SET and LTFAT combined low-slow small target micro-motion feature extraction method

Abstract

The invention relates to the field of radar detection, and particularly discloses a low-slow small target micro-motion feature extraction method combining SET and LTFAT, and the method comprises the steps: firstly carrying out the synchronous extraction of a radar echo signal through SET, so as to obtain the time-frequency distribution and energy characteristics of the signal; secondly, adaptive processing is carried out on the time-frequency domain local features by utilizing LTFAT, so that noise is suppressed, and the calculation redundancy is reduced; and finally, in combination with a multivariate index quantitative evaluation feature extraction result, the advantages of the fusion method in complex signal time-frequency analysis are fully played, and the blade micro-motion features of the target are effectively separated and accurately extracted. According to the method, the problems that the low-speed small target is easily interfered by complex background noise in traditional radar detection and the time-frequency feature extraction precision is not high are effectively solved, the technical scheme provided by the invention is better in the aspects of time-frequency resolution, anti-noise capability and feature stability, and certain technical support is provided for low-altitude security and unmanned aerial vehicle supervision.

Description

Technical Field

[0001] The present invention relates to the field of radar detection technology, and in particular to a method for extracting micro-motion features of low-speed, slow, and small targets by combining SET and LTFAT. Background Art

[0002] Low-altitude, slow-moving, small targets, due to their low-altitude flight, slow speed, and small cross-sectional area, play an important role in various fields. In civilian applications, they are deeply integrated into logistics and distribution, film and television production, environmental monitoring, and agricultural plant protection; in military applications, they are used in reconnaissance and surveillance, electronic warfare execution, and target drone training. Micro-motion feature extraction is a core component of radar signal processing. Its core goal is to accurately capture subtle but recognizable dynamic information about a target from the clutter of radar echo signals. Such features are particularly important for identifying low-altitude, slow-moving, small targets (such as drones) and analyzing target behavior in remote sensing scenarios. High-precision micro-motion feature extraction can deeply reveal the target's motion patterns, thereby optimizing the radar system's detection sensitivity and anti-interference capabilities, while also enhancing data analysis accuracy in complex environments, such as multi-target tracking in urban airspace. However, practical applications still face multiple challenges, such as the masking effect of complex background noise on weak signals, the reduced feature discernibility caused by low Doppler frequency shift, and the limitations of traditional algorithms in processing non-stationary, multi-component signals.

[0003] Currently, numerous scholars at home and abroad have conducted extensive and in-depth research on target micro-motion feature extraction, achieving a series of fruitful results. Among them, the most widely used algorithms include: Short-time Fourier Transform Method (SFT), Multi-scale Wavelet Analysis Method (MWA), Synchronous Extraction Transformation (SET), Local Time-Frequency Analysis Technique Method (LTF), Adaptive Feature Extraction Method (AFET), Hilbert Transform Method, etc. Some scholars have proposed a method combining SFT with SFT to determine blade micro-motion characteristics by calculating the signal-to-noise ratio and analyzing the time-frequency graph. Other researchers have used an improved SFT method to process and analyze instantaneous features.

[0004] Currently, the synchronous extraction transformation method offers high accuracy in instantaneous frequency extraction and strong algorithmic interpretability, but it still suffers from modal aliasing and the loss of high-frequency features. Local time-frequency analysis techniques offer strong local feature capture and high adaptability, but their computational complexity makes feature quantification difficult.

[0005] Therefore, a low-speed, slow, and small target micro-motion feature extraction method combining SET and LTFAT is developed to achieve more accurate and efficient feature extraction. Summary of the Invention

[0006] In response to the above-mentioned problems in the prior art, the present invention proposes a method for extracting micro-motion features of low-altitude, slow, and small targets by combining SET and LTFAT, which significantly improves the accuracy and noise resistance of micro-motion feature extraction, effectively reduces errors, and supports low-altitude security.

[0007] To achieve the above objectives, the present invention proposes a method for extracting micro-motion features of slow, small targets by combining SET and LTFAT, including:

[0008] S1. Signal preprocessing: preprocessing the input multi-band radar echo signal including denoising and normalization;

[0009] S2. Synchronous Extraction Transformation and Local Time-Frequency Analysis Fusion Processing: Applying the synchronous extraction transformation and local time-frequency analysis fusion extraction algorithm to extract the time-frequency features of the pre-processed multi-band radar echo signal, capturing key information including the instantaneous frequency, instantaneous amplitude, and time-frequency distribution of the signal;

[0010] S3. Feature selection and optimization: perform correlation analysis and feature importance evaluation on the extracted features, remove redundant features and retain the effective ones, and extract the target blade micro-motion features;

[0011] S4. Output extracted features: output the selected and optimized blade micro-motion features.

