Robust detection method and system for weak target based on spectral kurtosis weighting

Abstract

This invention provides a robust weak target detection method and system based on spectral kurtosis weighting, comprising: acquiring raw multi-channel array data and preprocessing it; performing spectral analysis on the preprocessed multi-channel array data to select target sub-bands containing target signals; first, focusing the target azimuth in the spatial domain, then extracting and completing the target sub-bands in the frequency domain, and finally returning to the time domain to form a coherently processable narrowband echo sequence; generating a frequency domain weighted mask based on a multi-shot spectral matrix for the narrowband echo sequence; combining the frequency domain weighted mask with power gain to obtain a comprehensive weighted mask, and using the comprehensive weighted mask to nonlinearly amplify the target spectrum to obtain multi-shot enhanced output data; aligning and accumulating the multi-shot enhanced output data according to different assumed velocities to form a range-velocity history map; performing detection and decision on the history map and outputting target information.

Description

Technical Field

[0001] This invention relates to the fields of sonar array signal processing and underwater weak target detection technology. Specifically, it relates to a robust weak target detection method and system based on spectral kurtosis weighting, and more specifically, it relates to a multi-shot weak target detection method and system based on azimuth focusing narrowband inverse transform and spectral kurtosis weighting. Background Technology

[0002] In complex marine environments, small targets, such as long-range or small-sized submersibles, produce extremely weak echo signals, often submerged in strong noise and reverberation, posing a challenge to reliable detection. Existing array signal processing methods and active sonar detection technologies have the following limitations: Weak signals are easily submerged in noise: Traditional detection methods, such as matched filters, rely on prior templates to correlate targets. When the target echo energy is lower than the background noise, a fixed threshold is insufficient to effectively distinguish the signal, easily leading to missed detections. Lowering the detection threshold to detect weak targets introduces a large number of false alarms, reducing reliability.

[0003] Severe clutter and reverberation interference: Strong reverberation and multipath scattering in shallow sea environments can mask weak target features. Conventional beamforming (CBF), while simple and robust, has wide beams and high sidelobes, easily introducing non-target azimuth clutter energy. Adaptive beamforming such as MVDR can suppress some interference, but it is sensitive to array model errors. Even when combined with constant false alarm rate (CFAR) detection, threshold control remains unstable when local clutter power fluctuates drastically, and detection performance drops sharply in low signal-to-clutter ratio scenarios.

[0004] High-speed target Doppler ambiguity: When a target moves at high speed relative to the sonar, a significant Doppler frequency shift occurs, causing velocity ambiguity and processing gain loss in the output of narrowband matched filtering or pulse compression. Although continuous wave (CW) transmission or broadband waveforms can alleviate range-velocity ambiguity, traditional single-pulse processing struggles to fully utilize Doppler information to enhance the target, and the coherence characteristics between multiple snapshots are not effectively exploited.

[0005] In summary, existing technologies lack a detection scheme that can effectively enhance weak target signals under conditions of strong noise, strong reverberation, and high-speed Doppler. This invention is proposed against this backdrop, aiming to overcome the aforementioned bottlenecks and provide a weak target detection method that utilizes multi-shot coherent accumulation, narrowband inverse transform focusing, and high-order statistics of spectral kurtosis to achieve layer-by-layer enhancement and robust detection of weak target echoes. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the purpose of this invention is to provide a robust weak target detection method and system based on spectral kurtosis weighting.

[0007] A robust weak target detection method based on spectral kurtosis weighting provided by the present invention includes: Step S1: Obtain the raw data of the multi-channel array, and use the data preprocessing module to preprocess the obtained raw data of the multi-channel array to obtain the preprocessed multi-channel array data; Step S2: Perform spectrum analysis on the preprocessed multi-channel array data using the adaptive frequency band extraction module to select the target sub-frequency band containing the target signal; Step S3: The preprocessed multi-channel array data is first focused on the target azimuth in the spatial domain by the beamforming and narrowband completion inverse transform module, and then the target sub-band is extracted and completed in the frequency domain. Finally, it is returned to the time domain to form a narrowband echo sequence that can be coherently processed. Step S4: For the narrowband echo sequence that can be coherently processed back to the time domain, a frequency domain weight mask is generated based on the multi-fast-shot spectral matrix through the spectral kurtosis calculation and weight generation module; Step S5: Combine the frequency domain weight mask with the power gain through the nonlinear enhancement module to obtain the comprehensive weight mask, and use the comprehensive weight mask to perform nonlinear amplification processing on the target spectrum to obtain the multi-shot enhanced output data; Step S6: The distance-velocity history graph construction module aligns and accumulates the data from the multi-shot enhancement output according to different assumed velocities to form a two-dimensional distance-velocity history graph; Step S7: Detect and determine the distance-velocity two-dimensional history graph through the peak detection and result output module and output the target information.

[0008] Preferably, step S1 includes: Step S1.1: Synchronously sample and time-stamp the acquired multi-channel array raw echo data to ensure that the start time of each channel is consistent and to establish a unified time base reference; Step S1.2: Bandpass filtering is performed on the noise interference outside the working frequency band in the acquired multi-channel array raw echo data. At the same time, DC component removal and pulse interference suppression are performed to obtain filtered and shaped multi-channel array echo data. Step S1.3: Downconvert the filtered and shaped multi-channel array echo data to baseband, and perform decimation and low-pass filtering to obtain the analytical signal; Step S1.4: Perform amplitude shaping on the analytical signal, control the dynamic range of the analytical signal to prevent signal amplitude overflow, and obtain the amplitude-shaped analytical signal; Step S1.5: Perform a short-time Fourier transform on the amplitude-shaped analytical signal to obtain a time-frequency representation of the signal, forming a unified data format.

[0009] Preferably, step S2 includes: Step S2.1: Calculate the average power spectrum of the beam or channel signal based on the preprocessed multi-channel array data, and then set candidate sub-bands in combination with prior target information; Step S2.2: Calculate the multi-frame energy stability and preliminary kurtosis index within each candidate sub-band. Based on the calculated multi-frame energy stability and preliminary kurtosis index within each candidate sub-band, evaluate whether the robustness of the signal and the interference level meet the preset requirements, and then determine whether the candidate sub-band contains the target signal. Step S2.3: Adaptively select one or more narrow frequency bands as key frequency bands based on the candidate sub-bands containing the target signal, and use the current key frequency band as the target sub-band containing the target signal.

