Micro-motion feature extraction method for low-speed, slow, and small targets based on GST-WT combination

Abstract

The present invention discloses a method for extracting micro-motion features of low-altitude, slow and small targets based on a GST-WT combination, which relates to the field of micro-motion feature extraction of low-altitude, slow and small targets. The method comprises the following steps: acquiring a multi-band radar echo signal, preprocessing the multi-band radar echo signal, and adopting a GST-WT combination model to perform time-frequency analysis on the preprocessed signal to obtain time-frequency features of an improved generalized S transform and a Morlet wavelet transform; performing linear interpolation on the time-frequency features of the improved generalized S transform; adopting a linear weighting strategy to fuse the time-frequency features to obtain fused time-frequency features; and quantitatively evaluating the feature extraction effect by combining energy entropy and energy concentration indicators. By giving full play to the advantages of GST global time-frequency analysis and WT local adaptation, the micro-motion features of the target are effectively separated and accurately extracted, and the time-frequency resolution, noise resistance and feature stability are improved, thereby providing technical support for the detection of low-altitude, slow and small targets in scenarios such as low-altitude security and unmanned aerial vehicle monitoring.

Description

Technical Field

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

[0002] Due to their low-altitude flight, slow speed, and small radar cross-section, small, low-altitude targets hold significant application value in numerous fields. In the civilian sector, they are widely used in logistics and distribution, film and television production, environmental monitoring, and agricultural plant protection. In the military, they undertake crucial tasks such as reconnaissance and surveillance, electronic warfare execution, and target training. Micro-motion feature extraction, a core technology in radar signal processing, aims to accurately extract minute but recognizable dynamic information about a target from complex radar echo signals. This type of feature is crucial for identifying small, low-altitude, slow-moving targets and analyzing their behavior in remote sensing scenarios. High-precision micro-motion feature extraction not only reveals the target's motion patterns but also improves the radar system's detection sensitivity and anti-interference capabilities, while enhancing its data analysis capabilities in complex environments, such as multi-target tracking in urban airspace. However, in practical applications, this technology still faces numerous challenges, including interference from complex background noise on weak signals, reduced feature recognition due to low Doppler shift, and the limitations of traditional algorithms in processing unstable, multi-band signals.

[0003] In recent years, scholars both domestically and internationally have devoted significant research efforts to target micro-motion feature extraction, achieving 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 techniques. One existing technique, combining singular value decomposition (SVD) with WT, extracts signal micro-motion features by analyzing energy entropy (EE) and energy concentration (EC). Another existing technique utilizes a modified GST algorithm to implement frequency correction, thereby processing micro-motion features with a broader range. While the GST algorithm enables comprehensive analysis in both time and frequency dimensions, providing a solid foundation for subsequent feature extraction, it still suffers from insufficient adaptability when processing non-stationary signals. It is difficult to flexibly adjust the analysis window based on signal characteristics, resulting in inaccurate capture of local signal features. Although the WT algorithm can flexibly adjust the size of the time-frequency window by introducing a scale factor, its computational complexity is high and it requires a lot of computing resources and time when processing large-scale data.

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

[0005] In order 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 integrating the global time-frequency analysis of the generalized S transform and the local adaptive characteristics of the wavelet transform, the advantages of the GST global time-frequency analysis and the WT local adaptation are fully utilized, and dual optimization is achieved in time-frequency resolution and feature stability. Significant improvements have been made in 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 objectives, the present invention provides a method for extracting micro-motion features of slow and small targets based on a GST-WT combination, comprising the following steps:

[0007] S1: Acquire multi-band radar echo signals and pre-process them, including extracting the positive modulation band, removing DC processing, intercepting the effective frequency band, and eliminating the signal trend item;

[0008] S2: Based on the preprocessed signal, the GST-WT combined model is used to perform 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;

[0009] 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;

[0010] S4: Based on the time-frequency features of Morlet wavelet transform and the time-frequency features of improved generalized S transform after linear interpolation, a linear weighting strategy is used to fuse them to obtain the fused time-frequency features;

[0011] S5: Calculate the energy entropy and energy concentration of the fused time-frequency features based on the fused time-frequency features;

[0012] S6: Determine whether the energy entropy and energy concentration in S5 meet the expected values; if so, output the current fused time-frequency features; if not, adjust the parameters of the GST-WT combination model and continue to execute S2-S5.

