Underwater sound transient signal detection method under Alpha stable distribution noise

Abstract

The invention relates to an underwater acoustic transient signal detection method, in particular to an underwater acoustic transient signal detection method under Alpha stable distribution noise. The invention provides an underwater acoustic transient signal detection method under Alpha stable distribution noise, and aims to solve the problems that the performance of a traditional signal detection method based on Gaussian hypothesis is remarkably reduced and the estimation precision of the arrival time is low due to the fact that actual marine environment noise usually has non-Gaussian characteristics such as sudden peaks and the like. The method comprises the following steps: step 1, acquiring an original underwater acoustic transient signal under a non-Gaussian background; step 2, carrying out noise reduction processing on the collected original underwater acoustic transient signal under the non-Gaussian background to obtain a noise-reduced underwater acoustic transient signal under the non-Gaussian background; and step 3, a short-time cross-correlation entropy detector is adopted to process the hydro-acoustic transient signal subjected to noise reduction processing in the step 2 under the non-Gaussian background, and the short-time cross-correlation entropy and the arrival time of the target signal are obtained. The method is applied to the field of underwater acoustic transient signal detection.

Description

Technical Field

[0001] The present invention relates to a method for detecting underwater acoustic transient signals. Background Art

[0002] With the rapid development of underwater acoustic anti-reconnaissance and electronic countermeasure technologies, it has become increasingly difficult to actively detect underwater targets. Different from steady-state signals, transient signals have an extremely short duration and are mainly generated along with changes in the states of underwater acoustic targets. They appear with a low frequency and have no repeatability, making them very difficult to suppress or eliminate. Therefore, the research on passive detection of transient signals has become increasingly important in the field of target stealth detection. However, due to the nonlinear, sudden, and unstable characteristics of transient signals themselves, the performance of traditional signal detection methods in complex environments has been significantly degraded. [1] In addition, traditional underwater acoustic signal detection methods usually assume that the noise is Gaussian distributed, but the actual ocean environmental noise often exhibits non-Gaussian characteristics, which deviate significantly from the Gaussian stationary background assumption, making the signal detection methods based on Gaussian distribution unable to effectively play their roles. [2,3] Therefore, more reliable methods are urgently needed for passive detection of underwater acoustic transient signals under non-Gaussian noise conditions.

[0003] The non-Gaussianity of ocean environmental noise usually manifests as large amplitude fluctuations and sudden spikes. In order to more accurately describe such complex noise characteristics, Ref. [4] proposed a stochastic process model based on Alpha-stable distribution, which has a flexible parametric form and can effectively capture the heavy-tailed characteristics and spike phenomena in the noise. Refs. [5, 6] analyzed the statistical characteristics of actual ocean environmental noise, and the research shows that compared with the Gaussian distribution, the Alpha-stable distribution has a more superior effect in noise fitting. Therefore, the Alpha-stable distribution has become an ideal tool for studying non-Gaussian noise in the ocean environment. With the development of the Alpha-stable distribution theory, related signal processing technologies can generally be divided into three categories: nonlinear transformation methods, fractional lower-order statistics, and correlation entropy based on information-theoretic learning.

[0004] Related scholars at home and abroad have proposed a variety of nonlinear transformation methods to reduce noise interference. Ref. [7] established a Gaussianization processor in the form of a U filter to make the processed background interference approximate the Gaussian distribution, and then coupled with a matched filter for asymptotic optimal detection of weak signals. Ref. [8] used the p-norm to constrain the relative magnitude of the signal amplitude, thereby suppressing impulse noise and improving the azimuth estimation effect in the ice-covered environment. There are also some nonlinear functions such as arctangent, sigmiod, power transformation, etc. that are applied to "suppress the large and enhance the small" to improve the quality of the received signal. [9-11] It is easy to think that in passive detection, nonlinear transformation will inevitably distort uncertain signals with unknown amplitudes, thus introducing new interference.

[0005] During the signal detection process, the received signal is usually not directly used as the detection basis. Instead, second-order or higher-order statistics such as mean square value, correlation, and power spectral density are used as detection quantities. [12-14] , However, the second-order and higher-order statistics of the Alpha-stable distribution are unbounded and divergent, resulting in the degradation of the performance of signal processing algorithms based on second-order and higher-order statistics. To avoid using second-order or higher-order statistics in signal processing algorithms, Nikias et al. proposed a signal processing method based on fractional lower-order statistics, effectively solving the problem of degradation of traditional signal processing algorithms under the Alpha-stable distribution. [4] . Subsequently, reference

[15] used fractional lower-order covariance to describe the correlation characteristics of complex symmetric Alpha-stable distribution clutter, and reconstructed the nonlinear weights of the locally optimal detector with fractional lower-order quadratic form, improving the radar weak target detection performance under non-Gaussian clutter background. Reference

[16] performed fractional lower-order moment operator operations on time signals and extended the fractional lower-order power spectrum theory to the generalized S-transform time-frequency algorithm. In addition, there are related literatures describing time delay estimation and direction-of-arrival estimation algorithms based on fractional lower-order statistics. [17-19] . The signal processing method based on fractional lower-order statistics requires certain statistical prior knowledge and introduces nonlinearity to linear estimation problems, resulting in algorithm complexity.

