Low slow small target micro-motion feature extraction method based on GST-WT combination

Abstract

The invention discloses a low-slow-small target micro-motion feature extraction method based on a GST-WT combination, and relates to the field of low-slow-small target micro-motion feature extraction, and the method comprises the steps: obtaining a multi-band radar echo signal, carrying out the preprocessing of the multi-band radar echo signal, carrying out the time-frequency analysis of the preprocessed signal through a GST-WT combination model, and carrying out the extraction of the micro-motion feature of a low-slow-small target. Obtaining time-frequency characteristics of improved generalized S transform and Morlet wavelet transform; carrying out linear interpolation on the time-frequency characteristics of the improved generalized S transform; fusing the time-frequency features by adopting a linear weighting strategy to obtain fused time-frequency features; the feature extraction effect is quantitatively evaluated in combination with the energy entropy and the energy concentration degree index, the advantages of GST global time-frequency analysis and WT local self-adaption are fully played, the micro-motion features of the target are effectively separated and accurately extracted, the time-frequency resolution, the anti-noise capability and the feature stability are improved, and the target tracking accuracy is improved. Technical support is provided for low-altitude, slow and small target detection in scenes of low-altitude security and protection, unmanned aerial vehicle supervision and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of micro-motion feature extraction for low, slow and small targets, and in particular to a method for extracting micro-motion features of low, slow and small targets based on the GST-WT combination. Background Art

[0002] Due to their characteristics of low-altitude flight, slow speed, and small radar cross-section, low, slow and small targets have important application values in many fields. In the civilian field, they have been widely used in multiple scenarios such as logistics distribution, film shooting, environmental monitoring, and agricultural plant protection; in the military field, they undertake important tasks such as reconnaissance and surveillance, electronic warfare execution, and target drone training. Micro-motion feature extraction, as the core technology of radar signal processing, mainly aims to accurately extract the tiny but distinguishable dynamic information of the target from complex radar echo signals. Such features are crucial for the recognition of low-altitude, slow-speed small targets and the analysis of target behaviors in remote sensing scenarios. By accurately extracting micro-motion features, not only can the motion laws of the target be deeply revealed, but also the detection sensitivity and anti-interference ability of the radar system can be improved, and at the same time, its data analysis ability in complex environments can be enhanced, such as achieving multi-target tracking in urban airspace. However, in practical applications, this technology still faces many challenges, such as the interference of complex background noise to weak signals, the decrease in feature distinguishability caused by low Doppler frequency shift, and the limitations of traditional algorithms in processing unstable and multi-band signals.

[0003] In recent years, scholars at home and abroad have devoted a lot of energy to researching the field of target micro-motion feature extraction and achieved remarkable results. Commonly used algorithms include Multiscale Analysis (MA), Generalized S Transform (GST), Wavelet Transform (WT), adaptive feature extraction algorithms, and the combination of Hilbert transform and time-frequency analysis technology. An algorithm that fuses singular value decomposition and WT in the prior art extracts the micro-motion features of the signal by analyzing Energy Entropy (EE) and Energy Concentration (EC). Another piece of prior art achieves frequency correction through an improved GST algorithm, thereby processing the micro-motion features with a wider width. Although the GST algorithm can conduct a comprehensive analysis in the time and frequency dimensions, providing a solid foundation for subsequent feature extraction, it still has insufficient adaptability in processing non-stationary signals and is difficult to flexibly adjust the analysis window according to signal characteristics, resulting in inaccurate capture of local features of the signal. While the WT algorithm can flexibly adjust the size of the time-frequency window by introducing a scale factor, its computational complexity is relatively high, and it requires a large amount of computing resources and time when processing large-scale data.