[0010] Preferably, step S3 includes: Step S3.1: Establish a beam pointing angle grid covering the mission azimuth range based on the array geometry parameters, and calculate the corresponding beam steering vector for each candidate azimuth. Step S3.2: Perform delay alignment and weighted summation of each array element in the frequency domain according to the steering vector to obtain the beam output in each direction. At the same time, reduce the sidelobe level by weighting the array elements to suppress non-target azimuth interference. Step S3.3: Find the direction of the main lobe with the highest energy among all candidate beam outputs, and determine it as the focusing azimuth for subsequent processing, so that the target energy is concentrated in the spatial domain and the background variance is reduced; Step S3.4: Call the target sub-band, extract the corresponding frequency range on the spectrum of the main lobe beam, and set the frequency components outside the range to zero or interpolate with low values ​​to form a narrowband spectrum; Step S3.5: To meet the spectral integrity requirements of the inverse transform, the narrowband spectrum is padded with positive and negative frequencies, including: constructing a conjugate symmetric spectrum for the real signal to avoid IFFT distortion; Step S3.6: Perform discrete inverse Fourier transform on the completed narrowband spectrum to obtain the time-domain narrowband echo sequence. This result is equivalent to applying bandpass filtering to the focused beam and concentrating the energy in the target frequency band into the time domain.

[0011] Preferably, step S4 includes: Step S4.1: Perform snapshot segmentation and windowing on the time-domain narrowband echo sequence, and then perform FFT on each snapshot to obtain the amplitude spectrum, thereby forming a multi-snapshot spectrum matrix organized according to snapshot-frequency point; Step S4.2: Collect multiple snapshot amplitude value sequences at each frequency point; Step S4.3: Based on the amplitude value sequence of multiple snapshots collected, estimate the background kurtosis distribution using data corresponding to non-target frequency bands or non-main lobe azimuths, and determine the kurtosis decision threshold accordingly. Step S4.4: Based on the multi-shot spectral matrix, obtain the robust kurtosis value of each frequency point according to the kurtosis decision threshold. Normalize the obtained robust kurtosis value of each frequency point and map it to a spectral kurtosis weight between 0 and 1. The higher the kurtosis, the more obvious the intermittent peak characteristics of the frequency point in the multi-shot, and the closer the weight is to 1. When the kurtosis is close to the background level, the weight approaches 0. At the same time, calculate the noise spectral density gain according to the parallel branch and normalize it to a continuous amplitude weight to characterize the confidence level of each frequency point in terms of energy. Step S4.5: Fuse and amplify the normalized spectral kurtosis weights and the normalized noise spectral density gain, and perform smoothing and clipping control on the fusion result to output the final frequency domain weight mask.

[0012] Preferably, step S5 includes: Step S5.1: Multiply the obtained frequency domain weight mask with the noise density matrix gain and spectrum point by point to obtain the initial weighted spectrum; Step S5.2: For the initial weighted spectrum, perform small-window smoothing on the fusion weights in both the frequency domain and slow time. The frequency domain smoothing operator is denoted as... H f The slow-time smoothing operator is denoted as H s The weights are obtained after one smoothing process, where the small window smoothing is achieved using a sliding weighted average. Step S5.3: Introduce nonlinear parameters to the obtained frequency domain weight mask. α Exponential modulation is performed to obtain exponential weights, wherein the exponential modulation is used to adjust the contrast of the weight differences. Then, the exponential weights are fused with the obtained first-smoothed weights according to the multiplicative rule to generate fused weights, and the fused weights are used to amplify and enhance the spectrum. Step S5.4: Continue to perform small window smoothing on the above intermediate results in the frequency domain and slow time dimension to obtain the intermediate spectrum results after secondary smoothing; Step S5.5: Calculate the local signal-to-noise ratio statistic and spectral kurtosis statistic, and adaptively update the weights after secondary smoothing to obtain the final weights. Apply the final weights to the corresponding spectrum of the preprocessed multi-channel array data to obtain the enhanced spectrum.

[0013] Preferably, step S6 includes: assuming a set of target radial velocity values, calculating the distance migration of the target between adjacent snapshots for each assumed velocity, and performing corresponding distance correction and translation on the enhanced spectrum of all snapshots, including: aligning and superimposing the enhanced spectrum at different times according to the assumed velocity; accumulating a comprehensive echo intensity sequence for each assumed velocity; and constructing a two-dimensional range-velocity energy distribution map by using velocity as the vertical axis and distance as the horizontal axis.

[0014] Preferably, step S7 includes: Step S7.1: Perform constant false alarm detection on the distance-velocity two-dimensional history graph and select significant peak points or continuous peak trajectories that meet the preset requirements as candidate targets; Step S7.2: Extract parameter information for each candidate target in multiple consecutive frames, including the corresponding range cell, velocity value, and the intensity of the peak value in the cumulative image.

[0015] Preferably, step S7.1 includes: clustering CFAR detection points in the distance-velocity plane according to a preset neighborhood, merging spatially adjacent peak points into the same candidate target region and selecting the largest point in the region as the representative peak; then performing gating matching and continuous hit statistics on the representative peak between adjacent snapshot / sliding accumulation windows, retaining those that meet the continuous hit threshold, otherwise judging them as isolated noise peaks and removing them, thereby removing isolated noise peaks and false alarms.

[0016] A robust weak target detection system based on spectral kurtosis weighting, provided by the present invention, includes: The data preprocessing module is used to acquire the raw data of the multi-channel array and preprocess the acquired raw data of the multi-channel array to obtain the preprocessed multi-channel array data. The adaptive frequency band extraction module is used to perform spectral analysis on the preprocessed multi-channel array data and select the target sub-frequency band containing the target signal; The beamforming and narrowband completion inverse transform module is used to first perform target azimuth focusing in the spatial domain, then perform target sub-band extraction and completion in the frequency domain, and finally return to the time domain to form a narrowband echo sequence that can be coherently processed. The spectral kurtosis calculation and weight generation module is used to generate a frequency domain weight mask based on a multi-fast-shot spectral matrix for narrowband echo sequences that can be coherently processed back to the time domain. The nonlinear enhancement module is used to combine the frequency domain weight mask with the power gain to obtain a comprehensive weight mask. The comprehensive weight mask is then used to perform nonlinear amplification of the target spectrum to obtain multi-shot enhanced output data. The distance-velocity history graph construction module is used to align and accumulate data from multiple snapshots of enhanced output according to different assumed velocities to form a two-dimensional distance-velocity history graph. The peak detection and result output module is used to detect and determine the target information from the distance-velocity two-dimensional history graph.