[20] .

[0006] In recent years, correlation entropy, as a similarity measure of stochastic processes based on kernel methods and information theory learning, was proposed by Professor Principe's team

[21] , becoming a hot research direction in the field of non-stationary signal processing and also having an important impact on the signal processing problem of Alpha-stable distribution noise. Reference

[22] used the maximum correlation entropy criterion to learn the sparse representation of face images and achieved good recognition performance even when the images were occluded or damaged. Reference

[23] proposed a preprocessing method based on correlation entropy with infinite norm. This method does not require prior information about the noise, uses Gaussian kernel functions to process array data, and improves the DOA estimation accuracy of nested arrays under non-Gaussian noise. Correlation entropy has a low dependence on signal prior knowledge. At the same time, it maps the linear space of time-domain signals to the reproducing Hilbert space with the help of kernel functions, has a good suppression effect on spike noise, and has good robustness. Due to its advantages, the signal processing method based on correlation entropy has been widely used in the fields of signal detection and parameter estimation, adaptive filtering, etc. [24-26] . SUMMARY OF THE INVENTION

[0007] The purpose of the present invention is to solve the problems that the actual marine environmental noise usually has non-Gaussian characteristics such as sudden spikes, resulting in a significant decline in the performance of traditional signal detection methods based on Gaussian assumptions and low accuracy of arrival time estimation. Therefore, an underwater acoustic transient signal detection method under Alpha-stable distribution noise is proposed.

[0008] The specific process of the underwater acoustic transient signal detection method under alpha-stable distribution noise is as follows:

[0009] Step 1: Collect the original underwater acoustic transient signal under non-Gaussian background;

[0010] Step 2: Denoise the original underwater acoustic transient signal collected under non-Gaussian background to obtain the underwater acoustic transient signal under non-Gaussian background after denoising;

[0011] Step 3: Use the short-time cross-correlation entropy detector to process the underwater acoustic transient signal under non-Gaussian background after denoising in Step 2 to obtain the short-time cross-correlation entropy and the arrival time of the target signal.

[0012] The beneficial effects of the present invention are as follows:

[0013] The present invention proposes a passive detection and arrival time estimation method for underwater acoustic transient signals under alpha-stable distribution noise. This method combines data cleaning and signal processing technologies, retains the main time-domain characteristics of useful signals, and effectively suppresses spike interference. At the same time, the short-time cross-correlation entropy feature of the received signal is constructed as the detection quantity to improve the detection performance of underwater acoustic transient signals under non-Gaussian background and the accuracy of arrival time estimation. The method proposed by the present invention has a low computational complexity and is expected to provide an effective technical means for the engineering application of underwater acoustic detection.

[0014] Actual ocean ambient noise usually has non-Gaussian characteristics such as sudden spikes, resulting in a significant decline or even failure of the performance of traditional signal detection methods based on Gaussian assumptions. Aiming at the problem of passive detection and time of arrival (TOA) estimation of unknown deterministic transient signals under non-Gaussian background, the present invention uses the Alpha stable distribution to model the non-Gaussian background noise and designs a data preprocessing denoising-short time cross-correntropy detection (DP-STCCED) method. This method first uses the idea of data cleaning to process the outliers of the noisy signal to achieve primary denoising, then uses multi-stage filtering technology to enhance the noise suppression effect, and finally constructs a detector using the short time cross-correntropy feature of the denoised signal and realizes TOA estimation. The simulation results show that the data preprocessing denoising-energy detection (DP-ED) after preprocessing denoising restores the detection performance to a certain extent. However, under the same conditions, the detection performance and TOA estimation accuracy of the DP-STCCED algorithm are significantly better than those of the DP-ED algorithm: when the characteristic exponent α = 1.5, the detection probability of DP-STCCED is still increased by about 30.2% compared with DP-ED at a low generalized signal-to-noise ratio of -11 dB, and the TOA estimation accuracy is increased by about 18.4%.

