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

Abstract

This invention relates to a sparse-driven minimum kernel risk-sensitive loss line spectrum enhancement method under non-Gaussian noise, belonging to the field of sonar detection technology. The purpose of this invention is to solve the problems that existing adaptive line spectrum enhancement methods cannot effectively suppress non-Gaussian noise and that their computational complexity prevents real-time processing. The process is as follows: 1. Obtain the frequency domain input signal of the ALE and set initial values ​​for the frequency domain adaptive weights; 2. Multiply the frequency domain input signal by the frequency domain adaptive weights to obtain the ALE output signal, and subtract the input signal from the output signal to obtain the estimation error; 3. Perform adaptive weight update iterations; 4. Repeat steps 2 and 3 until the frequency domain adaptive weights converge, obtaining the optimal frequency domain adaptive weights; 5. Multiply the frequency domain input signal by the optimal frequency domain adaptive weights to obtain the ALE output signal, which is the enhanced signal.

Description

Technical Field

[0001] This invention relates to a sparse-driven minimum kernel risk-sensitive loss line spectrum enhancement method, belonging to the field of sonar detection technology. Background Technology

[0002] Radiated noise from underwater targets is a primary target for passive sonar detection. The power spectrum of target radiated noise mainly consists of a broadband continuous spectrum and a narrowband line spectrum. Compared to the broadband continuous spectrum, the line spectrum exhibits better stability and higher intensity per unit bandwidth. Therefore, line spectrum extraction is of great significance for passive sonar detection.

[0003] With the development of stealth technology, the intensity of the line spectrum emitted by underwater targets has gradually decreased, while background noise remains high. Therefore, passive sonar systems typically operate in low signal-to-noise ratio (SNR) environments, posing a challenge to line spectrum detection. To improve the SNR of the line spectrum, adaptive line enhancers (ALEs) are widely used as preprocessors for passive sonar systems.

[0004] Conventional ALE (CALE) is widely used due to its simple principle, good performance, and low computational cost. The essence of CALE is to utilize the fact that the correlation radius of the line spectrum is much larger than that of broadband noise. It applies a time delay to the input signal of the ALE, ensuring that the line spectra of the original and delayed signals remain correlated while the broadband noise is uncorrelated. CALE constructs a second-order statistic of the error and performs adaptive filtering iteration based on the minimum mean square error criterion, which can suppress broadband noise while preserving the line spectrum. However, the minimum mean square error criterion introduces random noise components into the weight vector, causing imbalance in the ALE output signal and thus limiting the ALE output signal-to-noise ratio gain. To address this problem, a series of Sparsity-based ALEs (SALEs) have been proposed. SALEs, building on CALE, transform the adaptive iterative process from the time domain to the frequency domain. Utilizing the sparsity of the line spectrum in the frequency domain, a sparsity penalty function is introduced into the frequency domain cost function to suppress weight noise and achieve a higher signal-to-noise ratio gain. When applying these ALEs, it is usually assumed that the background noise follows a Gaussian distribution. However, due to various natural phenomena and human interference, underwater background noise often contains high-intensity transient impulses and outliers. This phenomenon is particularly pronounced in nearshore waters affected by industrial and shipping noise, and in polar waters affected by ice melt noise. These transient impulse noises and outliers cause the background noise to exhibit non-Gaussian characteristics. Under non-Gaussian noise backgrounds, second-order statistics diverge, leading to a significant decrease in the performance of CALE and SALE designs based on second-order error statistics under non-Gaussian noise conditions.