[0004] Therefore, a micro-motion feature extraction method for low, slow, and small targets based on the GST-WT combination is provided to solve the above problems. Summary of the Invention

[0005] To solve the above problems, the present invention provides a micro-motion feature extraction method for low, slow, and small targets based on the GST-WT combination. By fusing the global time-frequency analysis of the generalized S-transform and the local adaptability of the wavelet transform, the advantages of the GST global time-frequency analysis and the WT local adaptability are fully utilized, achieving double optimization in time-frequency resolution and feature stability, and significantly improving in terms of time-frequency resolution, noise resistance, and feature stability, providing technical support for the accurate identification of low, slow, and small targets.

[0006] To achieve the above object, the present invention provides a micro-motion feature extraction method for low, slow, and small targets based on the GST-WT combination, including the following steps: S1: Obtain multi-band radar echo signals, and preprocess the multi-band radar echo signals, including positive frequency band extraction, DC removal, effective frequency band interception, and signal trend item elimination; S2: Based on the preprocessed signals, perform time-frequency analysis using the GST-WT combination model to obtain the time-frequency features of the improved generalized S-transform and the time-frequency features of the Morlet wavelet transform; the GST-WT combination model includes the improved generalized S-transform and the Morlet wavelet transform; S3: Perform linear interpolation on the time-frequency features of the improved generalized S-transform to obtain the time-frequency features of the improved generalized S-transform after linear interpolation; S4: Based on the time-frequency features of the Morlet wavelet transform and the time-frequency features of the improved generalized S-transform after linear interpolation, adopt a linear weighting strategy for fusion to obtain the fused time-frequency features; S5: Calculate the energy entropy and energy concentration of the fused time-frequency features based on the fused time-frequency features; S6: Determine whether the energy entropy and energy concentration in S5 meet the expected values; if they meet the expected values, output the current fused time-frequency features, and if they do not meet the expected values, adjust the parameters of the GST-WT combination model and continue to execute S2-S5.

[0007] Preferably, the signal after positive frequency band extraction in S1 is expressed as: ; where is the original signal, is the number of range cells, is the time domain index.

[0008] Preferably, the signal after DC removal in S1 Expressed as: ; Wherein, is the frequency-domain index, is the Hamming window function.

[0009] Preferably, the specific steps for intercepting the effective frequency band in S1 include the following: According to the target distance Calculate the corresponding frequency point: ; Wherein, is the minimum frequency point, is the maximum frequency point, is the minimum distance, is the maximum distance, is the speed of light, is the modulation bandwidth of the radar signal, is the pulse repetition frequency, is the number of points of the fast Fourier transform (FFT), is the sampling frequency; Intercept the effective frequency band signal , wherein, .

[0010] Preferably, the sliding average method is used to eliminate the signal trend term in S1, which is specifically expressed as: ; Wherein, is the detrended signal.

[0011] Preferably, the time-frequency characteristics of the Morlet wavelet transform in S2 are expressed as: ; Wherein, is the mother wavelet, is the angular frequency, is the scale parameter, is the translation parameter, is conjugate function of.

[0012] Preferably, the time-frequency characteristics of the improved generalized S transform in S2 are expressed as: ; Wherein, is the base frequency, is the translation coefficient, is the continuous signal, is the exponential part, is the imaginary unit.

[0013] Preferably, the time-frequency result after linear interpolation of the time-frequency characteristics of the improved generalized S transform in S3 is expressed as: ; wherein, is the time-frequency characteristic obtained by the improved generalized S transform, is the integer function, is the frequency, is the time, is a custom function or operator, representing the linear interpolation operation on the time-frequency characteristic.

[0014] Preferably, the fused time-frequency characteristic in S4 is expressed as: ; wherein, , are the weighting coefficients, is the time-frequency characteristic after the Morlet wavelet transform.

[0015] Preferably, the energy entropy in S5 is expressed as: ; The energy concentration is expressed as: ; wherein, is the total number of time samples of the signal, is the normalized energy distribution probability, is the maximum value of the instantaneous energy of the signal, is the total energy of the signal.