[0015] Aiming at the problem of the performance decline or even failure of traditional signal detection methods under the non-Gaussian Alpha stable distribution noise background, the present invention designs a joint detection method of data preprocessing denoising-short time cross-correntropy (DP-STCCED), realizing the passive detection and time of arrival estimation of unknown deterministic transient signals under non-Gaussian background. This method does not need to rely on the prior knowledge of the background noise, and the data preprocessing denoising step can effectively restore the performance of traditional energy detection. However, the simulation experiments show that under the same conditions, the information theory feature short time cross-correntropy proposed by the present invention is more sensitive than the energy feature. At the same time, the influence of the generalized signal-to-noise ratio, characteristic exponent and kernel parameter on the DP-STCCED algorithm is analyzed, and the robustness of the algorithm against impulse interference is verified in many aspects. Brief Description of the Drawings

[0016] Figure 1 It is the flowchart of the detection algorithm;

[0017] Figure 2 It is the flowchart of the denoising algorithm;

[0018] Figure 3 It is the signal model diagram, (a) is the transient signal, (b) is the partial enlarged view of (a), (c) is the noisy signal, and (d) is the partial enlarged view of (c);

[0019] Figure 4 This is the result graph of data pre - processing noise reduction. (a) is the primary noise - reduced signal after outlier detection and median filtering. (b) is the local enlarged view of (a). (c) is the noise - reduced signal after modified mean filtering. (d) is the local enlarged view of (c);

[0020] Figure 5 This is the detection result graph. (a) ED, (b) DP - ED, (c) STCCED, (d) DP - STCCED;

[0021] Figure 6 This is the ROC curve graph, (α = 1.5, σ = 1);

[0022] Figure 7 This is the analysis graph of the influence of characteristic index, (σ = 1);

[0023] Figure 8 This is the analysis graph of the influence of kernel parameter, (α = 1.5);

[0024] Figure 9 This is the analysis graph of TOA estimation error. (a) Analysis of the influence of generalized signal - to - noise ratio (σ = 0.5), (b) Analysis of the influence of characteristic index (σ = 0.5), (c) Analysis of the influence of kernel parameter (α = 1.5). Specific implementation manners

[0025] Specific implementation manner one: The specific process of the underwater acoustic transient signal detection method under Alpha - stable distribution noise in this implementation manner is as follows:

[0026] Step 1: Collect the original underwater acoustic transient signal under non - Gaussian background;

[0027] Step 2: Perform noise reduction processing on the collected original underwater acoustic transient signal under non - Gaussian background to obtain the underwater acoustic transient signal under non - Gaussian background after noise reduction processing;

[0028] Step 3: Use the short - time cross - correlation entropy detector to process the underwater acoustic transient signal under non - Gaussian background after noise reduction processing in Step 2 to obtain the short - time cross - correlation entropy and the arrival time of the target signal.

[0029] Specific implementation manner two: The difference between this implementation manner and specific implementation manner one is that in Step 2, the collected original underwater acoustic transient signal under non - Gaussian background is subjected to noise reduction processing to obtain the underwater acoustic transient signal under non - Gaussian background after noise reduction processing;

[0030] Noise suppression is a key step in underwater acoustic detection. By effectively reducing noise, the quality of the received signal can be improved, thereby enhancing the detection performance under low signal-to-noise ratio conditions. However, the heavy-tailed characteristics of the Alpha stable distribution render the traditional noise reduction and detection algorithms in a Gaussian noise background almost ineffective, especially the energy detection widely used in engineering. Therefore, this invention combines the idea of data cleaning with signal processing methods and proposes a data preprocessing noise reduction algorithm based on outlier detection and multi-stage filtering, which can effectively suppress noise interference while preserving the signal characteristics. The algorithm flow is as Figure 2 shown.

[0031] The specific process is as follows:

[0032] Step 21: Perform outlier detection based on the interquartile range on the original underwater acoustic transient signal collected in a non-Gaussian background to obtain the original underwater acoustic transient signal sequence x(n) processed by outlier detection;

[0033] Non-Gaussian background noise usually exhibits significant short-time pulse characteristics, and its time-domain waveform contains a large number of spikes deviating from the normal amplitude range, which has a significant impact on the signal processing results. To suppress the spikes, the interquartile range method is used to perform outlier detection on the signal samples, and the extreme values in the sample data are filtered by setting an appropriate threshold.

[0034] Step 22: There are some missing values in the original signal sample sequence x(n) processed by outlier detection. Use the median filtering technique to process x(n), fill in the missing values, and reconstruct the signal sequence;

[0035] Median filtering is a robust non-linear filtering technique widely used in the field of signal processing. It has good suppression effects on salt-and-pepper noise and other types of impulse noise and can preserve the details of the signal. Its basic principle is to replace a point in the signal sequence with the median of the points in its neighborhood;

[0036] There are some missing values in the signal data processed by outlier detection. Using median filtering to process the signal sequence can further suppress the spikes and reconstruct the signal.

[0037] Step 23: Use the modified Alpha mean filtering technique to process the reconstructed signal sequence to obtain the final noise-reduced signal

[0038] Outlier detection based on the interquartile range and median filtering can effectively suppress the large-amplitude spikes in the signal samples. However, the remaining small-amplitude spikes will still have an adverse impact on signal detection. Therefore, this article uses modified mean filtering to smooth the reconstructed signal to further reduce background noise;

[0039] Other steps and parameters are the same as those in the first specific implementation manner.