[0012] Preferably, in S2, the specific steps of synchronous extraction transformation and local time-frequency analysis fusion processing are:

[0013] S21. Synchronous Extraction Transform (SET) processing: Apply the Synchronous Extraction Transform (SET) algorithm to the preprocessed multi-band radar echo data signal to obtain the signal's time-frequency distribution and energy characteristics. The correlation coefficient is derived using the instantaneous frequency position in the time-frequency spectrum to extract key information, including the signal's instantaneous frequency, instantaneous amplitude, and time-frequency distribution.

[0014] S22. Local Time-Frequency Analysis (LTFAT) Processing: Apply the local time-frequency analysis (LTFAT) technique to the signal after SET processing to extract local features. Adaptively process the local features in the time-frequency domain, record the peak locations, combine time factors, and use the local frequencies of the peak sequences to extract local features of the signal.

[0015] S23. Fusion the processing results of synchronous extraction transformation and local time-frequency analysis technology to construct a feature extraction fusion method.

[0016] Preferably, in S21, the specific steps of synchronously extracting and transforming the SET process include:

[0017] S211. Construct a time-frequency spectrum function that reflects the time-frequency characteristics of the signal through the convolution of the window function and the signal and its frequency domain representation: calculate the time-frequency spectrum function G(t,ω) of the signal s(t) to analyze the time-frequency characteristics of the signal. The specific expression of the time-frequency spectrum function G(t,ω) is:

[0018]

[0019] Where, The signal s(t) is obtained by Fourier transform, g ω The complex conjugate of the Fourier transform of (u) is

[0020] Among them, the standard expression of the signal s(t) and its frequency domain expression obtained by Fourier transform Used to construct time-spectral function;

[0021] S212, solve the instantaneous frequency position: the instantaneous frequency ω0(t,ω) is solved by the time-frequency spectrum function G e The first-order derivative of (t, ω) with respect to time t is obtained by combining the synchronous extraction operator δ[ω-ω0(t, ω)], where the specific expression of the instantaneous frequency position is:

[0022]

[0023] In the two-dimensional time-frequency plane, the instantaneous frequency is obtained by solving the limit, and the expression is:

[0024]

[0025] S213, extracting correlation coefficient: Through synchronous extraction transformation, the correlation coefficient is obtained using the instantaneous frequency position in the time-frequency spectrum, which is expressed as:

[0026] Te(t,ω)=G e (t,ω)·δ[ω-ω0(t,ω)];

[0027] Where δ[ω-ω0(t,ω)] is the synchronization extraction operator, which is used to extract the coefficient corresponding to the instantaneous frequency position in the time-frequency spectrum.

[0028] Preferably, in S211, the time-frequency spectrum function G(t,ω) is constructed by solving the existence of the frequency domain to realize the window function of the target function in the frequency domain.

[0029] Preferably, in S22, the specific steps of the local time-frequency analysis technology LTFAT processing include:

[0030] S221. For the discrete time series x(i) (i=1,2,3...,n), use LTFAT to solve its peak time series p(i) (i=1,2,3...,n). The peak time is expressed as:

[0031]

[0032] S222. Calculate the time scale T based on the peak time series p(i) s and peak scale P s , record the peak position; where the time scale T s and peak scale P s The calculation formula is:

[0033]

[0034] The peak position is represented by: flag(j)=i, p(i)≠0, j=1,2,…,m;

[0035] Where a represents the time scale factor, b represents the peak scale factor, and F s represents the sampling frequency, and m represents the number of non-zero values ​​in the peak sequence p(i);

[0036] S223. The discrete sequence x(i) is combined with the time factor c and the local frequency u of the peak sequence p(i) under (a, b, c) is used to extract the local features of the signal. The calculation formula of the local frequency u of the peak sequence p(i) is:

[0037]

[0038] Where, t * is the length of time throughout the sequence; N s is the number of non-zero peaks in the peak sequence p(i).