[0005] To improve performance in non-Gaussian noise environments, several improved Alternating Spectrum Envelope Analyzers (ALEs) have been proposed. One such ALE, Singular Spectrum Analysis-based ALE (SSA-ALE), utilizes the full eigenspectrum of the embedding matrix instead of the second-order error statistics, which is feasible in non-Gaussian noise. However, SSA-ALE requires prior knowledge of the signal period, making it unsuitable for passive sonar detection scenarios. Another ALE, Shannon entropy-improved ALE (Shannon-ALE), leverages the difference in temporal disorder between periodic line spectrum signals and random noise, introducing Shannon entropy—a measure of temporal disorder—into the cost function. Based on the minimum Shannon entropy criterion, it improves upon CALE. However, influenced by smoothing parameters and window length, Shannon entropy can broaden pulses to varying degrees, negatively impacting subsequent line spectrum detection. A least-mean p-power based ALE (PALE) uses the p-th order error statistic instead of the second-order statistic as the cost function, making it more robust to impulse noise and outlier interference. A sparsity-based PALE (SPALE) further improves PALE by leveraging the sparsity of the line spectrum in the frequency domain, achieving even better performance. However, SPALE is computationally expensive, posing a challenge for real-time processing. Therefore, it is necessary to further improve ALE to enhance its performance in non-Gaussian noise environments. Summary of the Invention

[0006] The purpose of this invention is to address the problems that existing adaptive line spectrum enhancement methods cannot effectively suppress non-Gaussian noise and that existing methods have high computational costs and cannot be applied to real-time processing. Therefore, this invention 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 the frequency domain adaptive weights;

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

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

[0011] Step 3: Perform adaptive weight update iteration according to the frequency domain adaptive weight iteration formula;

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

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

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

[0015] Step 11: Sample the received sonar data to obtain the original signal snapshot x(i). Decorrelate and delay the original signal snapshot x(i) to obtain the time-domain input signal X(i) of ALE, denoted 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 time step, and the superscript T indicates transpose.

[0018] Steps 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: Adaptive weights in the frequency domain Initialize to a zero vector.

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

[0021]

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

[0023] Preferably, the normalized discrete Fourier transform matrix Represented as:

[0024]

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

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

[0027] Step 21: Input the frequency domain signal With frequency domain adaptive weights Multiplying them together yields the ALE output signal;

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

[0029] Preferably, in step two-one, the frequency domain input signal is... With frequency domain adaptive weights Multiplying them yields the ALE output signal; represented as:

[0030]

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

[0032] Preferably, in step two, the estimation error e(i) is obtained by subtracting the original signal snapshot x(i) from the output signal y(i); expressed as...

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

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

[0035]

[0036] Where η is the step size, λ is the risk-sensitive parameter, and κ is the step size. σ (·) represents the kernel function, σ represents the kernel width, and ρ represents the zero attraction coefficient. This indicates a zero-attractive term.

[0037] Preferably, the zero attraction term Represented as:

[0038]

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

[0040] sgn(·) is a symbolic operator.

[0041] Preferably, in step five, the frequency domain input signal is multiplied by the optimal frequency domain adaptive weights to obtain the ALE output signal, which is the enhanced signal; the specific process is as follows:

[0042] Frequency domain input signal With optimal frequency domain adaptive weights Multiplying them yields the ALE output signal; represented as:

[0043]

[0044] The beneficial effects of this invention are as follows:

[0045] This invention addresses the issue of suboptimal performance of existing ALE methods under non-Gaussian noise conditions by proposing a sparse-driven minimum kernel risk-sensitive loss line spectrum enhancement (SMKRSL-ALE) method to effectively suppress non-Gaussian noise and improve ALE performance under non-Gaussian noise conditions.

[0046] This invention constructs a novel adaptive line spectrum enhancer suitable for non-Gaussian noise backgrounds, which can effectively suppress non-Gaussian noise and achieves good performance while having a moderate computational load.

[0047] This invention relates to an adaptive line spectrum enhancement method suitable for non-Gaussian noise backgrounds. This method effectively suppresses non-Gaussian noise while preserving line spectrum components, improving the output signal-to-noise ratio of ALE and achieving good performance in non-Gaussian backgrounds. Furthermore, the method has a moderate computational cost, meeting the requirements of real-time processing.