[0040] Embodiment 3 in detail: The difference between this embodiment and Embodiment 1 or 2 is that in step 21, the original underwater acoustic transient signal under non-Gaussian background collected is subjected to outlier detection based on the interquartile range, and the original underwater acoustic transient signal sequence x(n) after outlier detection processing is obtained;

[0041] The specific process is as follows:

[0042] Step 211. Ascendingly arrange the original underwater acoustic transient signal sequence x(n) = {x1, x2,..., x i ,..., x N} to obtain the arranged original underwater acoustic transient signal sequence x'(n) = {x'1, x'2,..., x' i ,..., x' N},

[0043] where i = 1, 2,..., N, N is the total number of sample points of the original underwater acoustic transient signal sequence, and i is the index of the i-th sample point of the original underwater acoustic transient signal sequence;

[0044] x i is the i-th sample point in the original underwater acoustic transient signal sequence under non-Gaussian background; x N is the N-th sample point in the original underwater acoustic transient signal sequence under non-Gaussian background;

[0045] x' i is the i-th sample point in the arranged original underwater acoustic transient signal sequence; x' N is the N-th sample point in the arranged original underwater acoustic transient signal sequence;

[0046] Divide x'(n) = {x'1, x'2,..., x' i ,..., x' N} into four equal parts, the first part is the first quartile Q1, the second part is the second quartile Q2, the third part is the third quartile Q3, and the fourth part is the fourth quartile Q4;

[0047] Obtain the IQR based on the first quartile Q1 and the third quartile Q3;

[0048] Step 212. Set the outlier detection thresholds T1 and T2;

[0049] where T1 represents the upper limit of the threshold; T2 represents the lower limit of the threshold;

[0050] If the data point x in the original underwater acoustic transient signal sequence x(n) = {x1, x2,..., x i ,..., x N}i <T1 or x i > T2, then the data point x i is marked as an outlier;

[0051] Finally, in order to maintain the original characteristics of the signal without introducing new noise interference, the data points marked as outliers are deleted to obtain the original underwater acoustic transient signal sequence x(n) after deleting outliers.

[0052] Other steps and parameters are the same as those in the first or second specific implementation manner.

[0053] Specific implementation manner four: The difference between this implementation manner and one of the first to third specific implementation manners is that in step 211, the first quartile Q1, the third quartile Q3, and the interquartile range IQR are respectively:

[0054]

[0055] where represents rounding up;

[0056] represents the last underwater acoustic signal sample in the first part when dividing x'(n) into four equal parts;

[0057] represents the last underwater acoustic signal sample in the third part when dividing x'(n) into four equal parts.

[0058] Other steps and parameters are the same as those in one of the first to third specific implementation manners.

[0059] Specific implementation manner five: The difference between this implementation manner and one of the first to fourth specific implementation manners is that in step 212, the outlier detection thresholds T1 and T2 are set; expressed as:

[0060] T1 = Q1 - c × IQR, T2 = Q3 + c × IQR

[0061] where T1 represents the upper limit of the threshold; T2 represents the lower limit of the threshold;

[0062] c is a constant, usually taking c = 1.5.

[0063] Other steps and parameters are the same as those in one of the first to fourth specific implementation manners.

[0064] Specific implementation manner six: The difference between this implementation manner and one of the first to fifth specific implementation manners is that in step 3, a short-time cross-correlation entropy detector is used to process the underwater acoustic transient signal in a non-Gaussian background after noise reduction in step 2 to obtain the short-time cross-correlation entropy and the arrival time of the target signal;

[0065] The specific process is as follows:

[0066] Step 31: Perform frame division on the underwater acoustic transient signal with non-Gaussian background after noise reduction in Step 2 to obtain the k-th frame signal

[0067] Step 32: Calculate the short-time cross-correlation entropy between adjacent frames and use it as the detection statistic;

[0068] Step 33: Determine the detection threshold, and make a decision on the detection statistic based on the detection threshold to obtain the detection result, where the detection result is whether there is a target signal;

[0069] Step 34: When a target signal exists in the detection result, estimate the arrival time of the target signal through the peak of the short-time cross-correlation entropy.

[0070] Other steps and parameters are the same as those in any one of the first to fifth specific embodiments.

[0071] Specific embodiment seven: The difference between this embodiment and any one of the first to sixth specific embodiments is that in the above Step 31, the underwater acoustic transient signal with non-Gaussian background after noise reduction in Step 2 is subjected to frame division to obtain the k-th frame signal which is expressed as:

[0072]

[0073] where w(n) is the window function, l is the total number of signal points in each frame, inc is the frame shift step, K is the total number of frames after frame division, k is the k-th frame, and n is the n-th signal point in the frame.