[0013] Preferably, the signal after the positive modulation band is extracted in S1 Expressed as:

[0014] ;

[0015] in, is the original signal, is the number of distance units, is the time domain index.

[0016] Preferably, the signal after DC removal in S1 Expressed as:

[0017] ;

[0018] in, is the frequency domain index, is the Hamming window function.

[0019] Preferably, intercepting the effective frequency band in S1 specifically includes the following steps:

[0020] According to the target distance Calculate the corresponding frequency:

[0021] ;

[0022] in, 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), Sampling frequency;

[0023] Intercept effective frequency band signals ,in, .

[0024] Preferably, the sliding average method is used in S1 to eliminate the signal trend term, which is specifically expressed as:

[0025] ;

[0026] in, It is a detrended signal.

[0027] Preferably, the time-frequency characteristics of the Morlet wavelet transform in S2 are expressed as:

[0028] ;

[0029] in, For my mother Xiaobo, is the angular frequency, is the scale parameter, is the translation parameter, for The conjugate function of .

[0030] Preferably, the time-frequency feature of the improved generalized S transform in S2 is expressed as:

[0031] ;

[0032] in, is the fundamental frequency, is the translation coefficient, is a continuous signal, is the index part, Is an imaginary unit.

[0033] Preferably, the time-frequency result after linear interpolation of the time-frequency characteristics of the improved generalized S transform in S3 is Expressed as:

[0034] ;

[0035] in, In order to improve the time-frequency characteristics obtained by generalized S transform, is the rounding function, is the frequency, For time, It is a custom function or operator, which indicates the linear interpolation operation on the time-frequency features.

[0036] Preferably, the fused time-frequency features in S4 Expressed as:

[0037] ;

[0038] in, 、 is the weighting coefficient, is the time-frequency feature after Morlet wavelet transform.

[0039] Preferably, the energy entropy in S5 is expressed as:

[0040] ;

[0041] Energy concentration is expressed as:

[0042] ;

[0043] in, is the total number of time samples of the signal, is the normalized energy distribution probability, is the maximum instantaneous energy of the signal, is the total signal energy.

[0044] Therefore, the present invention adopts the above-mentioned GST-WT combination-based method for extracting micro-motion features of low-speed, slow, and small targets. By preprocessing the multi-band radar echo signal, removing the DC component, intercepting the effective frequency band, and eliminating the signal trend term, the signal quality is improved. 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 improving the collaborative work of the generalized S transform and the wavelet transform. The generalized S transform result is linearly interpolated to make its frequency axis consistent with the wavelet transform, and a linear weighting strategy is used to fuse the time-frequency features. Finally, the feature extraction results are quantitatively evaluated by combining multiple indicators such as energy entropy and energy concentration. This method fully utilizes the advantages of GST global time-frequency analysis and WT local adaptation to effectively separate and accurately extract the micro-motion features of the target, providing certain technical support for the detection of low-speed, slow, and small targets.

[0045] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 Schematic diagram of the process of extracting micro-motion features of slow and small targets based on the GST-WT combination in the present invention;

[0047] Figure 2 Schematic diagram of the GST-WT feature extraction process in an embodiment of the present invention;

[0048] Figure 3 Figures 1 and 2 are data processing diagrams of the embodiments of the present invention; (a) is the data processing diagram of the DJI Mavic 2; (b) is the data processing diagram of the DJI Phantom; (c) is the data processing diagram of the DJI M350; and (d) is the data processing diagram of the DJI Inspire 2.

[0049] Figure 4 The GST energy distribution diagrams in the embodiments of the present invention are shown in Figure 1, where (a) is the GST energy distribution diagram of the DJI Mavic 2; (b) is the GST energy distribution diagram of the DJI Phantom; (c) is the GST energy distribution diagram of the DJI M350; and (d) is the GST energy distribution diagram of the DJI Inspire 2.

[0050] Figure 5 The WT energy distribution diagrams in the embodiments of the present invention are shown in Figure 1, where (a) is the WT energy distribution diagram of the DJI Mavic 2; (b) is the WT energy distribution diagram of the DJI Phantom; (c) is the WT energy distribution diagram of the DJI M350; and (d) is the WT energy distribution diagram of the DJI Inspire 2.

[0051] Figure 6These are the GST-WT energy distribution diagrams in the embodiments of the present invention, where (a) is the GST-WT energy distribution diagram of the DJI Mavic 2; (b) is the GST-WT energy distribution diagram of the DJI Phantom; (c) is the GST-WT energy distribution diagram of the DJI M350; and (d) is the GST-WT energy distribution diagram of the DJI Inspire 2. DETAILED DESCRIPTION

[0052] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0053] Unless otherwise defined, technical or scientific terms used in the present invention shall have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs.

