step 22, the original signal snapshot x(i) is subtracted from the output signal y(i) to obtain the estimated error e(i); expressed as e(i)=x(i)-y(i) (4).

8. The sparse driven minimum kernel risk sensitive loss line spectrum enhancement method under non-Gaussian noise according to claim 7, characterized in that: In the step 3, the adaptive weight update iteration is performed according to the frequency domain adaptive weight iteration formula; the specific process is: Among them, η is the step size, λ is the risk sensitive parameter, and κ σ (·) represents the kernel function, σ represents the kernel width, ρ represents the zero attraction coefficient, represents a zero attractor.

9. The sparse driven minimum kernel risk sensitive loss line spectrum enhancement method under non-Gaussian noise according to claim 8, characterized in that: The zero attraction term It is expressed as: Among them, β represents the threshold parameter of the weight, and |·| represents the modulo operation; sgn(·) is a sign operator.

10. The sparse driven minimum kernel risk sensitive loss line spectrum enhancement method under non-Gaussian noise according to claim 9, characterized in that: In step 5, the frequency domain input signal is multiplied by the optimal frequency domain adaptive weight to obtain the output signal of ALE, and the output signal is the enhanced signal; the specific process is: Input the frequency domain signal and the optimal frequency domain adaptive weight The output signal of ALE is obtained by multiplication; it is expressed as:

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