[0074] Assume the window function is a rectangular window, l = 100, inc = 50;

[0075] For example, the sequence of the underwater acoustic transient signal with non-Gaussian background after noise reduction in Step 2 contains 8000 signal points. Taking 100 points as one frame and the frame shift step as 50; then from the front to the back, the first 100 signal points are the first frame, the 50th signal point to the 150th signal point are the second frame, and the 100th signal point to the 200th signal point are the third frame.

[0076] Other steps and parameters are the same as those in any one of the first to sixth specific embodiments.

[0077] Specific embodiment eight: The difference between this embodiment and any one of the first to seventh specific embodiments is that in the above Step 32, the short-time cross-correlation entropy between adjacent frames is calculated and used as the detection statistic, which is expressed as:

[0078]

[0079] wherein, is the signal of the k-th frame, is the signal of the (k + 1)-th frame;

[0080] is the cross-correlation entropy between the signal of the k-th frame and the signal of the (k + 1)-th frame;

[0081] is the Gaussian kernel function for calculating the short-time cross-correlation entropy;

[0082] σ is the kernel parameter of the Gaussian kernel function, σ > 0;

[0083] Denote as as the detection statistic.

[0084] Other steps and parameters are the same as those in any one of the first to seventh specific embodiments.

[0085] Specific Embodiment Nine: The difference between this embodiment and any one of the first to eighth specific embodiments is that in step 33, the detection threshold is determined, and the detection statistic is judged based on the detection threshold to obtain the detection result, and the detection result is whether there is a target signal; it is expressed as:

[0086]

[0087] wherein, th(k) is the detection threshold of the k-th frame signal;

[0088] The detection threshold is expressed as:

[0089]

[0090] wherein,

[0091] th(k - 1) is the detection threshold of the (k - 1)-th frame signal, and the initial value th(0) is the average value of the detection statistics of the first 20 frames (including 20);

[0092] M is the threshold coefficient, which determines the sensitivity of the calculated threshold to the detection statistic, and let M = 1000;

[0093] When is greater than the detection threshold th(k), it is judged as H1, and H1 indicates that there is a target signal;

[0094] When is less than or equal to the detection threshold th(k), it is judged as H0, and H0 indicates that there is no target signal;

[0095] Other steps and parameters are the same as those in any one of the first to eighth specific embodiments.

[0096] Embodiment 10: The difference between this embodiment and any one of Embodiments 1 to 9 is that when the target signal exists in the detection result in step 34, the arrival time of the target signal is estimated through the short-time cross-correlation entropy peak; it is expressed as:

[0097]

[0098] where

[0099] t k is the time corresponding to each frame of signal,

[0100] is the estimated value of the arrival time of the target signal.

[0101] Other steps and parameters are the same as any one of Embodiments 1 to 9.

[0102] Signal mathematical model

[0103] The present invention uses the sum of three exponentially decaying sine functions to model the deterministic transient signal [1], and the expression is as follows:

[0104]

[0105] In the formula, a n and λ n are respectively the amplitude coefficient and the amplitude decay factor of the nth signal component, τ n `f n and are the time delay, frequency and initial phase of each component. s(t) is the deterministic transient signal, and t is the time;

[0106] Considering the detection of the deterministic transient signal with unknown parameters in the above formula as a binary hypothesis testing problem, that is:

[0107] H0: x(t) = n(t)

[0108] H1: x(t) = s(t) + n(t)

[0109] where x(t) represents the underwater acoustic signal received by the passive detection system; n(t) represents the background noise, which follows the Alpha stable distribution; H0 is the H0 hypothesis, and H1 is the H1 hypothesis;

[0110] Since there is no unified probability density function for this distribution, it is usually defined by the characteristic function as shown in the following formula,

[0111]

[0112] In the above formula, sgn(·) is the sign function, 0 < α ≤ 2, -1 ≤ β ≤ 1, γ > 0, -∞ < δ < ∞;

[0113] The properties of the Alpha-stable distribution are completely determined by the parameters α, β, γ, and δ:

[0114] α is the characteristic exponent, which determines the decay rate of the tail of the probability density function. The smaller the value of α, the slower the tail decay and the more prominent the impulse characteristic of the time-domain waveform;

[0115] β is the skewness exponent, which is used to determine the degree of symmetry of the distribution;

[0116] γ is the dispersion coefficient, which is related to the degree of dispersion of the samples relative to the mean;

[0117] δ is the location parameter, which is similar to the mean of the Gaussian distribution;

[0118] i is the imaginary unit, w is the angular frequency, ψ(w) is the characteristic function, which is the inverse Fourier transform of the probability density function;

[0119] If the random variable X has a characteristic function, it is denoted as X ∼ S α (β, γ, δ);

[0120] If X ∼ S α (0, γ, δ), it is said that X follows a symmetric Alpha-stable distribution;

[0121] If X ∼ S α (β, 1, 0), then it is said that X follows a standard Alpha-stable distribution;

[0122] The Alpha-stable distribution is a class of generalized Gaussian distributions. When 0 < α < 2, the Alpha-stable distribution can represent a fractional-order non-Gaussian distribution; when α = 2 and β = 0, the Alpha-stable distribution degenerates into a Gaussian distribution.