[0054] The words “include” or “comprising” and similar words used in the present invention mean that the elements before the word include the elements listed after the word, and do not exclude the possibility of also including other elements. The orientation or position relationship indicated by the terms “inside”, “outside”, “upper”, “lower”, etc. is based on the orientation or position relationship shown in the accompanying drawings. It is only for the convenience of describing the present invention and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, it cannot be understood as a limitation of the present invention. When the absolute position of the described object changes, the relative position relationship may also change accordingly. In the present invention, unless otherwise clearly stipulated and limited, the terms such as “attachment” should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral whole; it can be directly connected or indirectly connected through an intermediate medium, and it can be the internal connection of two elements or the interaction relationship between two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to the specific circumstances.

[0055] Example

[0056] The low-speed and small-target micro-motion feature extraction method based on GST-WT combination, such as Figure 1-Figure 2 As shown, the following steps are included:

[0057] S1: Acquire multi-band radar echo signals and pre-process them, including extracting the positive modulation band, removing DC processing, intercepting the effective frequency band, and eliminating the signal trend item;

[0058] Preprocess multi-band radar echo signals. A Hamming window function is used to extract the positive frequency band, and then DC removal is performed to remove the DC component from the signal. The corresponding frequency point is calculated based on the target distance, and the effective frequency band signal is intercepted. A sliding average method is then used to eliminate the signal trend term, reducing the impact of interference on subsequent analysis.

[0059] First, the multi-band radar echo data is processed by extracting the positive frequency band and removing DC:

[0060] ;

[0061] ;

[0062] in, is the Hamming window function, is the number of distance units, is the frequency domain index, is the time domain index, is the signal after the positive modulation frequency band is extracted, is the signal after DC removal processing, is the original signal.

[0063] According to the target distance Calculate the corresponding frequency:

[0064] ;

[0065] in, 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.

[0066] Intercept effective frequency band signals , , use the sliding average method to eliminate the signal trend term:

[0067] ;

[0068] in, It is a detrended signal.

[0069] S2: Based on the preprocessed signal, the GST-WT combined model is used to perform 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;

[0070] Generalized S transform method:

[0071] The generalized S transform is an efficient, fast, easy to understand, and widely used algorithm in signal processing. Its basic definition is:

[0072] ;

[0073] in, is a continuous signal, is the Gaussian window function, is the fundamental frequency, is the translation coefficient.

[0074] The Gaussian window function is defined as:

[0075] ;

[0076] Among them, the standard deviation The basic frequency The reciprocal of , also known as the coefficient of expansion.

[0077] Substituting the Gaussian window function into the basic definition of generalized S transform, we can get The specific expression of S transform is: ;

[0078] in, The index part.

[0079] Adjust the Gaussian window function, improve its width and frequency so that they are not completely opposite, and the generalized S transform can be obtained as follows:

[0080] ;

[0081] Among them, the window function The frequency dimension is determined by the parameter Decide, is the improved generalized Gaussian window function.

[0082] To ensure the reversibility of the S-transform, Need to meet:

[0083] ;

[0084] In the S transform, the modulation function mother wavelet of the Gaussian window function is:

[0085] ;

[0086] in, is a complex exponential function, Determines the window shape.

[0087] 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: ;

[0088] in, For continuous signals The S transform.

[0089] The time-frequency characteristics of the improved generalized S transform in this application are expressed as:

[0090] ;

[0091] in, is the fundamental frequency, is the translation coefficient, is a continuous signal, is the index part, Is an imaginary unit.

[0092] Wavelet transform is a very important tool in signal and image processing, which can analyze data in both time domain and frequency domain, thereby capturing the local information of the data. represents a two-dimensional signal, then the two-dimensional continuous wavelet transform can be defined as:

[0093] ;

[0094] in, are its horizontal and vertical coordinates respectively, represents the two-dimensional basic wavelet, yes The scale expansion and two-dimensional displacement of , then:

[0095] ;

[0096] in, 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.

[0097] The corresponding inverse wavelet transform of the above formula is:

[0098] ;

[0099] in, , Yes The Fourier transform of is the corresponding circular frequency. Reflects the spatial scale of the phenomenon, translation parameters Reflecting the phenomenon Plane position, its principle is the analytical correspondence between frequency and time domain.