[0016] Therefore, the present invention adopts the above-mentioned method for extracting the micro-motion characteristics of low, slow and small targets based on the GST-WT combination. By preprocessing the multi-band radar echo signal, the DC component is removed, the effective frequency band is intercepted and the signal trend item is eliminated to improve the signal quality; then, the GST-WT combination model is used to perform time-frequency analysis on the signal, and the time-frequency characteristics of the signal are obtained by the collaborative work of the improved generalized S transform and the wavelet transform; the linear interpolation is performed on the result of the generalized S transform to make its frequency axis consistent with the wavelet transform, and the linear weighting strategy is adopted to fuse the time-frequency characteristics; finally, the multi-index quantization evaluation of the feature extraction result is carried out by combining the energy entropy and the energy concentration. The advantages of the GST global time-frequency analysis and the WT local adaptability are fully exerted, the micro-motion characteristics of the target are effectively separated and accurately extracted, providing a certain technical support for the detection of low, slow and small targets.

[0017] Next, through the drawings and embodiments, the technical solutions of the present invention will be further described in detail. Description of the Drawings

[0018] Figure 1 It is a schematic flowchart of the method for extracting the micro-motion features of low, slow, and small targets based on the GST-WT combination in the present invention; Figure 2 It is a schematic flowchart of the GST-WT feature extraction process in an embodiment of the present invention; Figure 3 It is a data processing diagram in an embodiment of the present invention; among them, (a) is the data processing diagram of DJI Mavic 2; (b) is the data processing diagram of DJI Phantom; (c) is the data processing diagram of DJI M350; (d) is the data processing diagram of DJI Inspire 2; Figure 4 It is the GST energy distribution diagram in an embodiment of the present invention; among them, (a) is the GST energy distribution diagram of DJI Mavic 2; (b) is the GST energy distribution diagram of DJI Phantom; (c) is the GST energy distribution diagram of DJI M350; (d) is the GST energy distribution diagram of DJI Inspire 2; Figure 5 It is the WT energy distribution diagram in an embodiment of the present invention; among them, (a) is the WT energy distribution diagram of DJI Mavic 2; (b) is the WT energy distribution diagram of DJI Phantom; (c) is the WT energy distribution diagram of DJI M350; (d) is the WT energy distribution diagram of DJI Inspire 2; Figure 6 It is the GST-WT energy distribution diagram in an embodiment of the present invention; among them, (a) is the GST-WT energy distribution diagram of DJI Mavic 2; (b) is the GST-WT energy distribution diagram of DJI Phantom; (c) is the GST-WT energy distribution diagram of DJI M350; (d) is the GST-WT energy distribution diagram of DJI Inspire 2. Detailed implementation manners

[0019] The technical solutions of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0020] Unless otherwise defined, the technical terms or scientific terms used in the present invention shall have the ordinary meanings understood by those of ordinary skill in the field to which the present invention belongs.

[0021] In the present invention, words such as "including" or "comprising" mean that the elements before this word cover the elements listed after this word, and do not exclude the possibility of also covering other elements. The orientation or positional relationship indicated by terms such as "inside", "outside", "above", "below", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation of the present invention. When the absolute position of the object being described changes, the relative positional relationship may also change accordingly. In the present invention, unless otherwise clearly specified and defined, terms such as "attachment" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or integrated; it can be directly connected, or indirectly connected through an intermediate medium, and can be the communication inside two elements or the interaction relationship between two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0022] Embodiment A method for extracting micro-motion features of low, slow and small targets based on the GST-WT combination, as Figure 1 - Figure 2 shown, includes the following steps: S1: Obtain multi-band radar echo signals, and preprocess the multi-band radar echo signals, including positive frequency band extraction, DC removal processing, intercepting the effective frequency band, and eliminating the signal trend term; Preprocess the multi-band radar echo signals. Use the Hamming window function for positive frequency band extraction, and then remove the DC component in the signal through DC removal processing. Calculate the corresponding frequency points according to the target distance, intercept the effective frequency band signals, and then use the moving average method to eliminate the signal trend term to reduce the influence of interference on subsequent analysis.