[0123] Example:

[0124] Simulation experiments and results

[0125] The present invention uses the standard symmetric Alpha-stable distribution as the background noise to verify the performance of the algorithm in this paper. At this time, the dispersion coefficient γ = 1. Since the Alpha-stable distribution does not have a finite second moment, the generalized signal-to-noise ratio GSNR is used to measure the intensity of the signal and the background noise during the simulation process. The expression is GSNR = 10lg(η s 2 / γ), where η s 2 represents the variance of the signal. The setting of the generalized signal-to-noise ratio will be achieved by adjusting the amplitude of the given signal s(n),

[0126]

[0127] Where s1(n) is the signal after adjusting the amplitude according to the set signal-to-noise ratio, and Var[s(n)] represents the variance of the signal before amplitude adjustment.

[0128] The set signal observation duration is 2 s, the pulse width of the transient target signal is 5 - 10 ms, and the value range of the transient signal parameters is set as follows: amplitude coefficient a n ∈(0, 1]; amplitude attenuation factor λ n ∈(0, 1000]; time delay τ n ∈[0, 10] ms; frequency f n ∈(0, 5] kHz; initial phase

[0129] Data preprocessing noise reduction and detection results

[0130] Set the arrival time of the transient target signal to 1.5 s, pulse width 5 ms, generalized signal-to-noise ratio GSNR = 0 dB, and characteristic exponent α = 1.5 for simulation experiments. The kernel parameter for calculating the short-time cross-correlation entropy is σ = 1. Figure 3 It is the signal model and local waveform. Figure 4 The signal and local waveform during the data preprocessing noise reduction process are plotted. Figure 3 In (d) and Figure 4 The comparison results in (d) show that after outlier detection and multi-level filtering noise reduction processing, the pulse interference that seriously affects the performance of the detector in the original signal is effectively eliminated, and at the same time, the Alpha-stable distribution background noise is effectively suppressed.

[0131] Figure 5 The detection results of the energy detector and the short-time cross-correlation entropy detector before and after noise reduction are shown. From Figure 5 In (a) of 5, (b) of 5, it can be seen that the data preprocessing noise reduction not only restores the detection performance of the energy detector but also significantly improves the accuracy of arrival time estimation. Comparing Figure 5 The short-time cross-correlation entropy characteristics before and after noise reduction in (c) of 5 and (d) of 5, it can be found that the noise reduction processing effectively enhances the significance of the short-time cross-correlation entropy characteristics of the signal, and its peak-to-average ratio has increased by about 10 dB. In addition, by comparing Figure 5 The characteristics in the energy domain in (a) and Figure 5 The characteristics in the cross-correlation entropy domain in (c), it can be seen that the short-time cross-correlation entropy characteristics show stronger noise robustness than the energy characteristics and can still maintain good feature recognition under noise interference.

[0132] Detection performance analysis

[0133] Figure 6The receiver operating characteristic (ROC) curves of three detectors, namely STCCED, DP-STCCED, and DP-ED, are plotted under the condition of low generalized signal-to-noise ratio from -7 dB to -11 dB, and the number of Monte Carlo experiments is 1000 times. The experimental results show that under the condition of false alarm probability P f = 0.1, the detection probability P d of the DP-STCCED algorithm reaches 0.885 at -9 dB, which is 59.2% higher than that of DP-ED. When the signal-to-noise ratio drops from -7 dB to -11 dB, the AUC area of DP-ED decreases by 49.7%, while that of DP-STCCED only decreases by 26.2%, confirming the stability advantage of the latter under the condition of low generalized signal-to-noise ratio.

[0134] Under the constant false alarm threshold, Figure 7 the value range of the characteristic exponent of the Alpha-stable distribution background noise is set to [0.7, 1.9] to study the influence of this parameter on the detection performance of the DP-ED and DP-STCCED algorithms. The experimental results show that the detection probability is significantly positively correlated with the characteristic exponent. This is because as the characteristic exponent increases, the spike pulses in the noise gradually weaken, thus improving the detection probability of the energy detector and the short-time cross-correlation entropy detector.

[0135] Furthermore, the present invention analyzes the influence of the kernel parameter on the detection performance of the DP-STCCED algorithm, and sets 5 different kernel parameters for simulation experiments. As Figure 8 can be seen, the detection probability under each generalized signal-to-noise ratio increases with the decrease of the kernel parameter, which indicates that a smaller kernel parameter is beneficial to improving the anti-interference performance of the detection algorithm.