[0039] Preferably, in S23, the specific steps of fusing the processing results of the synchronous extraction transformation and the local time-frequency analysis technology to construct a feature extraction fusion method include:

[0040] S231. Model the multi-band radar echo data as a function of instantaneous amplitude and instantaneous frequency. Transform and derive the original signal. The expression is:

[0041]

[0042] Where, is the derivative with respect to time, g * is the result of Fourier transform of the function;

[0043] S232. Transform the original signal and calculate the related instantaneous frequency by deriving the formula; wherein the related instantaneous frequency is:

[0044]

[0045] S233. Extracting time-frequency domain energy features based on the instantaneous frequency to obtain a related synchronous extraction transformation; wherein the obtained related synchronous extraction transformation is:

[0046] Te(t,ω)=STFT(t,ω)·δ[ω-ω0(t,ω)];

[0047] S234, by applying Taylor expansion at the relevant time point t, the instantaneous amplitude IA function A of the i-th component i (u)=A i (t) and the instantaneous phase IP function And instantaneous phase function expansion, reconstruct the signal And derive its local time-frequency analysis expression; among them, the local time-frequency analysis expression is:

[0048]

[0049] S235. Analyze the spectrum energy distribution. The spectrum energy expression is:

[0050]

[0051] S236. Design a frequency extraction operator to extract the time-frequency energy peak. The frequency extraction operator expression is:

[0052]

[0053] Preferably, in S231, the multi-band radar echo signal is an original signal, which is expressed as:

[0054]

[0055] Where A i (t) and are the instantaneous amplitude and instantaneous frequency respectively.

[0056] Preferably, in S3, the target blade micro-motion features are extracted as follows:

[0057] S31. Verify the pattern separation conditions and make separability assumptions;

[0058] S32. Use the frequency extraction operator to directly obtain the instantaneous frequency and amplitude information corresponding to the maximum value of the time-frequency energy, and complete the blade micro-motion feature extraction.

[0059] Preferably, in S31, the spectrum energy is concentrated on an instantaneous frequency trajectory with a fuzzy energy distribution.

[0060] Preferably, in S33, the specific steps of the separable hypothesis are:

[0061] The frequency spacing between two arbitrary modes satisfies When, according to the zero-point characteristic of the Fourier transform of the window function g * (ω)≤g * (0), reconstruct the frequency extraction operator to verify the pattern separability; where the reconstructed frequency extraction operator expression is:

[0062]

[0063] Where i∈{1,2,...,n-1} and Δ represents the distance between two patterns.

[0064] Therefore, the present invention proposes a method for extracting micro-motion features of slow and small targets by combining SET and LTFAT, which has the following beneficial effects:

[0065] (1) The fusion strategy of the present invention combines the global time-frequency characteristics of SET with the local detail capture capability of LTFAT, effectively suppressing noise interference and improving feature stability under complex signals;

[0066] (2) The present invention uses local feature adaptive processing and frequency extraction operators to directly locate the maximum value of time-frequency energy through frequency extraction operators, reducing redundant calculations while ensuring accurate extraction of blade micro-motion features;

[0067] (3) The present invention provides reliable technical support for low-altitude security and drone monitoring, and its characteristic stability meets the needs of actual scenarios.

[0068] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 This is an extraction flow chart of the method for extracting micro-motion features of slow and small targets by combining SET and LTFAT of the present invention;

[0070] Figure 2These are the processed images of DJI Mavic 2, DJI Elf, DJI M350, and DJI Inspire 2. (a) is the processed image of DJI Mavic 2, (b) is the processed image of DJI Elf, (c) is the processed image of DJI M350, and (d) is the processed image of DJI Inspire 2.

[0071] Figure 3 These are the SET energy distribution diagrams of DJI Mavic 2, DJI Elf, DJI M350, and DJI Inspire 2. (a) is the SET energy distribution diagram of DJI Mavic 2, (b) is the SET energy distribution diagram of DJI Elf, (c) is the SET energy distribution diagram of DJI M350, and (d) is the SET energy distribution diagram of DJI Inspire 2.

[0072] Figure 4 These are the SET-LTFAT energy distribution diagrams of DJI Mavic 2, DJI Phantom, DJI M350 and DJI Inspire 2. (a) is the SET-LTFAT energy distribution diagram of DJI Mavic 2, (b) is the SET-LTFAT energy distribution diagram of DJI Phantom, (c) is the SET-LTFAT energy distribution diagram of DJI M350, and (d) is the SET-LTFAT energy distribution diagram of DJI Inspire 2. DETAILED DESCRIPTION

[0073] To make the technical solutions, advantages, and purposes of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below. The described embodiments are part of the embodiments of the present invention, not all of them. Based on the described embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0074] 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.