[0023] First, perform positive frequency band extraction and DC removal processing on the multi-band radar echo data: ; ; Among them, is the Hamming window function, is the number of range cells, is the frequency domain index, is the time domain index, is the signal after positive frequency band extraction, is the signal after DC removal processing, is the original signal.

[0024] According to the target distance calculate the corresponding frequency points: ; Among them, is the minimum frequency point, is the maximum frequency point, is the minimum distance, is the maximum distance, represents the speed of light, is the modulation bandwidth of the radar signal, is the pulse repetition frequency, is the number of points of the fast Fourier transform (FFT), sampling frequency.

[0025] Intercept the signal in the effective frequency band , , and use the moving average method to eliminate the signal trend term: ; wherein, is the detrended signal.

[0026] S2: Based on the preprocessed signal, use the GST-WT combined model for time-frequency analysis to obtain the time-frequency characteristics of the improved generalized S transform and the time-frequency characteristics of the Morlet wavelet transform; the GST-WT combined model includes the improved generalized S transform and the Morlet wavelet transform; Generalized S transform method: The generalized S transform is an algorithm that is efficient, fast, and easy to understand in signal processing and can be widely used. Its basic definition formula is: ; wherein, is the continuous signal, is the Gaussian window function, is the base frequency, is the translation coefficient.

[0027] The Gaussian window function is defined as: ; where the standard deviation is the reciprocal of the base frequency and is also called the dilation coefficient.

[0028] Substituting the Gaussian window function into the basic definition formula of the generalized S transform, the specific expression of the S transform of can be obtained as: ; wherein, is the exponential part.

[0029] Adjust the Gaussian window function to improve its width and frequency so that they are not exactly opposite, and the generalized S transform can be obtained as: ; Among them, the window function has a frequency dimension determined by the parameter and is the improved generalized Gaussian window function.

[0030] To ensure the invertibility of the S transform, it is necessary to satisfy: ; In the S transform, the modulating function mother wavelet of the Gaussian window function is: ; Among them, is the complex exponential function, which determines the window shape.

[0031] It can be seen that the time-frequency spectrum of the S transform is gradually integrated along the time axis, and its inverse transform form can be realized: ; Among them, is the continuous signal of the S transform.

[0032] The time-frequency characteristics of the improved generalized S transform in this application are expressed as: ; Among them, is the base frequency, is the translation coefficient, is the continuous signal, is the exponential part, is the imaginary unit.

[0033] Wavelet transform is a very important tool in signal and image processing. It can analyze data simultaneously in the time domain and the frequency domain, so as to capture the local information of the data. Let represent a two-dimensional signal, then the two-dimensional continuous wavelet transform can be defined as: ; Among them, are its abscissa and ordinate respectively, represents the two-dimensional basic wavelet, is the scale stretching and two-dimensional displacement of, then: ; Among them, is the wavelet transform coefficient, which provides the local information of the signal at different scales and positions, is the scale factor, is the translation parameter.

[0034] The corresponding inverse wavelet transform of the above formula is as follows: ; wherein, , is the Fourier transform of , and is the corresponding circular frequency. The scale factor reflects the spatial scale of the phenomenon, and the translation parameter reflects the plane position of the phenomenon. The principle is the correspondence between frequency and time-domain analysis.

[0035] The wavelet transform organically combines the time domain and frequency domain of the signal. From the perspective of filtering, the wavelet transform of the signal is to let the signal pass through a band-pass filter bank. Due to the introduction of the scale factor , while covering the entire time domain through the translation of the parameter , the time-frequency window changes adaptively with the speed of the signal to be analyzed; when extracting the information of high-frequency fast-changing components, the time-frequency window should be as narrow as possible, while allowing the frequency-domain window to be appropriately widened. When extracting low-frequency slow-changing signals, the frequency window should be appropriately widened, and the frequency window is correspondingly reduced to ensure a higher frequency resolution and achieve the feature extraction of the target signal.