[0136] TOA Estimation Error Analysis

[0137] To evaluate the arrival time estimation performance of the DP-ED and DP-STCCED algorithms, Figure 9 the TOA estimation error analysis results of the Monte Carlo simulation experiment (the number of independent repetitions M = 1000) are shown. The TOA estimation error calculation formula is where is the arrival time estimation value, and T i is the true arrival time. In the experiment, the true arrival time of the valid signal follows a uniform distribution. Considering the influence of the kernel parameter on the detection performance, the kernel parameter for short-time cross-correlation entropy calculation is set to σ = 0.5. Figure 9Figure (a) compares the variation trends of the TOA estimation errors of each algorithm with the generalized signal-to-noise ratio when the characteristic exponent is 1.2, 1.5, and 1.8. Experiments show that when the characteristic exponent decreases from 1.8 to 1.2, the increase in the TOA estimation error of the DP-ED algorithm reaches 90% under the extreme condition of -20 dB, while the increase in the estimation error of the proposed DP-STCCED algorithm is always lower than 48% in the generalized signal-to-noise ratio range of -20 dB to 5 dB, verifying its robustness against impulse interference. Figure 9 Figure (b) further plots the TOA estimation errors varying with the characteristic exponent at generalized signal-to-noise ratios of -7 dB, -9 dB, and -11 dB. The TOA estimation accuracy of each algorithm decreases with the decrease in the generalized signal-to-noise ratio, but the TOA estimation accuracy of the DP-STCCED algorithm is better than that of the DP-ED algorithm under different characteristic exponents.

[0138] The influence of the kernel parameter on the TOA estimation is as Figure 9 shown in Figure (c). When the kernel parameter increases from 0.1 to 0.9, the estimation error of the DP-STCCED algorithm decreases by about 43% on average, indicating that a larger kernel parameter is beneficial to improving the sensitivity of the TOA estimation. Through comprehensive analysis Figure 9 it can be seen that the decrease in the generalized signal-to-noise ratio, the decrease in the characteristic exponent, and the increase in the kernel parameter all result in a reduction in the TOA estimation accuracy of the detection algorithm, among which the influence of the generalized signal-to-noise ratio and the kernel parameter is more significant than that of the characteristic exponent.

[0139] References

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[0166] 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 can make various corresponding changes and deformations according to the present invention, but these corresponding changes and deformations should all fall within the protection scope of the appended claims of the present invention.

Claims

1. An underwater acoustic transient signal detection method under alpha-stable distribution noise, characterized in that: The specific process of the method is as follows: Step 1: Collect the original underwater acoustic transient signal under non-Gaussian background; Step 2: Denoise the original underwater acoustic transient signal collected under non-Gaussian background to obtain the underwater acoustic transient signal under non-Gaussian background after denoising; Step 3: Use a short-time cross-correlation entropy detector to process the underwater acoustic transient signal under non-Gaussian background after denoising in Step 2 to obtain the short-time cross-correlation entropy and the arrival time of the target signal.

2. The method for detecting underwater acoustic transient signals under Alpha-stable distribution noise according to claim 1, wherein: In Step 2, the original underwater acoustic transient signal collected under non-Gaussian background is denoised to obtain the underwater acoustic transient signal under non-Gaussian background after denoising; The specific process is as follows: Step 21: Perform outlier detection based on the interquartile range on the original underwater acoustic transient signal collected under non-Gaussian background to obtain the original underwater acoustic transient signal sequence x(n) after outlier detection processing; Step 22: Use median filtering technology to process x(n), fill in the missing values, and reconstruct the signal sequence; Step 23: Process the reconstructed signal sequence using the modified Alpha mean filtering technique to obtain the final noise-reduced signal 3. The method for detecting underwater acoustic transient signals under Alpha-stable distribution noise according to claim 2, wherein: In Step 21, outlier detection based on the interquartile range is performed on the original underwater acoustic transient signal collected under non-Gaussian background to obtain the original underwater acoustic transient signal sequence x(n) after outlier detection processing; The specific process is as follows: Step 211: Ascendingly sort the original underwater acoustic transient signal sequence x(n) = {x1, x2, …, x i , …, x N} collected under a non-Gaussian background to obtain the sorted original underwater acoustic transient signal sequence x'(n) = {x'1, x'2, …, x' i , …, x' N}, i = 1, 2,..., N, where N is the total number of sample points of the original underwater acoustic transient signal sequence, and i is the index of the i-th sample point of the original underwater acoustic transient signal sequence; x i is the i-th sample point in the original underwater acoustic transient signal sequence under non-Gaussian background; x N is the N-th sample point in the original underwater acoustic transient signal sequence under non-Gaussian background; x' i is the i-th sample point in the original underwater acoustic transient signal sequence after arrangement; x' N is the N-th sample point in the original underwater acoustic transient signal sequence after arrangement; Divide \(x'(n)=\{x'_1,x'_2,\cdots,x' i ,\cdots,x' N \}\) into four equal parts, the first part is the first quartile \(Q_1\), the second part is the second quartile \(Q_2\), the third part is the third quartile \(Q_3\), and the fourth part is the fourth quartile \(Q_4\); Based on the first quartile Q1 and the third quartile Q3, obtain the IQR; Step 212: Set the outlier detection thresholds T1 and T2; Among them, T1 represents the upper limit of the threshold; T2 represents the lower limit of the threshold; If in the original underwater acoustic transient signal sequence x(n) = {x1, x2, …, x i , …, x N}, the data point x i < T1 or x i > T2, then the data point x i is marked as an outlier; Delete the data points marked as outliers to obtain the original underwater acoustic transient signal sequence x(n) after deleting outliers.