[0100] 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 bandpass filter group. Due to the introduction of the scale factor , through the parameters While covering the entire time domain through translation, the time-frequency window adaptively changes with the speed of the analyzed signal. When extracting information about high-frequency, fast-varying 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-varying signals, the time-frequency window should be appropriately widened, and the frequency window correspondingly reduced to ensure high frequency resolution and achieve feature extraction of the target signal.

[0101] The time-frequency characteristics of the Morlet wavelet transform in this application are expressed as:

[0102] ;

[0103] in, For my mother Xiaobo, is the angular frequency, is the scale parameter, is the translation parameter, for The conjugate function of .

[0104] 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;

[0105] Perform linear interpolation on the generalized S transform and adjust the frequency axis of the generalized S transform to make its frequency axis consistent with that of the wavelet transform in preparation for subsequent data fusion, ensuring that the results of the two transforms can be effectively combined in the frequency dimension.

[0106] Time-frequency results after linear interpolation of the time-frequency characteristics of the improved generalized S transform Expressed as:

[0107] ;

[0108] in, In order to improve the time-frequency characteristics obtained by generalized S transform, is the rounding function, is the frequency, For time, It is a custom function or operator, which indicates the linear interpolation operation on the time-frequency features.

[0109] S4: Based on the time-frequency features of Morlet wavelet transform and the time-frequency features of improved generalized S transform after linear interpolation, a linear weighting strategy is used to fuse them to obtain the fused time-frequency features;

[0110] Use linear weighting strategy to fuse time-frequency features. Set weighting coefficient , the time-frequency features of wavelet transform and generalized S transform after linear interpolation are fused to obtain comprehensive time-frequency features.

[0111] Fusion of time-frequency features Expressed as:

[0112] ;

[0113] in, 、 is the weighting coefficient, , which is desirable in this application , is the time-frequency feature after Morlet wavelet transform.

[0114] S5: Calculate the energy entropy and energy concentration of the fused time-frequency features based on the fused time-frequency features. Use energy entropy (EE) and energy concentration (EC) as evaluation metrics to assess the performance of feature extraction. Calculate the EE and EC values for the fused time-frequency features and compare them for different targets to determine the quality of the current feature extraction results.

[0115] Energy entropy is expressed as:

[0116] ;

[0117] Energy concentration is expressed as:

[0118] ;

[0119] in, is the total number of time samples of the signal, is the normalized energy distribution probability, is the maximum instantaneous energy of the signal, is the total signal energy.

[0120] S6: Determine whether the energy entropy and energy concentration in S5 meet the expected values; if so, output the current fused time-frequency features; if not, adjust the parameters of the GST-WT combination model and continue to execute S2-S5 until the feature extraction effect meets the expected requirements.

[0121] The parameters of the GST-WT combination model specifically include the scale parameter of the Morlet wavelet and the Gaussian window parameter of the improved generalized S transform.

[0122] Example 1

[0123] To fully analyze the practical effectiveness of the micro-motion feature extraction method proposed in this embodiment, a low-speed, slow, and small target detection dataset published by the Journal of Radars was used for simulation analysis, using target data with a modulation bandwidth of 100 MHz and a fixed modulation period of 0.3 ms in the Ku+L band. This dataset contains five types of low-speed, slow, and small targets, including the DJI Mavic 2, DJI Elf, DJI M350, DJI Inspire 2, and DJI M600. Considering that the rotor characteristics of the DJI series of drones are basically consistent, and to provide a reference for the tracking research of drone targets under multi-band radar, this embodiment randomly selected detection data from the DJI Mavic 2, DJI Elf, DJI M350, and DJI Inspire 2 for simulation experiments. The relevant information of the selected low-speed, slow, and small targets is shown in Table 1.

[0124] Table 1 Related information of selected low, slow and small targets

[0125] ;

[0126] These four types of low, slow and small targets have a high usage base, and the radar echo data detected is clear, complete and fully representative. The data waveform after DC removal and distance preprocessing is as follows Figure 3 shown.

[0127] The results of processing four low-speed and small target data with GST model, WT model and GST-WT combined model are as follows: Figure 4-Figure 6 shown.