[0017] Compared with the prior art, the present invention has the following beneficial effects: 1. Significantly enhanced weak signals and improved detection probability: This invention achieves multi-level signal-to-noise ratio enhancement through spatial gain of beamforming, focusing gain of narrowband inverse transform, and time gain of multi-pulse coherent accumulation, superimposed with frequency domain gain of spectral kurtosis and nonlinear weighting; weak targets stand out above background noise after being enhanced step by step, and can be reliably detected even under extremely low initial signal-to-noise ratio conditions, greatly improving the detectability of weak targets; 2. Strong clutter reverberation suppression and robustness in complex scenarios: This invention utilizes the differences in statistical characteristics between the target and the interference for multi-dimensional filtering; the spectral kurtosis weight in this invention specifically highlights the "intermittent / non-Gaussian" target components and suppresses the "stationary near-Gaussian" reverberation clutter; at the same time, combined with spatial beam pointing to suppress energy in non-target directions, the method is greatly improved in the robustness of the method in complex environments such as strong reverberation and multipath, and can maintain stable detection performance in scenarios where the performance of traditional algorithms drops sharply; 3. Low false alarm rate and adaptive threshold: This invention utilizes spectral kurtosis information to assist in detection and decision-making, which is equivalent to adaptively adjusting the threshold according to data characteristics, making the algorithm adaptive to different sea state backgrounds and reducing the uncertainty of manually setting the threshold. 4. Balancing Fine-grained Continuous Enhancement with Engineering Feasibility: This invention achieves fine-grained signal enhancement through frequency-by-frequency and frame-by-frame continuous weight modulation, avoiding problems such as excessive suppression or missed target detection. For example, the fused nonlinear mask provides flexible gain control, allowing adjustment of the weight fusion strategy and intensity according to on-site requirements, making the algorithm adaptable to different target / noise distributions. Furthermore, each module mainly involves low-complexity operations such as FFT transformation, complex multiplication, and windowing smoothing, making it suitable for implementation on embedded platforms such as DSP / FPGA / GPU, demonstrating good engineering feasibility. The method flow is compatible with conventional pulse compression processing and can also be combined with MVDR beamforming, linear frequency modulation (LFM / HFM) systems, etc., possessing good scalability and upgrade capabilities. Attached Figure Description

[0018] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a flowchart of a robust weak target detection method based on spectral kurtosis weighting.

[0019] Figure 2 This is a flowchart of the data preprocessing process.

[0020] Figure 3 This is a block diagram for adaptive frequency band extraction.

[0021] Figure 4 This is a flowchart of beamforming and narrowband completion inverse transform.

[0022] Figure 5This is a flowchart of spectral kurtosis calculation and weight generation.

[0023] Figure 6 This is a flowchart for non-linear enhancement.

[0024] Figure 7 Build a flowchart for the distance-velocity timeline.

[0025] Figure 8 This is a flowchart for peak detection and result output.

[0026] Figures 9a to 9d The figures show the simulation and experimental data results. Detailed Implementation

[0027] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0028] Example 1 According to the present invention, a robust weak target detection method based on spectral kurtosis weighting is provided, such as... Figures 2 to 8 As shown, it includes: Step S1: Obtain the raw data of the multi-channel array, and use the data preprocessing module to preprocess the obtained raw data of the multi-channel array to obtain the preprocessed multi-channel array data; Step S2: Perform spectrum analysis on the preprocessed multi-channel array data using the adaptive frequency band extraction module to select the target sub-frequency band containing the target signal; Step S3: The preprocessed multi-channel array data is first focused on the target azimuth in the spatial domain by the beamforming and narrowband completion inverse transform module, and then the target sub-band is extracted and completed in the frequency domain. Finally, it is returned to the time domain to form a narrowband echo sequence that can be coherently processed. Step S4: For the narrowband echo sequence that can be coherently processed back to the time domain, a frequency domain weight mask is generated based on the multi-fast-shot spectral matrix through the spectral kurtosis calculation and weight generation module; Step S5: Combine the frequency domain weight mask with the power gain through the nonlinear enhancement module to obtain the comprehensive weight mask, and use the comprehensive weight mask to perform nonlinear amplification processing on the target spectrum to obtain the multi-shot enhanced output data; Step S6: The distance-velocity history graph construction module aligns and accumulates the data from the multi-shot enhancement output according to different assumed velocities to form a two-dimensional distance-velocity history graph; Step S7: Detect and determine the distance-velocity two-dimensional history graph through the peak detection and result output module and output the target information.

[0029] Specifically, step S1 includes: Step S1.1: Synchronously sample and time-stamp the acquired multi-channel array raw echo data to ensure that the start time of each channel is consistent and to establish a unified time base reference; Step S1.2: Bandpass filtering is performed on the noise interference outside the working frequency band in the acquired multi-channel array raw echo data. At the same time, DC component removal and pulse interference suppression are performed to obtain filtered and shaped multi-channel array echo data. Step S1.3: Downconvert the filtered and shaped multi-channel array echo data to baseband, and perform decimation and low-pass filtering to obtain the analytical signal; Step S1.4: Perform amplitude shaping on the analytical signal, control the dynamic range of the analytical signal to prevent signal amplitude overflow, and obtain the amplitude-shaped analytical signal; Step S1.5: Perform a short-time Fourier transform on the amplitude-shaped analytical signal to obtain a time-frequency representation of the signal, forming a unified data format.

[0030] Specifically, step S2 includes: Step S2.1: Calculate the average power spectrum of the beam or channel signal based on the preprocessed multi-channel array data, and then set candidate sub-bands in combination with prior target information; Step S2.2: Calculate the multi-frame energy stability and preliminary kurtosis index within each candidate sub-band. Based on the calculated multi-frame energy stability and preliminary kurtosis index within each candidate sub-band, evaluate whether the robustness of the signal and the interference level meet the preset requirements, and then determine whether the candidate sub-band contains the target signal. Step S2.3: Adaptively select one or more narrow frequency bands as key frequency bands based on the candidate sub-bands containing the target signal, and use the current key frequency band as the target sub-band containing the target signal.