[0036] The time-frequency characteristics of the Morlet wavelet transform in this application are expressed as: ; wherein, is the mother wavelet, is the angular frequency, is the scale parameter, is the translation parameter, is conjugate function of.

[0037] S3: Perform linear interpolation on the time-frequency characteristics of the improved generalized S transform to obtain the time-frequency characteristics of the improved generalized S transform after linear interpolation; Perform linear interpolation on the generalized S transform, adjust the frequency axis of the generalized S transform to make its frequency axis consistent with the wavelet transform to prepare for subsequent data fusion, and ensure that the results of the two transforms can be effectively combined in the frequency dimension.

[0038] The time-frequency result after linear interpolation of the time-frequency characteristics of the improved generalized S transform is expressed as: ; wherein, is the time-frequency characteristic obtained by the improved generalized S transform, is the integer function, is the frequency, is time, is a custom function or operator, representing a linear interpolation operation on time-frequency features.

[0039] S4: Based on the time-frequency features of the Morlet wavelet transform and the time-frequency features of the improved generalized S-transform after linear interpolation, a linear weighting strategy is adopted for fusion to obtain the fused time-frequency features; Adopt a linear weighting strategy to fuse time-frequency features. Set the weighting coefficient , and fuse the time-frequency features of the wavelet transform and the generalized S-transform after linear interpolation to obtain comprehensive time-frequency features.

[0040] The fused time-frequency features are expressed as: ; where , are the weighting coefficients, , in this application, can be taken, is the time-frequency feature after the Morlet wavelet transform.

[0041] S5: Calculate the energy entropy and energy concentration of the fused time-frequency features based on the fused time-frequency features; use the energy entropy (Energy Entropy, EE) and energy concentration (Energy Concentration, EC) as evaluation indicators to evaluate the feature extraction effect. Calculate the energy entropy EE and energy concentration EC of the fused time-frequency features, and compare the values of the energy entropy EE and energy concentration EC on different targets to judge the quality of the current feature extraction result.

[0042] The energy entropy is expressed as: ; The energy concentration is expressed as: ; where is the total number of time samples of the signal, is the normalized energy distribution probability, is the maximum value of the instantaneous energy of the signal, is the total energy of the signal.

[0043] S6: Judge whether the energy entropy and energy concentration in S5 meet the expected values; if they meet the expected values, output the current fused time-frequency features, if they do not meet the expected values, adjust the parameters of the GST-WT combined model, and continue to execute S2-S5 until the feature extraction effect meets the expected requirements.

[0044] The parameters of the GST-WT combined model specifically include the scale parameter of the Morlet wavelet and the Gaussian window parameter of the improved generalized S transform.

[0045] Example 1 To fully analyze the actual effect of the micro-motion feature extraction method proposed in this example, a low, slow, and small target detection dataset published in Radar Science and Technology was used. Target data with a modulation bandwidth of 100 MHz and a fixed modulation period of 0.3 ms in the Ku+L band was used for simulation analysis. There are 5 types of low, slow, and small targets in this dataset, including DJI Mavic 2, DJI Phantom, DJI M350, DJI Inspire 2, and DJI M600. Considering that the rotor characteristics of DJI series drones are basically the same, in order to provide some reference for the tracking research of drone targets by multi-band radars, the detection data of DJI Mavic 2, DJI Phantom, DJI M350, and DJI Inspire 2 were randomly selected for simulation experiments in this example. The relevant information of the selected low, slow, and small targets is shown in Table 1.

[0046] Table 1 Relevant information of the selected low, slow, and small targets ;

[0047] These four types of low, slow, and small targets are highly used, and the detected radar echo data is clear and complete, with sufficient representativeness. The data waveforms after DC removal and range preprocessing are as Figure 3 shown.

[0048] The results of processing the data of the four types of low, slow, and small targets with the GST model, WT model, and GST-WT combined model are as Figure 4 - Figure 6 shown.