[0128] Figure 4 The GST energy distribution of four low, slow, and small targets, DJI Mavic 2, DJI Phantom, DJI M350, and DJI Inspire 2, is given. 5 ~1.5×10 5 Hz, time 0~2×10 4 The energy is relatively concentrated in the frequency band and time period, indicating that the frequency band and time period contain important micro-motion feature information; the DJI Phantom 5 ~1.5×10 5 The energy between Hz is concentrated and compact, which means that its micro-motion characteristics are outstanding in this narrow frequency range; DJI M350 is at 0.5×10 5 ~1.8×10 5 There are multiple energy concentration areas between 0.5×10 5 ~1.1×10 5 There is a specific concentrated frequency band between Hz, reflecting its unique micro-motion characteristic frequency characteristics.

[0129] Figure 5The WT energy distribution of four low, slow, and small targets, DJI Mavic 2, DJI Phantom, DJI M350, and DJI Inspire 2, is given. DJI Mavic 2 has a frequency of about 0.5×10 5 ~2.5×10 5 Hz, and the energy is relatively concentrated between 0 and 0.8s, indicating that it contains key micro-motion features within this frequency and time range; the DJI Phantom has a relatively concentrated energy between 0.5×10 5 ~2.5×10 5 Hz, and the energy concentration between 0 and 1s is more obvious and the concentrated area is relatively compact, indicating that its micro-motion characteristics are prominent in this frequency and time range; DJI M350 has a frequency of 0.5×10 5 ~2×10 5 Hz, there are multiple energy concentration areas between 0 and 1.5s, and the distribution range is relatively wide, which means that it has a variety of micro-vibration characteristic frequency components with different intensities; DJI Inspire 2 has a frequency of 0.5×10 5 ~3×10 5 There is a specific energy concentration frequency band between Hz and time 0~0.8s, reflecting its unique micro-motion characteristic frequency characteristics.

[0130] Figure 6 The energy distribution of four low-speed and slow small targets, DJI Mavic 2, DJI Phantom, DJI M350 and DJI Inspire 2, after GST-WT fusion transformation is given. 5 Hz~3×10 5 Hz, time 0~2×10 -4 The energy shows a concentrated trend between s, indicating that there are important micro-motion features in this frequency and time period; the DJI Phantom has a frequency of 1×10 5 Hz~4×10 5 Hz, time 0~1×10 -4 The energy concentration between s is significant and the concentrated area is relatively concentrated, indicating that its micro-motion characteristics are obvious in this area; DJI M350 at a frequency of 1.5×10 5 Hz~3.5×10 5 Hz, time 0~1×10 -4 There are multiple energy concentration areas between s and the distribution is relatively wide, which means that it has multiple micro-vibration characteristic frequency components with different intensities; DJI Inspire 2 has a frequency of 1×10 5 Hz~3×10 5 Hz, time 0~1×10 -4s, there is a specific energy concentration frequency band, reflecting the unique micro-motion characteristic frequency characteristics in this region. In the temporal dimension, the energy distribution of the four drones is relatively stable, reflecting their stable motion during the observation period. Due to the differences in the physical structure and motion patterns of each target, the energy distribution exhibits different characteristics, which is important for accurate target identification.

[0131] The extraction effect is analyzed and judged by extracting the indicators of its micro-motion characteristics. The statistical results of each model indicator are shown in Table 2 below:

[0132] Table 2 Statistical results of each model indicator

[0133] ;

[0134] according to Figure 4-Figure 6 As shown in Table 2, the GST model has a mean energy entropy (EE) of 9.2233 and an average energy concentration (EC) of 0.0038, indicating a relatively dispersed energy distribution, insufficient time-frequency resolution, and weak noise suppression. The WT model has a mean energy entropy (EE) of 10.5837 and an average energy concentration (EC) of 0.0039. Its higher EE values indicate more significant noise interference, while its EC does not significantly improve, reflecting its limited ability to capture local features in complex signals. In contrast, the GST-WT fusion model has a mean energy entropy (EE) of 3.7133, a decrease of 60.16% and 65.23% compared to the GST and WT models, respectively. Its mean energy concentration (EC) is 0.1396, an increase of 36.7 times and 35.8 times compared to the GST and WT models, respectively. These results demonstrate that the GST-WT combined model significantly suppresses noise interference while enhancing energy focusing by combining the global time-frequency analysis capabilities of the generalized S-transform with the local adaptive properties of the wavelet transform. The DJI M350's energy concentration (EC) improved from 0.0035 for the GST model to 0.1808 for the GST-WT model, demonstrating the precise separation and concentrated presentation of its micro-motion characteristic frequency components. Furthermore, the standard deviations of energy entropy (EE) and energy concentration (EC) for the GST-WT model across different aircraft models were 0.645 and 0.044, respectively, significantly lower than those for the GST and WT models, demonstrating its stability and robustness in multi-target scenarios.