[0048] This invention discloses an adaptive line spectrum enhancement method suitable for non-Gaussian noise backgrounds. The invention primarily achieves effective suppression of non-Gaussian noise by incorporating a kernel risk-sensitive loss into the cost function of the adaptive line spectrum enhancer and employing a criterion of minimizing the kernel risk-sensitive loss for adaptive weight iterative updates. Furthermore, a pseudo-L0 norm sparse penalty function is introduced into the cost function to effectively suppress weight noise, further improving the output signal-to-noise ratio of the line spectrum enhancer and enhancing its performance. This invention effectively suppresses non-Gaussian background noise, achieving effective enhancement of the target line spectrum under non-Gaussian noise backgrounds. This invention pertains to a passive sonar line spectrum signal processing method and can be used as a preprocessor for pre-processing in passive sonar target line spectrum detection. Attached Figure Description

[0049] Figure 1 This is a block diagram of the SMKRSL-ALE principle proposed in this invention;

[0050] Figure 2 This is the LOFAR spectrum of the ALE input signal in the implementation example of this invention, where Frequency / Hz represents the frequency in Hertz.

[0051] Figure 3The following are the LOFAR spectra of the ALE output signals in the implementation examples of this invention, wherein (a) is the LOFAR spectra of the CALE output signal, (b) is the LOFAR spectra of the SALE output signal, (c) is the LOFAR spectra of the PALE output signal, (d) is the LOFAR spectra of the SPALE output signal, and (e) is the LOFAR spectra of the SMKRSL-ALE output signal. Detailed Implementation

[0052] Specific Implementation Method 1: The specific process of the sparse-driven minimum kernel 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 the frequency domain adaptive weights;

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

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

[0056] Step 3: Perform adaptive weight update iteration according to the frequency domain adaptive weight iteration formula;

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

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

[0059] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that, in step one, the frequency domain input signal of ALE is acquired, and the initial value of the frequency domain adaptive weight is set; the specific process is as follows:

[0060] Step 11: Sample the received sonar data to obtain the original signal snapshot x(i). Decorrelate and delay the original signal snapshot x(i) to obtain the time-domain input signal X(i) of ALE, denoted 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 time step, and the superscript T indicates transpose.

[0063] Steps 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: Adaptive weights in the frequency domain Initialize to a zero vector.

[0065] The other steps and parameters are the same as in Specific Implementation Method 1.

[0066] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method 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 the frequency-domain input signal. The expression is:

[0067]

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

[0069] Other steps and parameters are the same as in specific implementation method one or two.

[0070] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that the normalized discrete Fourier transform matrix... Represented as:

[0071]

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

[0073] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0074] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that, in step two, the frequency domain input signal is multiplied by the frequency domain adaptive weights to obtain the ALE output signal, and the output signal is subtracted from the input signal to obtain the estimation error; the specific process is as follows:

[0075] Step 21: Input the frequency domain signal With frequency domain adaptive weights Multiplying them together yields the ALE output signal;

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

[0077] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0078] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that, in step Two-One, the frequency domain input signal is... With frequency domain adaptive weights Multiplying them yields the ALE output signal; represented as:

[0079]

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

[0081] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0082] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that, in step two, the estimation error e(i) is obtained by subtracting the original signal snapshot x(i) from the output signal y(i); expressed as...

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

[0084] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0085] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One through Seven in that, in step three, adaptive weight update iteration is performed based on the frequency domain adaptive weight iteration formula; the specific process is as follows:

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

[0087]

[0088] in,

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

[0090] The first term on the right side of the equals sign KRSL represents nuclear risk-sensitive losses;

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

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

[0093] Wherein, the kernel width σ > 0, and the commonly used Gaussian kernel function is employed, κ σ (xy)=exp(-(xy) 2 / 2σ 2 ), where 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) Adaptive weight vector in the frequency domain conjugate Taking the partial derivative, we obtain the gradient vector of the cost function, expressed as:

[0095]

[0096] Gradient vector based on cost function and frequency domain input signal The frequency domain weight iterative formula is obtained by iteratively updating along the negative direction of the gradient vector.

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

[0098]

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

[0100] To reduce computational complexity, the exponent term... It can be approximated as a first-order Taylor expansion, expressed as:

[0101]

[0102]

[0103] Where η is the step size, λ is the risk-sensitive parameter, and κ is the step size. σ (·) represents the kernel function, σ represents the kernel width, and ρ represents the zero attraction coefficient. This indicates a zero-attractive term.