[0075] like Figure 1 As shown, according to the present invention, a method for extracting micro-motion features of slow and small targets by combining SET and LTFAT is provided, comprising:

[0076] S1. Signal preprocessing: preprocessing the input multi-band radar echo signal including denoising and normalization;

[0077] S2. Synchronous Extraction Transformation and Local Time-Frequency Analysis Fusion Processing: Applying the synchronous extraction transformation and local time-frequency analysis fusion extraction algorithm to extract the time-frequency features of the pre-processed multi-band radar echo signal, capturing key information including the instantaneous frequency, instantaneous amplitude, and time-frequency distribution of the signal;

[0078] In S2, the specific steps of synchronous extraction transformation and local time-frequency analysis fusion processing are as follows:

[0079] S21. Synchronous Extraction Transform (SET) processing: Apply the Synchronous Extraction Transform (SET) algorithm to the preprocessed multi-band radar echo data signal to obtain the signal's time-frequency distribution and energy characteristics. The correlation coefficient is derived using the instantaneous frequency position in the time-frequency spectrum to extract key information, including the signal's instantaneous frequency, instantaneous amplitude, and time-frequency distribution.

[0080] In S21, the specific steps of synchronous extraction transformation SET processing include:

[0081] S211. Construct a time-frequency spectrum function that reflects the time-frequency characteristics of the signal through convolution of the window function and the signal and its frequency domain representation: calculate the time-frequency spectrum function G(t,ω) of the signal s(t) to analyze the time-frequency characteristics of the signal;

[0082] The standard expression of signal s(t) is:

[0083]

[0084] Where g(ut) represents the basic window function;

[0085] Let g w (u) = g(ut)·e -iωu , the time-spectral function G(t,ω) is obtained by Parseval's theorem, and the expression of the time-spectral function is:

[0086]

[0087] Where, The signal s(t) is obtained by Fourier transform, g ω The complex conjugate of the Fourier transform of (u) is

[0088] Among them, the standard expression of the signal s(t) and its frequency domain expression obtained by Fourier transform are used to construct the time-frequency spectrum function;

[0089] In S211, the time-frequency spectrum function G(t,ω) is constructed by solving the existence of the frequency domain to realize the window function of the objective function in the frequency domain, specifically:

[0090] Let ut = t', we can get:

[0091]

[0092] Let ut = τ, introduce a signal frequency ω0 and express the relevant frequency domain The window function of the objective function is constructed in the frequency domain, and the obtained time-frequency spectrum function G(t,ω) is:

[0093]

[0094] In the formula, when the spectrum function G e When ω=ω0 in (t,ω), the maximum correlation amplitude is achieved

[0095] S212, solve the instantaneous frequency position: the instantaneous frequency ω0(t,ω) is solved by the time-frequency spectrum function G e The first-order derivative of (t, ω) with respect to time t is obtained by combining the synchronous extraction operator δ[ω-ω0(t, ω)], where the specific expression of the instantaneous frequency position is:

[0096]

[0097] In the two-dimensional time-frequency plane, the instantaneous frequency is obtained by solving the limit, and the expression is:

[0098]

[0099] S213, extracting correlation coefficient: Through synchronous extraction transformation, the correlation coefficient is obtained using the instantaneous frequency position in the time-frequency spectrum, which is expressed as:

[0100] Te(t,ω)=G e (t,ω)·δ[ω-ω0(t,ω)];

[0101] Where δ[ω-ω0(t,ω)] is the synchronization extraction operator, which is used to extract the coefficient corresponding to the instantaneous frequency position in the time-frequency spectrum.

[0102] S22. Local Time-Frequency Analysis (LTFAT) Processing: Apply the local time-frequency analysis (LTFAT) technique to the signal after SET processing to extract local features. Adaptively process the local features in the time-frequency domain, record the peak locations, combine time factors, and use the local frequencies of the peak sequences to extract local features of the signal.

[0103] In S22, the specific steps of the local time-frequency analysis technology LTFAT processing include:

[0104] S221. For the discrete time series x(i) (i=1, 2, 3..., n), use LTFAT to solve its peak time series p(i) (i=1, 2, 3..., n). The peak time is expressed as:

[0105]

[0106] S222. Calculate the time scale T based on the peak time series p(i) s and peak scale P s , record the peak position; where the time scale T s and peak scale P s The calculation formula is:

[0107]

[0108] In the peak sequence, p(i) corresponds to the correlation value of the local peak, and the peak position is represented by: flag(j) = i, p(i) ≠ 0, j = 1, 2, ..., m;

[0109] Where a represents the time scale factor, b represents the peak scale factor, and F s represents the sampling frequency, and m represents the number of non-zero values ​​in the peak sequence p(i);

[0110] Since there is a time interval between adjacent non-zero peaks, the number of time intervals is m-1. These m-1 time intervals can be combined to form a new sequence, which is expressed as:

[0111]

[0112] The time interval scale Δ of the peak sequence p(i) s Defined as:

[0113]

[0114] S223. The discrete sequence x(i) is combined with the time factor c and the local frequency u of the peak sequence p(i) under (a, b, c) is used to extract the local features of the signal. The calculation formula of the local frequency u of the peak sequence p(i) is:

[0115]

[0116] Where, t * is the length of time throughout the sequence; N s is the number of non-zero peaks in the peak sequence p(i).