[0031] Specifically, step S3 includes: Step S3.1: Establish a beam pointing angle grid covering the mission azimuth range based on the array geometry parameters, and calculate the corresponding beam steering vector for each candidate azimuth. Step S3.2: Perform delay alignment and weighted summation of each array element in the frequency domain according to the steering vector to obtain the beam output in each direction. At the same time, reduce the sidelobe level by weighting the array elements to suppress non-target azimuth interference. Step S3.3: Find the direction of the main lobe with the highest energy among all candidate beam outputs, and determine it as the focusing azimuth for subsequent processing, so that the target energy is concentrated in the spatial domain and the background variance is reduced; Step S3.4: Call the target sub-band, extract the corresponding frequency range on the spectrum of the main lobe beam, and set the frequency components outside the range to zero or interpolate with low values ​​to form a narrowband spectrum; Step S3.5: To meet the spectral integrity requirements of the inverse transform, the narrowband spectrum is padded with positive and negative frequencies, including: constructing a conjugate symmetric spectrum for the real signal to avoid IFFT distortion; Step S3.6: Perform discrete inverse Fourier transform on the completed narrowband spectrum to obtain the time-domain narrowband echo sequence. This result is equivalent to applying bandpass filtering to the focused beam and concentrating the energy in the target frequency band into the time domain.

[0032] Specifically, step S4 includes: Step S4.1: Perform snapshot segmentation and windowing on the time-domain narrowband echo sequence, and then perform FFT on each snapshot to obtain the amplitude spectrum, thereby forming a multi-snapshot spectrum matrix organized according to snapshot-frequency point; Step S4.2: Collect multiple snapshot amplitude value sequences at each frequency point; Step S4.3: Based on the amplitude value sequence of multiple snapshots collected, estimate the background kurtosis distribution using data corresponding to non-target frequency bands or non-main lobe azimuths, and determine the kurtosis decision threshold accordingly. Step S4.4: Based on the multi-shot spectral matrix, obtain the robust kurtosis value of each frequency point according to the kurtosis decision threshold. Normalize the obtained robust kurtosis value of each frequency point and map it to a spectral kurtosis weight between 0 and 1. The higher the kurtosis, the more obvious the intermittent peak characteristics of the frequency point in the multi-shot, and the closer the weight is to 1. When the kurtosis is close to the background level, the weight approaches 0. At the same time, calculate the noise spectral density gain according to the parallel branch and normalize it to a continuous amplitude weight to characterize the confidence level of each frequency point in terms of energy. Step S4.5: Fuse and amplify the normalized spectral kurtosis weights and the normalized noise spectral density gain, and perform smoothing and clipping control on the fusion result to output the final frequency domain weight mask.

[0033] Specifically, step S5 includes: Step S5.1: Multiply the obtained frequency domain weight mask with the noise density matrix gain and spectrum point by point to obtain the initial weighted spectrum; Step S5.2: For the initial weighted spectrum, perform small-window smoothing on the fusion weights in both the frequency domain and slow time. The frequency domain smoothing operator is denoted as... H f The slow-time smoothing operator is denoted as H s The weights are obtained after one smoothing process, where the small window smoothing is achieved using a sliding weighted average. Step S5.3: Introduce nonlinear parameters to the obtained frequency domain weight mask.α Exponential modulation is performed to obtain exponential weights, wherein the exponential modulation is used to adjust the contrast of the weight differences. Then, the exponential weights are fused with the obtained first-smoothed weights according to the multiplicative rule to generate fused weights, and the fused weights are used to amplify and enhance the spectrum. Step S5.4: Continue to perform small window smoothing on the above intermediate results in the frequency domain and slow time dimension to obtain the intermediate spectrum results after secondary smoothing; Step S5.5: Calculate the local signal-to-noise ratio statistic and spectral kurtosis statistic, and adaptively update the weights after secondary smoothing to obtain the final weights. Apply the final weights to the corresponding spectrum of the preprocessed multi-channel array data to obtain the enhanced spectrum.

[0034] Specifically, step S6 includes: assuming a set of target radial velocity values, calculating the distance migration of the target between adjacent snapshots for each assumed velocity, and performing corresponding distance correction and translation on the enhanced spectrum of all snapshots, including: aligning and superimposing the enhanced spectrum at different times according to the assumed velocity; accumulating a comprehensive echo intensity sequence for each assumed velocity; and constructing a two-dimensional range-velocity energy distribution map by using velocity as the vertical axis and distance as the horizontal axis.

[0035] Specifically, step S7 includes: Step S7.1: Perform constant false alarm detection on the distance-velocity two-dimensional history graph and select significant peak points or continuous peak trajectories that meet the preset requirements as candidate targets; Step S7.2: Extract parameter information for each candidate target in multiple consecutive frames, including the corresponding range cell, velocity value, and the intensity of the peak value in the cumulative image.

[0036] Specifically, step S7.1 includes: clustering CFAR detection points in the distance-velocity plane according to a preset neighborhood, merging spatially adjacent peak points into the same candidate target region and selecting the largest point in the region as the representative peak; then performing gating matching and continuous hit statistics on the representative peak between adjacent snapshot / sliding accumulation windows, retaining those that meet the continuous hit threshold, otherwise judging them as isolated noise peaks and removing them, thereby removing isolated noise peaks and false alarms.

[0037] Example 2 Example 2 is a preferred example of Example 1. This invention provides a robust weak target detection system based on spectral kurtosis weighting, offering a comprehensive solution to the technical challenge of detecting weak underwater targets under low signal-to-noise ratio conditions. The invention combines physical array gain and statistical feature discrimination to progressively focus and enhance the target signal at each key stage of the signal processing flow, while suppressing random noise and interference. Specifically, it employs a technical approach of spatial azimuth focusing + narrowband spectrum completion inverse transform + spectral kurtosis weighting fusion + multi-shot cumulative detection, extracting robust features of the target layer by layer to achieve significant enhancement and reliable detection of weak target signals.