[0049] Figure 4 The GST energy distribution of the four types of low, slow, and small targets, namely DJI Mavic 2, DJI Phantom, DJI M350, and DJI Inspire 2, is given. For DJI Mavic 2, the energy is relatively concentrated between frequencies of 0.5×10 5 ~1.5×10 5 Hz and times of 0~2×10 4 s, indicating that the important micro-motion feature information is contained in this frequency band and time period; for DJI Phantom, the energy is concentrated and relatively compact between 0.5×10 5 ~1.5×10 5 Hz, meaning that its micro-motion features are prominent in this relatively narrow frequency range; for DJI M350, there are multiple energy concentration regions and a wide distribution between 0.5×10 5 ~1.8×10 5 Hz, indicating that there are multiple frequency components of micro-motion features with different intensities; for DJI Inspire 2, between 0.5×10 5 ~1.1×10 5There is a specific concentrated frequency band between [frequency value] Hz, reflecting its unique micro-vibration characteristic frequency characteristics.

[0050] Figure 5 The WT energy distribution of four low, slow, and small targets, namely DJI Mavic 2, DJI Phantom, DJI M350, and DJI Inspire 2, is given. For DJI Mavic 2, there is a relatively concentrated energy area when the frequency is approximately in the range of 0.5×10 5 ~2.5×10 5 Hz and the time is from 0 to 0.8 s, indicating that it contains key micro-vibration characteristics within this frequency and time range; for DJI Phantom, the energy concentration trend is relatively obvious and the concentrated area is relatively compact when the frequency is 0.5×10 5 ~2.5×10 5 Hz and the time is from 0 to 1 s, showing that its micro-vibration characteristics are prominent in this frequency and time interval; for DJI M350, there are multiple energy concentrated areas with a relatively wide distribution range when the frequency is 0.5×10 5 ~2×10 5 Hz and the time is from 0 to 1.5 s, meaning it has multiple micro-vibration characteristic frequency components with different intensities; for DJI Inspire 2, there is a specific energy concentrated frequency band when the frequency is 0.5×10 5 ~3×10 5 Hz and the time is from 0 to 0.8 s, reflecting its unique micro-vibration characteristic frequency characteristics.

[0051] Figure 6 The energy distribution of four low, slow, and small targets, namely DJI Mavic 2, DJI Phantom, DJI M350, and DJI Inspire 2, after GST-WT fusion transformation is given. For DJI Mavic 2, the energy shows a concentrated trend when the frequency is from 1×10 5 Hz to 3×10 5 Hz and the time is from 0 to 2×10 -4 s, indicating that important micro-vibration characteristics are included within this frequency and time period; for DJI Phantom, the energy concentration trend is significant and the concentrated area is relatively concentrated when the frequency is from 1×10 5 Hz to 4×10 5 Hz and the time is from 0 to 1×10 -4 s, showing that its micro-vibration characteristics are obvious in this area; for DJI M350, there are multiple energy concentrated areas with a relatively wide distribution when the frequency is from 1.5×10 5 Hz to 3.5×10 5 Hz and the time is from 0 to 1×10 -4 s, meaning it has multiple micro-vibration characteristic frequency components with different intensities; for DJI Inspire 2, the energy shows a concentrated trend when the frequency is from 1×10 5 Hz to 3×10 5 Hz and the time is from 0 to 1×10 -4 It should be noted that the specific frequency values in the original text are not fully represented in the translation due to the lack of complete information. You may need to fill in the correct frequency values in the translation according to the actual situation.There is a specific energy concentration frequency band among the s, indicating unique micro-motion characteristic frequency characteristics in this region. In the time dimension, the energy distributions of the four types of drones are relatively stable, reflecting their stable motion states during the observation period. Due to the differences in the physical structures and motion patterns of each target, the energy distributions show different characteristics, which is of great significance for accurately identifying the targets.