[0117] S23. Fusion the processing results of synchronous extraction transformation and local time-frequency analysis technology to construct a feature extraction fusion method.

[0118] In S23, the specific steps of fusing the processing results of the synchronous extraction transformation and the local time-frequency analysis technology to construct a feature extraction fusion method include:

[0119] S231. Model the multi-band radar echo data as a function of instantaneous amplitude and instantaneous frequency. Transform and derive the original signal. The expression is:

[0120]

[0121] Where, is the derivative with respect to time, g * is the result of Fourier transform of the function;

[0122] In S231, the multi-band radar echo signal is the original signal, which is expressed as:

[0123]

[0124] Where A i (t) and are the instantaneous amplitude and instantaneous frequency respectively;

[0125] S232. Transform the original signal and calculate the related instantaneous frequency by deriving the formula; wherein the related instantaneous frequency is:

[0126]

[0127] S233. Extracting time-frequency domain energy features based on the instantaneous frequency to obtain a related synchronous extraction transformation; wherein the obtained related synchronous extraction transformation is:

[0128] Te(t,ω)=STFT(t,ω)·δ[ω-ω0(t,ω)];

[0129] S234, by applying Taylor expansion at the relevant time point t, the instantaneous amplitude IA function A of the i-th component i (u)=A i (t) and the instantaneous phase IP function And instantaneous phase function expansion, reconstruct the signal And derive its local time-frequency analysis expression; among them, the local time-frequency analysis expression is:

[0130]

[0131] S235. Analyze the spectrum energy distribution. The spectrum energy expression is:

[0132]

[0133] S236. Design a frequency extraction operator to extract the time-frequency energy peak. The frequency extraction operator expression is:

[0134]

[0135] S3. Feature selection and optimization: perform correlation analysis and feature importance evaluation on the extracted features, remove redundant features and retain the effective ones, and extract the target blade micro-motion features;

[0136] In S3, the target blade micro-motion features are extracted as follows:

[0137] S31. Verify the pattern separation conditions and make separability assumptions;

[0138] S32. Use the frequency extraction operator to directly obtain the instantaneous frequency and amplitude information corresponding to the maximum value of the time-frequency energy, and complete the blade micro-motion feature extraction.

[0139] In S31, the spectrum energy is concentrated on the instantaneous frequency trajectory with fuzzy energy distribution.

[0140] In S33, the specific steps of the separable assumption are:

[0141] The frequency spacing between two arbitrary modes satisfies When, according to the zero-point characteristic of the Fourier transform of the window function g * (ω)≤g * (0), reconstruct the frequency extraction operator to verify the pattern separability; where the reconstructed frequency extraction operator expression is:

[0142]

[0143] Where i∈{1,2,...,n-1} and Δ represents the distance between two patterns.

[0144] S4. Output extracted features: output the selected and optimized blade micro-motion features.

[0145] The low-speed, slow, small target micro-motion feature extraction method proposed in this invention that combines SET and LTFAT is experimented and analyzed.

[0146] The simulation analysis used a dataset for detecting low-speed, slow, and small targets published by the Journal of Radars. The dataset included five types of low-speed, slow, and small targets, including the DJI Mavic 2, DJI Phantom, DJI M350, DJI Inspire 2, and DJI M600. The dataset used Ku+L band targets with a modulation bandwidth of 100 MHz and a modulation period of 0.3 ms.

[0147] We randomly selected detection data from the DJI Mavic 2, DJI Phantom, DJI M350, and DJI Inspire 2 for the simulation experiment. The relevant information of the selected targets is shown in Table 1.

[0148] Table 1 Related information of selected low, slow and small targets

[0149]

[0150] For the selected low, slow and small target, the data waveform after DC removal and distance dimension processing is as follows Figure 2 shown.

[0151] The experiment uses blade length and rotation speed as evaluation indicators in the blade micro-motion characteristics to evaluate the feature extraction effects of the synchronous extraction transformation method and the synchronous extraction transformation and local time-frequency analysis fusion extraction method. The blade length calculation formula is:

[0152]

[0153] The speed calculation formula is:

[0154]

[0155] Where, f dmax is the maximum Doppler frequency, λ is the wavelength, f flash is the blade flicker frequency, f rot is the rotational speed, L is the blade length, and β is the radar pitch angle.