[0135] Compared with the single GST and WT models, the energy entropy EE of the GST-WT combined model was reduced by 60.16% and 65.23% respectively; the energy concentration EC was 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, as well as its ability to accurately separate 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 monitoring. By taking advantage of multi-band radar data processing, it can improve the monitoring reliability of targets in complex electromagnetic environments. Compared with a single model, the GST-WT combined model achieves dual optimization in time-frequency resolution and feature stability by integrating the global time-frequency analysis of the generalized S transform and the local adaptive characteristics of the wavelet transform. Significant improvements have been made in time-frequency resolution, noise resistance, and feature stability, providing technical support for the accurate identification of low, slow, and small targets. In addition, in response to the challenges of current models in ultra-dense multi-target scene applications, the synergistic mechanism of the GST-WT combination model and the deep learning model can be explored in the future. By leveraging the deep learning model's autonomous learning ability for multi-dimensional micro-motion features, the accuracy and reliability of target extraction in complex scenes can be further enhanced.

[0136] Therefore, the present invention adopts the above-mentioned method for extracting micro-motion features of low-speed, 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 to perform time-frequency analysis on the signal, and the time-frequency characteristics of the signal are obtained through the collaborative use of the improved generalized S transform and wavelet transform; then, the time-frequency analysis results are subjected to data fusion; finally, the energy entropy and energy concentration indicators are combined to quantitatively evaluate the feature extraction effect. This solves the problem in the prior art that low-speed, slow, and small targets are easily interfered with by complex background noise in traditional radar detection, and the time-frequency feature extraction accuracy is low. It improves the time-frequency resolution, noise resistance, and feature stability, and provides technical support for the accurate identification of low-speed, slow, and small targets.

[0137] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for extracting micro-motion features of slow and small targets based on a GST-WT combination, characterized by: The specific steps include: S1: Acquire multi-band radar echo signals and pre-process them, including extracting the positive modulation band, removing DC processing, intercepting the effective frequency band, and eliminating the signal trend item; Intercepting the effective frequency band specifically includes the following steps: According to the target distance Calculate the corresponding frequency: ； in, 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 effective frequency band signals ,in, ; The sliding average method is used to eliminate the signal trend term, which is specifically expressed as: ； in, It is the signal after detrending; S2: Based on the preprocessed signal, the GST-WT combined model is used to perform 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; The time-frequency characteristics of Morlet wavelet transform are expressed as: ； in, For my mother Xiaobo, is the angular frequency, is the scale parameter, is the translation parameter, for The conjugate function of The time-frequency characteristics of the improved generalized S transform are expressed as: ； in, is the fundamental frequency, is the translation coefficient, is a continuous signal, is the index part, is an imaginary unit; 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; Time-frequency results after linear interpolation of the time-frequency characteristics of the improved generalized S transform Expressed as: ； in, In order to improve the time-frequency characteristics obtained by generalized S transform, is the rounding function, is the frequency, For time, It is a custom function or operator, which indicates the linear interpolation operation of time-frequency features; S4: Based on the time-frequency features of Morlet wavelet transform and the time-frequency features of improved generalized S transform after linear interpolation, a linear weighting strategy is used to fuse them to obtain the fused time-frequency features; Fusion of time-frequency features Expressed as: ； in, 、 is the weighting coefficient, is the time-frequency feature after Morlet wavelet transform; 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 so, output the current fused time-frequency features; if not, adjust the parameters of the GST-WT combination model and continue to execute S2-S5.

2. The method for extracting micro-motion features of slow and small targets based on the GST-WT combination according to claim 1, characterized in that: The signal after the positive modulation band is extracted in S1 Expressed as: ； in, is the original signal, is the number of distance units, is the time domain index.

3. The method for extracting micro-motion features of slow and small targets based on the GST-WT combination according to claim 2, characterized in that: Signal after DC removal in S1 Expressed as: ； in, is the frequency domain index, is the Hamming window function.

4. The method for extracting micro-motion features of slow and small targets based on the GST-WT combination according to claim 1, characterized in that: Energy entropy in S5 is expressed as: ； Energy concentration is expressed as: ； in, is the total number of time samples of the signal, is the normalized energy distribution probability, is the maximum instantaneous energy of the signal, is the total signal energy.

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