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

[0105] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0106] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One through Eight in that the zero attraction term... Represented as:

[0107]

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

[0109] sgn(·) is a sign operator that takes the sign of a numerical value.

[0110] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0111] Specific Implementation Method Ten: This implementation method differs from Specific Implementation Methods One to Nine in that, in step five, the frequency domain input signal is multiplied by the optimal frequency domain adaptive weights to obtain the ALE output signal, which is the enhanced signal; the specific process is as follows:

[0112] Frequency domain input signal With optimal frequency domain adaptive weights Multiplying them yields the ALE output signal; represented as:

[0113]

[0114] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.

[0115] This invention may have other embodiments. Without departing from the spirit and essence of this invention, those skilled in the art can make various corresponding changes and modifications according to this invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A sparse-driven minimum kernel risk-sensitive loss line spectrum enhancement method under non-Gaussian noise, characterized in that: The specific process of the method is as follows: Step 1: Obtain the frequency domain input signal of ALE and set the initial value of the frequency domain adaptive weights; The ALE is an adaptive line spectrum enhancer; Step 2: Multiply the frequency domain input signal by the frequency domain adaptive weights to obtain the ALE output signal, and subtract the input signal from the output signal to obtain the estimation error; Step 3: Perform adaptive weight update iteration according to the frequency domain adaptive weight iteration formula; Step 4: Repeat steps 2 to 3 until the frequency domain adaptive weights converge, obtaining the optimal frequency domain adaptive weights; Step 5: Multiply the frequency domain input signal with the optimal frequency domain adaptive weights to obtain the ALE output signal, which is the enhanced signal; In step three, adaptive weight update iteration is performed according to the frequency domain adaptive weight iteration formula; the specific process is as follows: Where η is the step size, λ is the risk-sensitive parameter, and κ is the step size. σ (·) represents the kernel function, σ represents the kernel width, and ρ represents the zero attraction coefficient. Indicates zero attraction. Let e(i) represent the frequency domain adaptive weights, and let e(i) represent the estimation error. The zero attraction item Represented as: Where β represents the threshold parameter of the weight, and |·| represents the modulo operation; sgn(·) is a symbolic operator; In step five, the frequency domain input signal is multiplied by the optimal frequency domain adaptive weights to obtain the ALE output signal, which is the enhanced signal; the specific process is as follows: Frequency domain input signal With optimal frequency domain adaptive weights Multiplying them yields the ALE output signal; represented as:

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 step one, the frequency domain input signal of ALE is obtained, and the initial value of the frequency domain adaptive weight is set; the specific process is as follows: Step 11: Sample the received sonar data to obtain the original signal snapshot x(i). Decorrelate and delay the original signal snapshot x(i) to obtain the time-domain input signal X(i) of ALE, denoted as: X(i)=[x(i-Δ),x(i-Δ-1),…,x(i-Δ-L+1)] T (1) Where L represents the filter length, Δ represents the delay, i represents the i-th time step, and the superscript T indicates transpose. Steps 1 and 2: Perform Discrete Fourier Transform on the time-domain input signal X(i) to obtain the frequency-domain input signal. Step 13: Adaptive weights in the frequency domain Initialize to a 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 steps one and two, the time-domain input signal X(i) is subjected to a discrete Fourier transform to obtain the frequency-domain input signal. The expression is: in, This 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 Represented 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 step two, the frequency domain input signal is multiplied by the frequency domain adaptive weights to obtain the ALE output signal, and the output signal is subtracted from the input signal to obtain the estimation error; the specific process is as follows: Step 21: Input the frequency domain signal With frequency domain adaptive weights Multiplying them together yields the ALE output signal; Step 22: Subtract the original signal snapshot x(i) from the output signal y(i) to obtain the estimation 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 two, the frequency domain input signal is... With frequency domain adaptive weights Multiplying them yields the ALE output signal; represented as: in, represents the frequency domain adaptive weight vector; the superscript H indicates finding the conjugate; 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 two, the estimation error e(i) is obtained by subtracting the original signal snapshot x(i) from the output signal y(i); expressed as... e(i)=x(i)-y(i) (4).

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