[0156] The blade length and rotation speed parameters of these four types of low, slow and small targets are shown in Table 2:

[0157] Table 2 UAV technical parameters

[0158]

[0159] The results of synchronous extraction transformation, synchronous extraction transformation and local time-frequency analysis fusion extraction of 4 types of low, slow and small targets are as follows: Figure 3 、 Figure 4 shown.

[0160] Figure 3 The energy distribution of the synchronous extraction transformation method has the same problem, that is, the energy is relatively dispersed. 3 s) are widely distributed and no concentrated clustering of target signals is formed; the frequency dimension (0~4.5×10 3 Hz), there is no obvious main peak of energy, low frequency (0~1.5×10 3 Hz) and high frequency (3×10 3 ~4.5×10 3 Hz) regions all show scattered high-energy points, but their distribution is disorderly, which reflects that the synchronous extraction transformation method is not capable of localizing the time and frequency of the signal, and it is difficult to focus on the target micro-motion characteristics.

[0161] The color bar shows a large dynamic range of energy. There are continuous high-energy bands in the low-frequency band, which may be noise interference. Although there are local high-energy points in the high-frequency band, they are not obviously distinguished from the noise energy, and the target micro-motion characteristics are submerged, indicating that the synchronous extraction transformation method has weak anti-noise ability and cannot effectively separate the signal and noise.

[0162] In the early stage (0~3×10 3 s), the low-frequency energy is diffused, and there is no clear characteristic frequency aggregation; at the late time (5~8×10 3 s), high-frequency energy points are scattered and lack a stable pattern. This indicates that the synchronous extraction transform has insufficient resolution for time-frequency analysis of non-stationary signals, making it difficult to accurately capture the time-frequency variation patterns of the micro-motion characteristics of low-speed, small, and slow targets, affecting the accuracy of subsequent feature extraction.

[0163] Figure 4 The energy distribution advantage of the synchronous extraction transformation and local time-frequency analysis fusion extraction method is significant.

[0164] In terms of frequency, different models show their own concentration characteristics. The energy of the DJI Mavic 2 is highly focused on a specific frequency band, with low energy around 20Hz and 80Hz, and high energy in the adjacent 10-30Hz and 70-90Hz frequency bands, which accurately correspond to key micro-motion characteristics such as blade rotation; the energy of the DJI Phantom is concentrated in the range of 10Hz-20Hz and 30Hz-70Hz, with low energy around 20Hz-30Hz and 80Hz, highlighting the rotation characteristics of the rotor; the DJI M350 has low energy bands between 30Hz-60Hz and 80Hz-100Hz, with high energy in the areas of 10Hz-30Hz and 60Hz-80Hz on both sides, which are related to the rotation of the fuselage rotor; the DJI Inspire 2 has low energy around 20Hz, 50Hz and 80Hz, and high energy in the areas of 30Hz-40Hz and 60Hz-70Hz, clearly showing the characteristic frequency of rotor rotation.

[0165] In terms of time, all models demonstrated excellent stability. The DJI Mavic 2 maintained stable energy distribution across all frequencies from approximately 0.01×10-1 to 0.05×10-1 seconds, while the DJI Phantom, M350, and DJI Inspire 2 observed from 0.01s to 0.05s, unaffected by flight variations, interference, or attitude changes, enabling continuous and stable capture of micro-motion information. Regarding noise suppression, the blue low-energy areas in the images for each model played a significant role, effectively shielding against environmental noise and equipment interference, highlighting the true micro-motion signature energy and providing strong support for accurate identification and tracking of each model during low-altitude monitoring.

[0166] The extraction effect is analyzed and judged by extracting the indicators of its micro-motion characteristics. The results are shown in Table 3:

[0167] Table 3 Statistical results of model extraction indicators

[0168]

[0169] according to Figure 3 and Figure 4The analysis results and the statistical results in Table 3 show that the average leaf length error for the synchronous extraction transform method is 2.32 cm, with the maximum error reaching 2.70 cm for the DJI M350, and an average error rate of approximately 20.11%. The average rotational speed error is 468.84 rpm, with the maximum error reaching 1296.88 rpm for the DJI M350, and an average error rate of approximately 30.98%. This indicates that the synchronous extraction transform method is susceptible to modal aliasing and noise interference in complex signals, resulting in significant feature extraction deviations. The average leaf length error for the synchronous extraction transform combined with local time-frequency analysis extraction method is 0.87 cm, with the maximum error reaching 1.72 cm for the DJI Mavic 2, and an average error rate of approximately 7.50%. The standard deviation of the leaf length error for the synchronous extraction transform combined with local time-frequency analysis extraction method is significantly lower than that for the synchronous extraction transform method, indicating that it performs more stably across different data batches. The average rotational speed error was 27.04 rpm, with the maximum error being 126.47 rpm for the DJI Inspire 2, resulting in an average error rate of 4.64%. This demonstrates the superiority of the synchronous extraction transform and local time-frequency analysis fusion extraction method in separating high-frequency noise from target signals. The improvement in the rotational speed error rate for the DJI M350 was particularly significant, with the error rate dropping from 74.11% to 6.04%.