4. The method for detecting underwater acoustic transient signals under Alpha-stable distribution noise according to claim 3, characterized in that: The first quartile Q1, the third quartile Q3, and the interquartile range IQR in Step 211 are respectively: In the formula, Denotes rounding up; Indicates the last 1 underwater acoustic signal sample of the first part when dividing x'(n) into four equal parts; Indicates the last 1 underwater acoustic signal sample of the third part when x'(n) is divided into four equal parts.

5. The method for detecting underwater acoustic transient signals under Alpha-stable distribution noise according to claim 4, wherein: In Step 212, setting the outlier detection thresholds T1 and T2 is expressed as: T1 = Q1 - c × IQR, T2 = Q3 + c × IQR Among them, T1 represents the upper limit of the threshold; T2 represents the lower limit of the threshold; c is a constant.

6. The method for detecting underwater acoustic transient signals under Alpha-stable distribution noise according to claim 5, characterized in that: In Step 3, a short-time cross-correlation entropy detector is used to process the underwater acoustic transient signal under non-Gaussian background after denoising in Step 2 to obtain the short-time cross-correlation entropy and the arrival time of the target signal; The specific process is as follows: Step 31: For the underwater acoustic transient signal in the non-Gaussian background after noise reduction processing in Step 2 Perform frame segmentation to obtain the k-th frame signal Step 32: Calculate the short-time cross-correlation entropy between adjacent frames and use it as the detection statistic; Step 33: Determine the detection threshold, and make a decision on the detection statistic based on the detection threshold to obtain the detection result, where the detection result is whether there is a target signal; Step 34: Based on the detection result that the target signal exists, estimate the arrival time of the target signal through the short-time cross-correlation entropy peak.

7. The method for detecting underwater acoustic transient signals under Alpha-stable distribution noise according to claim 6, wherein: The underwater acoustic transient signal in the non-Gaussian background after noise reduction in step 2 in step 31 is framed to obtain the k-th frame signal which is expressed as: In the formula, w(n) is the window function, l is the total number of signal points in each frame, inc is the frame step size, K is the total number of frames after frame division, k is the k-th frame, and n is the n-th signal point in the frame.

8. The method for detecting underwater acoustic transient signals under Alpha-stable distribution noise according to claim 7, characterized in that: In Step 32, calculating the short-time cross-correlation entropy between adjacent frames and using it as the detection statistic is expressed as: In the formula, is the signal of the k-th frame, is the signal of the (k + 1)-th frame; is the cross-correlation entropy between the k-th frame signal and the (k + 1)-th frame signal; is a Gaussian kernel function for calculating short-time cross-correlation entropy; σ is the kernel parameter of the Gaussian kernel function, σ > 0; Let be briefly denoted as as the detection statistic.

9. The method for detecting underwater acoustic transient signals under Alpha-stable distribution noise according to claim 8, characterized in that: In step 33, the detection threshold is determined, and based on the detection threshold, a decision is made on the detection statistic to obtain a detection result, where the detection result is whether there is a target signal; it is expressed as: In the formula, th(k) is the detection threshold of the k-th frame signal; The detection threshold is expressed as: Wherein, th(k - 1) is the detection threshold of the (k - 1)-th frame signal, and the initial value th(0) is the average value of the detection statistics of the first 20 frames; M is the threshold coefficient, and let M = 1000; When is greater than the detection threshold th(k), it is determined as H1, where H1 indicates the presence of a target signal; When is less than or equal to the detection threshold th(k), it is determined as H0, where H0 indicates the absence of a target signal.

10. The method for detecting underwater acoustic transient signals under Alpha-stable distribution noise according to claim 9, characterized in that: In step 34, when there is a target signal in the detection result, the arrival time of the target signal is estimated through the short-time cross-correlation entropy peak; it is expressed as: Wherein, t k is the time corresponding to each frame of signal, is the estimated arrival time of the target signal.

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