[0038] This invention utilizes theories such as sonar beamforming, coherent accumulation, and higher-order statistical analysis. First, conventional or adaptive beamforming is used to focus on the target's azimuth in space, acquiring spatial gain to reduce clutter from non-target directions. Then, adaptive subband extraction and narrowband reconstruction are performed on the beam output spectrum; a narrow frequency band where the target may exist is selected, the spectrum is completed, and an inverse Fourier transform (IFFT) is performed to concentrate the target energy in the time domain and correct for Doppler-induced time delay bias. Next, utilizing the consistency of data between multiple snapshot frames, spectral kurtosis is calculated to measure the non-Gaussian sharpness of each frequency component in slow time, generating frequency domain weights accordingly. The kurtosis weights are combined with traditional power gain to form a nonlinear enhancement filter, providing higher gain to significant target frequencies and suppressing stable background noise. Finally, the enhanced multi-frame signals undergo range-velocity joint processing to construct a target range-velocity history map. By accumulating energy under different velocity assumptions, the energy of the moving target is superimposed and enhanced along its trajectory, appearing as a peak in the map, thus achieving weak target detection and parameter estimation.

[0039] Each stage of the processing has a clear physical basis: beamforming utilizes array directionality to obtain azimuth gain; narrowband inverse transform utilizes target Doppler consistency to focus energy in the time domain; spectral kurtosis utilizes the difference in statistical characteristics between the target and noise for discrimination enhancement; and multi-shot accumulation utilizes the correlation between target echoes and continuous pulses to improve the signal-to-noise ratio. These modules are interconnected and complementary, forming a complete weak signal enhancement and detection chain.

[0040] Specifically, the robust weak target detection system based on spectral kurtosis weighting, such as Figure 1 As shown, it includes: To address the problems of noise overload, multipath sidelobe leakage, and Doppler mismatch in high-speed targets in existing active sonar single-pulse processing, this invention proposes a multi-shot weak target detection system combining azimuth focusing narrowband inverse transform and spectral kurtosis weighting. The system establishes a joint processing flow of data preprocessing – adaptive frequency band extraction – spatial beam focusing – narrowband spectrum reconstruction – spectral kurtosis weight generation – nonlinear enhancement – ​​history map accumulation – peak detection. Through parameter adaptation and information feedback between modules, significant enhancement and robust detection of weak targets are achieved. Compared to the closest existing technology, this invention fully utilizes multi-shot coherent gain and higher-order statistical discrimination. Compared to traditional CBF methods that only utilize single-pulse spatial gain, this invention further introduces cross-pulse coherent superposition and spectral kurtosis filtering on the basis of spatial domain gain, resulting in a more thorough improvement in the signal-to-noise ratio and clutter suppression of the target signal. Compared to methods that directly use matched filtering or kurtosis threshold detection, this invention significantly improves the target signal dominance before detection through multi-stage processing, thus lowering the detection threshold and controlling the false alarm rate, enabling reliable detection of previously difficult-to-detect weak targets.

[0041] The data preprocessing module includes steps such as signal synchronization, filtering, and normalization. First, the raw echo data received by the multi-element array is synchronously sampled and time-stamped to ensure consistent start times for each channel and establish a unified time base reference. Then, basic preprocessing is performed: bandpass filtering is applied to remove noise interference outside the operating frequency band; the signal is down-converted to baseband and decimated and low-pass filtered to obtain an analytical signal; next, amplitude shaping is performed, such as removing DC components, suppressing pulse interference, and normalizing the amplitude to stabilize the signal's statistical characteristics. Finally, a short-time Fourier transform (STFT) is performed on the preprocessed data to obtain a time-frequency representation, providing a unified data format for subsequent processing. The preprocessing module outputs clean and standardized multi-channel or beam signals, laying the foundation for frequency band selection and subsequent accumulation processing.

[0042] The adaptive frequency band extraction module analyzes the preprocessed spectral data to select the optimal sub-band containing the target signal. Specific steps include: calculating the average power spectrum of the beam or channel signal; setting candidate sub-bands based on prior target information (e.g., the target's characteristic frequency range); evaluating the signal's robustness and interference level by calculating multi-frame energy stability and preliminary kurtosis indices within each candidate band, thereby determining whether the band contains the target signal; and adaptively selecting one or more narrow frequency bands as the focus bands for subsequent processing. By limiting the processing bandwidth, interference from irrelevant noise to subsequent processes can be reduced, highlighting the target's frequency domain range. This module essentially achieves frequency domain filtering gain: concentrating the target energy with a smaller bandwidth creates favorable conditions for subsequent narrowband inverse transform and coherent accumulation.

[0043] Beamforming and Narrowband Completion Inverse Transformation Module: The beamforming and narrowband completion inverse transformation module is used to first perform target azimuth focusing in the spatial domain after preprocessing multi-channel array data, then perform target subband extraction and completion in the frequency domain, and finally return to the time domain to form a narrowband echo sequence that can be coherently processed. The process includes: First, establishing a beam pointing angle grid covering the target azimuth range based on array geometric parameters, and calculating the corresponding beam steering vector for each candidate azimuth; then, performing delay alignment and weighted summation of each array element in the frequency domain according to the steering vector to obtain the conventional beam output for each azimuth, while reducing sidelobe levels through array element weighting (e.g., Chebyshev windowing) to suppress non-target azimuth interference; second, finding the main lobe direction with the highest energy among all candidate beam outputs and determining it as the focusing azimuth for subsequent processing, so that the target energy is concentrated in the spatial domain and the background variance is reduced; subsequently, calling the target sub-band [fa, fb] given by the previous adaptive frequency band extraction module, extracting the corresponding frequency interval on the spectrum of the main lobe beam, and separating the frequencies outside the interval. The components are zeroed out or interpolated with low values ​​to form a narrowband spectrum, thereby limiting the processing bandwidth and reducing irrelevant noise. Next, to meet the spectral integrity requirements of the inverse transform, the narrowband spectrum is padded with positive and negative frequencies. In particular, for real signals, a conjugate symmetric spectrum needs to be constructed to avoid IFFT distortion. Then, a discrete inverse Fourier transform is performed on the padded narrowband spectrum to obtain a time-domain narrowband echo sequence. This result is equivalent to applying a bandpass filter to the focused beam and concentrating the energy in the target frequency band into the time domain. Finally, since the narrowband reconstruction manifests the frequency shift caused by Doppler as a relative time shift in the time domain, it makes it easier to align multiple echo frames under a unified frequency band and a unified reference, thereby significantly improving the instantaneous signal-to-noise ratio and phase consistency of the output signal and providing a stable input for subsequent coherent accumulation and detection decision.