[0170] The average leaf length error of the synchronous extraction transformation and local time-frequency analysis fusion extraction method is reduced by 12.61% compared with the synchronous extraction transformation method. The average rotational speed error of the synchronous extraction transformation and local time-frequency analysis fusion extraction method is reduced by 26.34% compared with the synchronous extraction transformation method, which fully verifies the ability of the synchronous extraction transformation and local time-frequency analysis fusion extraction method to extract complex micro-motion features.

[0171] Therefore, the present invention provides a method for extracting micro-motion features of low-altitude, slow, and small targets by combining SET and LTFAT. The synchronous extraction transformation and local time-frequency analysis fusion extraction method is significantly superior to a single method in terms of blade length and rotational speed, verifying its high-precision extraction capability for complex micro-motion features. This method is suitable for scenarios such as low-altitude security and drone monitoring. By processing multi-band radar data, it improves monitoring reliability in complex environments and electromagnetic interference. Compared with traditional methods, SET-LTFAT performs better in time-frequency resolution, noise resistance, and multimodal feature separation efficiency, providing technical support for complex radar signal processing.

[0172] 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 by combining SET and LTFAT, characterized by: include: S1. Signal preprocessing: preprocessing the input multi-band radar echo signal including denoising and normalization; S2. Synchronous Extraction Transformation and Local Time-Frequency Analysis Fusion Processing: Applying the synchronous extraction transformation and local time-frequency analysis fusion extraction algorithm to extract the time-frequency features of the pre-processed multi-band radar echo signal, capturing key information including the instantaneous frequency, instantaneous amplitude, and time-frequency distribution of the signal; S3. Feature selection and optimization: perform correlation analysis and feature importance evaluation on the extracted features, remove redundant features and retain the effective ones, and extract the target blade micro-motion features; S4. Output extracted features: output the selected and optimized blade micro-motion features.

2. The method for extracting micro-motion features of slow and small targets by combining SET and LTFAT according to claim 1 is characterized in that: In S2, the specific steps of synchronous extraction transformation and local time-frequency analysis fusion processing are as follows: S21. Synchronous Extraction Transform (SET) processing: Apply the Synchronous Extraction Transform (SET) algorithm to the preprocessed multi-band radar echo data signal to obtain the signal's time-frequency distribution and energy characteristics. The correlation coefficient is derived using the instantaneous frequency position in the time-frequency spectrum to extract key information, including the signal's instantaneous frequency, instantaneous amplitude, and time-frequency distribution. S22. Local Time-Frequency Analysis (LTFAT) Processing: Apply the local time-frequency analysis (LTFAT) technique to the signal after SET processing to extract local features. Adaptively process the local features in the time-frequency domain, record the peak locations, combine time factors, and use the local frequencies of the peak sequences to extract local features of the signal. S23. Fusion the processing results of synchronous extraction transformation and local time-frequency analysis technology to construct a feature extraction fusion method.

3. The method for extracting micro-motion features of low-speed, slow, and small targets by combining SET and LTFAT according to claim 2, characterized in that: In S21, the specific steps of synchronous extraction transformation SET processing include: S211. Construct a time-frequency spectrum function that reflects the time-frequency characteristics of the signal through the convolution of the window function and the signal and its frequency domain representation: calculate the time-frequency spectrum function G(t,ω) of the signal s(t) to analyze the time-frequency characteristics of the signal. The specific expression of the time-frequency spectrum function G(t,ω) is: Where, The signal s(t) is obtained by Fourier transform, g ω The complex conjugate of the Fourier transform of (u) is Among them, the standard expression of the signal s(t) and its frequency domain expression obtained by Fourier transform Used to construct time-spectral function; S212, solve the instantaneous frequency position: the instantaneous frequency ω0(t,ω) is solved by the time-frequency spectrum function G e The first-order derivative of (t, ω) with respect to time t is obtained by combining the synchronous extraction operator δ[ω-ω0(t, ω)], where the specific expression of the instantaneous frequency position is: In the two-dimensional time-frequency plane, the instantaneous frequency is obtained by solving the limit, and the expression is: S213, extracting correlation coefficient: Through synchronous extraction transformation, the correlation coefficient is obtained using the instantaneous frequency position in the time-frequency spectrum, which is expressed as: Te(t,ω)=G e (t,ω)·δ[ω-ω0(t,ω)]; Where δ[ω-ω0(t,ω)] is the synchronization extraction operator, which is used to extract the coefficient corresponding to the instantaneous frequency position in the time-frequency spectrum.