[0052] By extracting the indexes of their micro-motion characteristics to analyze and judge the extraction effect, the statistical results of the indexes of each model are shown in Table 2 below: Table 2 Statistical Results of Indexes of Each Model ;

[0053] According to Figure 4 - Figure 6 and Table 2, the average value of the energy entropy EE of the GST model is 9.2233, and the average value of the energy concentration EC is 0.0038, indicating that its energy distribution is relatively dispersed, the time-frequency resolution is insufficient, and the ability to suppress noise is weak. The average value of the energy entropy EE of the WT model is 10.5837, and the average value of the energy concentration EC is 0.0039. Its higher energy entropy EE value indicates that the noise interference is more significant, and the energy concentration EC has not increased significantly, reflecting its limited ability to capture local features in complex signals. In contrast, the average value of the energy entropy EE of the GST-WT fusion model is 3.7133, which is reduced by 60.16% and 65.23% compared with the GST model and the WT model respectively; the average value of the energy concentration EC is 0.1396, which is increased by 36.7 times and 35.8 times compared with the GST model and the WT model respectively. This result shows that the GST-WT combined model significantly suppresses noise interference and enhances the energy focusing ability by integrating the global time-frequency analysis ability of the generalized S transform and the local adaptive characteristics of the wavelet transform. The energy concentration EC of DJI M350 is increased from 0.0035 of the GST model to 0.1808 of the GST-WT model, indicating that the frequency components of its micro-motion characteristics are accurately separated and concentrated. In addition, the standard deviations of the energy entropy EE and the energy concentration EC of the GST-WT model among different models are 0.645 and 0.044 respectively, which are significantly lower than those of the GST model and the WT model, verifying its stability and robustness in multi-target scenarios.

[0054] Compared with the single GST and WT models, the energy entropy (EE) of the GST-WT combined model decreased by 60.16% and 65.23% respectively; the energy concentration (EC) increased by 36.7 times and 35.8 times respectively, verifying the effectiveness and feasibility of the combined model in noise suppression and energy focusing capabilities, as well as its precise separation ability for complex micro-motion features. At the application level, the GST-WT combined model can be adapted to scenarios such as low-altitude security and drone supervision, and improve the monitoring reliability of targets in complex electromagnetic environments through the advantages of multi-band radar data processing. Compared with the single model, the GST-WT combined model realizes double optimization in time-frequency resolution and feature stability by integrating the global time-frequency analysis of the generalized S transform and the local adaptability of the wavelet transform. It has been significantly improved in terms of time-frequency resolution, noise resistance, and feature stability, providing technical support for the precise recognition of low, slow, and small targets. In addition, in response to the challenges of the current model in the application of ultra-dense multi-target scenarios, in the future, the collaborative mechanism between the GST-WT combined model and the deep learning model can be explored, and the accuracy and reliability of target extraction in complex scenarios can be further enhanced by leveraging the autonomous learning ability of the deep learning model for multi-dimensional micro-motion features.

[0055] Therefore, the present invention adopts the above-mentioned method for extracting micro-motion features of low, slow, and small targets based on the GST-WT combination. First, the multi-band radar echo signal is preprocessed to remove the DC component, intercept the effective frequency band, and eliminate the trend term of the signal; then the GST-WT combination method is used for time-frequency analysis of the signal, and the time-frequency characteristics of the signal are obtained through the cooperation of the improved generalized S transform and the wavelet transform; then the data fusion is performed on the time-frequency analysis results; finally, the energy entropy and energy concentration indicators are combined to quantitatively evaluate the feature extraction effect. It solves the problems in the prior art that low, slow, and small targets are vulnerable to complex background noise interference and the time-frequency feature extraction accuracy is not high in traditional radar detection, improves the time-frequency resolution, noise resistance, and feature stability, and provides technical support for the precise recognition of low, slow, and small targets.