[0044] Spectral kurtosis calculation and weight generation module: Based on multi-fast spectral matrix, a frequency domain weight mask is generated. The process includes calculating spectral kurtosis (sliding window / median robust) from multi-fast spectral matrix, spectral kurtosis weight normalization and noise spectral density gain are generated in parallel, and the two are fused and amplified to obtain the final frequency domain weight mask. First, the narrowband time-domain signal is segmented into snapshots and windowed. Then, an FFT is performed on each snapshot to obtain the amplitude spectrum, thus forming a multi-snapshot spectrum matrix organized according to "snapshot-frequency point". Next, the amplitude value sequence of multiple snapshots is collected at each frequency point. To enhance the robustness of kurtosis estimation, a sliding window method is used in the slow time dimension for statistics. That is, a fixed-length window is gradually slid across the snapshot sequence, and the local kurtosis of the frequency point is calculated in each window. Robust statistics are introduced during the calculation process to suppress the influence of abnormal snapshots. The median is used as the central quantity, and the abnormal amplitude is limited or truncated by combining the median absolute deviation, so that a small amount of burst noise does not dominate the fourth-order statistical results. Second, to achieve adaptive threshold control, the background kurtosis distribution is estimated using data without target frequency bands or non-main lobe azimuth, and the kurtosis decision threshold is determined accordingly. The purpose is to distinguish between "normal fluctuations in background noise" and "significant non-Gaussian bursts caused by suspected targets". This avoids misidentifying interference frequencies as target frequencies and reduces the risk of false alarms in subsequent weighted amplification. Subsequently, the robust kurtosis values ​​of each frequency point are normalized and mapped to spectral kurtosis weights between 0 and 1. Higher kurtosis indicates a more pronounced intermittent spike characteristic in multiple snapshots, with a weight closer to 1, while kurtosis close to the background level results in a weight close to 0. Simultaneously, the noise spectral density gain is calculated according to parallel branches and normalized to a continuous amplitude weight to characterize the energy confidence level of each frequency point, thus fusing it with the spectral kurtosis weights on the same dimension. Finally, the normalized spectral kurtosis weights and the normalized noise spectral density gain are fused and amplified, and necessary smoothing and clipping control are performed on the fusion result to output the final frequency domain weight mask. This mask is used to weight the spectrum frequency-by-frequency point to highlight the difference between "signal discontinuities and noise continuity," providing a basis for subsequent enhancement and detection.

[0045] Nonlinear Enhancement Module: This module combines spectral kurtosis weighting with traditional power gain to nonlinearly amplify the target spectrum. First, it calculates the continuous gain weight for each frequency point, for example, allocating amplitude gain based on the instantaneous signal-to-noise ratio according to the Wiener filtering principle: frequencies dominated by the target are assigned a gain close to 1, while frequencies dominated by noise are assigned a low gain, thus reducing the overall background noise variance from a power perspective. Then, the continuous gain is fused with the aforementioned kurtosis mask according to a multiplicative rule to obtain the fused weight. During fusion, a nonlinear exponential adjustment can be appropriately introduced so that when both weights are high, the output weight is closer to 1, and when either weight is low, the output is lower, achieving a "strong-strong combination" effect. Simultaneously, the fused weight is smoothed using a small window in the frequency domain and slow time to avoid inter-band discontinuities or time-domain ringing artifacts caused by sharp abrupt changes. The smoothed total weight mask is the final weight mask formed after frequency domain and slow-time small window smoothing and amplitude control, resulting from the fusion of spectral kurtosis weighting and traditional power gain. Finally, the smoothed total weight mask is applied to the original aligned spectrum (frequency-by-frequency multiplication) to obtain the enhanced spectrum. This module achieves nonlinear amplification of weak signals by fusing power estimation and high-order kurtosis discrimination: on the one hand, it ensures that strong target frequency components are preserved (avoiding over-filtering that damages the signal); on the other hand, it further enhances the frequencies of weak targets with high kurtosis, thereby greatly improving the contrast between the target and the background. Compared with traditional linear filtering or binary thresholding methods, the continuous-value nonlinear enhancement of this invention can finely balance noise suppression and target signal preservation, improving the robustness of weak target detection.

[0046] The range-velocity history map construction module aligns and accumulates the data from the multi-shot enhancement output according to different assumed velocities (Doppler) to form a two-dimensional range-velocity history map. The multi-shot enhancement output data is the enhancement result output by the nonlinear enhancement module, preferably a range-domain echo energy sequence obtained by inverse transform / envelope extraction of the aligned multi-shot enhancement spectrum sequence. Specifically, for each transmit / receive snapshot, the target echo after the above enhancement processing is obtained (usually represented as an energy distribution on a series of range cells). The enhanced target echo refers to the aforementioned range-domain echo energy sequence, which is represented as an energy distribution on the range cells and used for subsequent range migration correction and accumulation according to the assumed velocity. This module assumes a set of target radial velocity values. For each assumed velocity, it calculates the target's range migration between adjacent snapshots (estimated based on Doppler or a known transmission period), and then performs corresponding range correction and translation on the echo energy of all snapshots: aligning and superimposing the energy at different times according to the assumed velocity. In this way, a comprehensive echo intensity sequence is obtained by accumulating data for each assumed velocity. By using velocity as the vertical axis and distance as the horizontal axis, a two-dimensional "distance-velocity" energy distribution map can be constructed. In this history map, if a target is moving at the assumed velocity, its echo energy will accumulate along the corresponding velocity trajectory due to correct alignment, forming a continuous high-intensity peak trajectory. Conversely, clutter and noise, lacking a unified motion pattern, will cancel each other out or be evenly distributed during the accumulation process, exhibiting a low-amplitude, disordered distribution. Therefore, the distance-velocity history map can further enhance the signal dominance of moving targets while providing a basis for estimating target velocity.