4. The method for extracting micro-motion features of slow, small targets by combining SET and LTFAT according to claim 3, characterized in that: In S211, the time-frequency spectrum function G(t,ω) realizes the window function construction of the target function in the frequency domain by solving the existence of the frequency domain.

5. The method for extracting micro-motion features of slow, small targets by combining SET and LTFAT according to claim 2, characterized in that: In S22, the specific steps of the local time-frequency analysis technology LTFAT processing include: S221. For the discrete time series x(i) (i=1, 2, 3..., n), use LTFAT to solve its peak time series p(i) (i=1, 2, 3..., n). The peak time is expressed as: S222. Calculate the time scale T based on the peak time series p(i) s and peak scale P s , record the peak position; where the time scale T s and peak scale P s The calculation formula is: The peak position is represented by: flag(j)=i, p(i)≠0, j=1,2,…,m; Where a represents the time scale factor, b represents the peak scale factor, and F s represents the sampling frequency, and m represents the number of non-zero values ​​in the peak sequence p(i); S223. The discrete sequence x(i) is combined with the time factor c and the local frequency u of the peak sequence p(i) under (a, b, c) is used to extract the local features of the signal. The calculation formula of the local frequency u of the peak sequence p(i) is: Where, t * is the length of time throughout the sequence; N s is the number of non-zero peaks in the peak sequence p(i).

6. The method for extracting micro-motion features of low-speed, slow, small targets by combining SET and LTFAT according to claim 2, characterized in that: In S23, the specific steps of fusing the processing results of the synchronous extraction transformation and the local time-frequency analysis technology to construct a feature extraction fusion method include: S231. Model the multi-band radar echo data as a function of instantaneous amplitude and instantaneous frequency. Transform and derive the original signal. The expression is: Where, is the derivative with respect to time, g * is the result of Fourier transform of the function; S232. Transform the original signal and calculate the related instantaneous frequency by deriving the formula; wherein the related instantaneous frequency is: S233. Extracting time-frequency domain energy features based on the instantaneous frequency to obtain a related synchronous extraction transformation; wherein the obtained related synchronous extraction transformation is: Te(t,ω)=STFT(t,ω)·δ[ω-ω0(t,ω)]; S234, by applying Taylor expansion at the relevant time point t, the instantaneous amplitude IA function A of the i-th component i (u)=A i (t) and the instantaneous phase IP function And instantaneous phase function expansion, reconstruct the signal And derive its local time-frequency analysis expression; among them, the local time-frequency analysis expression is: S235. Analyze the spectrum energy distribution. The spectrum energy expression is: S236. Design a frequency extraction operator to extract the time-frequency energy peak. The frequency extraction operator expression is:

7. The method for extracting micro-motion features of slow, small targets by combining SET and LTFAT according to claim 6, characterized in that: In S231, the multi-band radar echo signal is the original signal, which is expressed as: Where A i (t) and are the instantaneous amplitude and instantaneous frequency respectively.

8. The method for extracting micro-motion features of low-speed, slow, small targets by combining SET and LTFAT according to claim 1, characterized in that: In S3, the target blade micro-motion features are extracted as follows: S31. Verify the pattern separation conditions and make separability assumptions; S32. Use the frequency extraction operator to directly obtain the instantaneous frequency and amplitude information corresponding to the maximum value of the time-frequency energy, and complete the blade micro-motion feature extraction.

9. The method for extracting micro-motion features of slow, small targets by combining SET and LTFAT according to claim 8, characterized in that: In S31, the spectrum energy is concentrated on the instantaneous frequency trajectory with fuzzy energy distribution.

10. The method for extracting micro-motion features of slow, small targets by combining SET and LTFAT according to claim 8, characterized in that: In S33, the specific steps of the separable assumption are: The frequency spacing between two arbitrary modes satisfies When, according to the zero-point characteristic of the Fourier transform of the window function g * (ω)≤g * (0), reconstruct the frequency extraction operator to verify the pattern separability; where the reconstructed frequency extraction operator expression is: Where i∈{1,2,...,n-1} and Δ represents the distance between two patterns.

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