[0056] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for extracting micro-motion features of low, slow and small targets based on the GST-WT combination, characterized in that: Specifically, it includes the following steps: S1: Obtain multi-band radar echo signals, and preprocess the multi-band radar echo signals, including positive frequency band extraction, DC removal processing, effective frequency band interception, and signal trend item elimination; S2: Based on the preprocessed signals, perform time-frequency analysis using the GST-WT combined model to obtain the time-frequency characteristics of the improved generalized S transform and the time-frequency characteristics of the Morlet wavelet transform; The GST-WT combined model includes the improved generalized S transform and the Morlet wavelet transform; S3: Perform linear interpolation on the time-frequency characteristics of the improved generalized S transform to obtain the time-frequency characteristics of the improved generalized S transform after linear interpolation; S4: Based on the time-frequency characteristics of the Morlet wavelet transform and the time-frequency characteristics of the improved generalized S transform after linear interpolation, adopt a linear weighting strategy for fusion to obtain the fused time-frequency characteristics; S5: Calculate the energy entropy and energy concentration of the fused time-frequency characteristics based on the fused time-frequency characteristics; S6: Determine whether the energy entropy and energy concentration in S5 meet the expected values; If the expected values are met, output the currently fused time-frequency characteristics. If the expected values are not met, adjust the parameters of the GST-WT combined model and continue to execute S2-S5.

2. The method for extracting micro-motion features of low, slow and small targets based on the GST-WT combination according to claim 1, characterized in that The signal after extracting the positive tuning frequency band in S1 It is expressed as: ； Among them, is the original signal, is the number of range cells, is the time domain index.

3. The method for extracting micro-motion features of low, slow, and small targets based on the GST-WT combination according to claim 2, wherein: The signal after DC removal in S1 It is expressed as: ； Among them, is the frequency domain index, is the Hamming window function.

4. The method for extracting the micro-motion features of low, slow, and small targets based on the GST-WT combination according to claim 3, wherein: The specific steps for intercepting the effective frequency band in S1 are as follows: According to the target distance Calculate the corresponding frequency point: ； Among them, is the minimum frequency point, is the maximum frequency point, is the minimum distance, is the maximum distance, is the speed of light, is the modulation bandwidth of the radar signal, is the pulse repetition frequency, is the number of points of the fast Fourier transform (FFT), is the sampling frequency; Intercept the signal of the effective frequency band , where .

5. The method for extracting micro-motion features of low, slow, and small targets based on the GST-WT combination according to claim 4, characterized in that: The signal trend item elimination in S1 using the moving average method is specifically expressed as: ； Among them, is the detrended signal.

6. The method for extracting micro-motion features of low, slow and small targets based on the GST-WT combination according to claim 5, wherein: The time-frequency characteristics of the Morlet wavelet transform in S2 are expressed as: ； Among them, is the mother wavelet, is the angular frequency, is the scale parameter, is the translation parameter, is the conjugate function of.

7. The method for extracting the micro-motion features of low, slow and small targets based on the GST-WT combination according to claim 6, characterized in that: The time-frequency characteristics of the improved generalized S transform in S2 are expressed as: ； wherein, is the base frequency, is the translation coefficient, is the continuous signal, is the exponential part, is the imaginary unit.

8. The micro-motion feature extraction method for low, slow and small targets based on the GST-WT combination according to claim 7, wherein: The time-frequency result after linearly interpolating the time-frequency characteristics of the improved generalized S transform in S3 is expressed as: ； Among them, is the time-frequency feature obtained by improving the generalized S transform, is the rounding function, is the frequency, is the time, is a custom function or operator, representing a linear interpolation operation on the time-frequency feature.

9. The method for extracting micro-motion features of low, slow and small targets based on the GST-WT combination according to claim 8, wherein: The fused time-frequency features in S4 which are expressed as: ； Among them, and are weighting coefficients, is the time-frequency feature after Morlet wavelet transform.

10. The low, slow and small target micro-motion feature extraction method based on the GST-WT combination according to claim 1, wherein: The energy entropy in S5 is expressed as: ； The energy concentration is expressed as: ； Among them, is the total number of signal time samples, is the normalized energy distribution probability, is the maximum value of the signal instantaneous energy, is the total energy of the signal.

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