[0047] Peak Detection Result Output Module: This module performs detection and judgment on the range-velocity history map and outputs target information. First, it performs Constant False Alarm Rate (CFAR) detection on the history map, filtering out significant peak points or continuous peak trajectories as candidate targets. Then, it extracts parameter information for each candidate target across multiple consecutive frames, including the corresponding range cell, velocity value, and the intensity of the peak in the cumulative map. Specifically, it first performs connected component clustering on the CFAR detection points in the range-velocity plane according to a preset neighborhood, merging spatially adjacent peak points into the same candidate target region and selecting the largest point within the region as the representative peak. Next, it performs gating matching and continuous hit statistics on this representative peak between adjacent snapshot / sliding cumulative windows. Peaks meeting the consecutive hit count (or hit ratio within K frames) threshold are retained; otherwise, they are judged as isolated noise peaks and removed, thus eliminating isolated noise peaks and false alarms. Finally, it outputs a confirmed target list, including the target's spatial orientation (determined by the beam pointing angle), range and velocity estimates, and confidence indices (such as detection statistics, signal-to-noise ratio gain, etc.). Furthermore, this module can feed back target detection results and statistical information to the preceding processing stage for adaptive adjustment of certain parameters (such as updating the detection threshold and optimizing the weight fusion coefficients), forming a closed-loop optimization mechanism. Through the above steps, this invention successfully transforms the "enhanced signal features" into usable target detection results, significantly reducing the false alarm rate while achieving reliable detection and parameter estimation of weak targets.

[0048] like Figure 9a and Figure 9d As shown, Figure 9a and Figure 9b To simulate the target extraction of high-speed small targets, a comparison is made between the traditional CBF method and the enhanced method described in this invention. Figure 9c and Figure 9d To test the target extraction of high-speed small targets, a comparison was made between the traditional CBF method and the enhanced method described in this invention.

[0049] This embodiment achieves layer-by-layer enhancement and robust multi-shot detection of echo signals from weak targets. From data preprocessing to result output, the modules are closely integrated, making full use of spatial domain gain, frequency domain focusing, and slow-time coherence to significantly improve the signal-to-noise ratio and detectability of weak targets. In complex marine environments, this method can reliably detect previously difficult-to-detect underwater weak targets with a low false alarm rate and provide estimates of their distance and velocity, meeting the requirements of practical sonar detection.

[0050] Those skilled in the art will understand that, in addition to implementing the system, apparatus, and their modules provided by this invention in purely computer-readable program code, the same program can be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system, apparatus, and their modules provided by this invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; alternatively, modules for implementing various functions can be considered both software programs implementing the method and structures within the hardware component.

[0051] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A robust weak target detection method based on spectral kurtosis weighting, characterized in that, include: Step S1: Obtain the raw data of the multi-channel array, and use the data preprocessing module to preprocess the obtained raw data of the multi-channel array to obtain the preprocessed multi-channel array data; Step S2: Perform spectrum analysis on the preprocessed multi-channel array data using the adaptive frequency band extraction module to select the target sub-frequency band containing the target signal; Step S3: The preprocessed multi-channel array data is first focused on the target azimuth in the spatial domain by the beamforming and narrowband completion inverse transform module, and then the target sub-band is extracted and completed in the frequency domain. Finally, it is returned to the time domain to form a narrowband echo sequence that can be coherently processed. Step S4: For the narrowband echo sequence that can be coherently processed back to the time domain, a frequency domain weight mask is generated based on the multi-fast-shot spectral matrix through the spectral kurtosis calculation and weight generation module; Step S5: Combine the frequency domain weight mask with the power gain through the nonlinear enhancement module to obtain the comprehensive weight mask, and use the comprehensive weight mask to perform nonlinear amplification processing on the target spectrum to obtain the multi-shot enhanced output data; Step S6: The distance-velocity history graph construction module aligns and accumulates the data from the multi-shot enhancement output according to different assumed velocities to form a two-dimensional distance-velocity history graph; Step S7: Detect and determine the distance-velocity two-dimensional history graph through the peak detection and result output module and output the target information.

2. The robust weak target detection method based on spectral kurtosis weighting according to claim 1, characterized in that, Step S1 includes: Step S1.1: Synchronously sample and time-stamp the acquired multi-channel array raw echo data to ensure that the start time of each channel is consistent and to establish a unified time base reference; Step S1.2: Bandpass filtering is performed on the noise interference outside the working frequency band in the acquired multi-channel array raw echo data. At the same time, DC component removal and pulse interference suppression are performed to obtain filtered and shaped multi-channel array echo data. Step S1.3: Downconvert the filtered and shaped multi-channel array echo data to baseband, and perform decimation and low-pass filtering to obtain the analytical signal; Step S1.4: Perform amplitude shaping on the analytical signal, control the dynamic range of the analytical signal to prevent signal amplitude overflow, and obtain the amplitude-shaped analytical signal; Step S1.5: Perform a short-time Fourier transform on the amplitude-shaped analytical signal to obtain a time-frequency representation of the signal, forming a unified data format.

3. The robust weak target detection method based on spectral kurtosis weighting according to claim 1, characterized in that, Step S2 includes: Step S2.1: Calculate the average power spectrum of the beam or channel signal based on the preprocessed multi-channel array data, and then set candidate sub-bands in combination with prior target information; Step S2.2: Calculate the multi-frame energy stability and preliminary kurtosis index within each candidate sub-band. Based on the calculated multi-frame energy stability and preliminary kurtosis index within each candidate sub-band, evaluate whether the robustness of the signal and the interference level meet the preset requirements, and then determine whether the candidate sub-band contains the target signal. Step S2.3: Adaptively select one or more narrow frequency bands as key frequency bands based on the candidate sub-bands containing the target signal, and use the current key frequency band as the target sub-band containing the target signal.

4. The robust weak target detection method based on spectral kurtosis weighting according to claim 1, characterized in that, Step S3 includes: Step S3.1: Establish a beam pointing angle grid covering the mission azimuth range based on the array geometry parameters, and calculate the corresponding beam steering vector for each candidate azimuth. Step S3.2: Perform delay alignment and weighted summation of each array element in the frequency domain according to the steering vector to obtain the beam output in each direction. At the same time, reduce the sidelobe level by weighting the array elements to suppress non-target azimuth interference. Step S3.3: Find the direction of the main lobe with the highest energy among all candidate beam outputs, and determine it as the focusing azimuth for subsequent processing, so that the target energy is concentrated in the spatial domain and the background variance is reduced; Step S3.4: Call the target sub-band, extract the corresponding frequency range on the spectrum of the main lobe beam, and set the frequency components outside the range to zero or interpolate with low values ​​to form a narrowband spectrum; Step S3.5: To meet the spectral integrity requirements of the inverse transform, the narrowband spectrum is padded with positive and negative frequencies, including: constructing a conjugate symmetric spectrum for the real signal to avoid IFFT distortion; Step S3.6: Perform discrete inverse Fourier transform on the completed narrowband spectrum to obtain the time-domain narrowband echo sequence. This result is equivalent to applying bandpass filtering to the focused beam and concentrating the energy in the target frequency band into the time domain.

5. The robust weak target detection method based on spectral kurtosis weighting according to claim 1, characterized in that, Step S4 includes: Step S4.1: Perform snapshot segmentation and windowing on the time-domain narrowband echo sequence, and then perform FFT on each snapshot to obtain the amplitude spectrum, thereby forming a multi-snapshot spectrum matrix organized according to snapshot-frequency point; Step S4.2: Collect multiple snapshot amplitude value sequences at each frequency point; Step S4.3: Based on the amplitude value sequence of multiple snapshots collected, estimate the background kurtosis distribution using data corresponding to non-target frequency bands or non-main lobe azimuths, and determine the kurtosis decision threshold accordingly. Step S4.4: Based on the multi-shot spectral matrix, obtain the robust kurtosis value of each frequency point according to the kurtosis decision threshold. Normalize the obtained robust kurtosis value of each frequency point and map it to a spectral kurtosis weight between 0 and 1. The higher the kurtosis, the more obvious the intermittent peak characteristics of the frequency point in the multi-shot, and the closer the weight is to 1. When the kurtosis is close to the background level, the weight approaches 0. At the same time, calculate the noise spectral density gain according to the parallel branch and normalize it to a continuous amplitude weight to characterize the confidence level of each frequency point in terms of energy. Step S4.5: Fuse and amplify the normalized spectral kurtosis weights and the normalized noise spectral density gain, and perform smoothing and clipping control on the fusion result to output the final frequency domain weight mask.

6. The robust weak target detection method based on spectral kurtosis weighting according to claim 1, characterized in that, Step S5 includes: Step S5.1: Multiply the obtained frequency domain weight mask with the noise density matrix gain and spectrum point by point to obtain the initial weighted spectrum; Step S5.2: For the initial weighted spectrum, perform small-window smoothing on the fusion weights in both the frequency domain and slow time. The frequency domain smoothing operator is denoted as... H f The slow-time smoothing operator is denoted as H s The weights are obtained after one smoothing process, where the small window smoothing is achieved using a sliding weighted average. Step S5.3: Introduce nonlinear parameters to the obtained frequency domain weight mask. α Exponential modulation is performed to obtain exponential weights, wherein the exponential modulation is used to adjust the contrast of the weight differences. Then, the exponential weights are fused with the obtained first-smoothed weights according to the multiplicative rule to generate fused weights, and the fused weights are used to amplify and enhance the spectrum. Step S5.4: Continue to perform small window smoothing on the above intermediate results in the frequency domain and slow time dimension to obtain the intermediate spectrum results after secondary smoothing; Step S5.5: Calculate the local signal-to-noise ratio statistic and spectral kurtosis statistic, and adaptively update the weights after secondary smoothing to obtain the final weights. Apply the final weights to the corresponding spectrum of the preprocessed multi-channel array data to obtain the enhanced spectrum.

7. The robust weak target detection method based on spectral kurtosis weighting according to claim 1, characterized in that, Step S6 includes: assuming a set of target radial velocity values, calculating the distance migration of the target between adjacent snapshots for each assumed velocity, and performing corresponding distance correction and translation on the enhanced spectrum of all snapshots, including: aligning and superimposing the enhanced spectrum at different times according to the assumed velocity; accumulating a comprehensive echo intensity sequence for each assumed velocity; and constructing a two-dimensional range-velocity energy distribution map by using velocity as the vertical axis and distance as the horizontal axis.

8. The robust weak target detection method based on spectral kurtosis weighting according to claim 1, characterized in that, Step S7 includes: Step S7.1: Perform constant false alarm detection on the distance-velocity two-dimensional history graph and select significant peak points or continuous peak trajectories that meet the preset requirements as candidate targets; Step S7.2: Extract parameter information for each candidate target in multiple consecutive frames, including the corresponding range cell, velocity value, and the intensity of the peak value in the cumulative image.

9. The robust weak target detection method based on spectral kurtosis weighting according to claim 8, characterized in that, Step S7.1 includes: clustering CFAR detection points in the distance-velocity plane according to a preset neighborhood, merging spatially adjacent peak points into the same candidate target region and selecting the largest point in the region as the representative peak; then performing gating matching and continuous hit statistics on the representative peak between adjacent snapshot / sliding accumulation windows, retaining those that meet the continuous hit threshold, otherwise judging them as isolated noise peaks and removing them, thereby removing isolated noise peaks and false alarms.

10. A robust weak target detection system based on spectral kurtosis weighting, characterized in that, include: The data preprocessing module is used to acquire the raw data of the multi-channel array and preprocess the acquired raw data of the multi-channel array to obtain the preprocessed multi-channel array data. The adaptive frequency band extraction module is used to perform spectral analysis on the preprocessed multi-channel array data and select the target sub-frequency band containing the target signal; The beamforming and narrowband completion inverse transform module is used to first perform target azimuth focusing in the spatial domain, then perform target sub-band extraction and completion in the frequency domain, and finally return to the time domain to form a narrowband echo sequence that can be coherently processed. The spectral kurtosis calculation and weight generation module is used to generate a frequency domain weight mask based on a multi-fast-shot spectral matrix for narrowband echo sequences that can be coherently processed back to the time domain. The nonlinear enhancement module is used to combine the frequency domain weight mask with the power gain to obtain a comprehensive weight mask. The comprehensive weight mask is then used to perform nonlinear amplification of the target spectrum to obtain multi-shot enhanced output data. The distance-velocity history graph construction module is used to align and accumulate data from multiple snapshots of enhanced output according to different assumed velocities to form a two-dimensional distance-velocity history graph. The peak detection and result output module is used to detect and determine the target information from the distance-velocity two-dimensional history graph.

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