Low and slow target micro-motion feature extraction method combining set and ltfat

Abstract

The application relates to the field of radar detection, and particularly discloses a low, slow and small target micro-motion feature extraction method combining SET and LTFAT, which comprises the following steps: firstly, synchronously extracting a radar echo signal through SET to obtain the time-frequency distribution and energy characteristics of the signal; secondly, adaptively processing local features in the time-frequency domain through LTFAT to suppress noise and reduce calculation redundancy; and finally, combining multi-element index to quantitatively evaluate the feature extraction result, giving full play to the advantages of the fusion method in complex signal time-frequency analysis, effectively separating and accurately extracting the blade micro-motion features of the target. The application effectively solves the problems that low, slow and small targets are easily disturbed by complex background noise in traditional radar detection and the time-frequency feature extraction precision is not high, and the technical scheme provided by the application is better in time-frequency resolution, noise resistance and feature stability, thereby providing certain technical support for low-altitude security and unmanned aerial vehicle supervision.

Description

Technical Field

[0001] This invention relates to the field of radar detection technology, specifically to a method for extracting micro-motion features of low-speed, small targets by combining SET and LTFAT. Background Technology

[0002] Low-altitude, slow-moving, and small targets play a crucial role in various fields due to their characteristics such as low-altitude flight, slow speed, and small cross-sectional area. In civilian applications, they are deeply integrated into logistics and distribution, film and television shooting, environmental monitoring, and agricultural plant protection; in military applications, they are used for tasks such as reconnaissance and surveillance, electronic warfare, and target drone training. Micro-motion feature extraction is a core component of radar signal processing, with the core objective of accurately capturing minute but recognizable dynamic information of targets from mixed radar echo signals. These features are particularly important for the identification of low-altitude, slow-moving, and small targets (such as drones) and the analysis of target behavior in remote sensing scenarios. High-precision extraction of micro-motion features can reveal the target's motion patterns, thereby optimizing the radar system's detection sensitivity and anti-interference capabilities, while also enhancing the 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 recognizability due to low Doppler frequency shift, and the limitations of traditional algorithms when processing non-stationary, multi-component signals.

[0003] Currently, numerous scholars both domestically and internationally have conducted extensive and in-depth research on target micro-motion feature extraction, achieving a series of fruitful results. Among these, commonly used algorithms include: Short-time Fourier Transform Method, Multi-scale Wavelet Analysis Method, Synchronous Extraction Transformation, Local Time-Frequency Analysis Technique Method, Adaptive Feature Extraction Method, and Hilbert Transform Method, etc. Some scholars have proposed a method combining synchronous extraction transformation and short-time Fourier transform, using signal-to-noise ratio calculation and time-frequency analysis to determine blade micro-motion characteristics; other researchers have utilized improved synchronous extraction transformation methods to process and analyze instantaneous features.

[0004] Currently, synchronous extraction and transformation methods offer high accuracy in instantaneous frequency extraction and strong algorithm interpretability, but they still suffer from modal aliasing and the tendency to lose high-frequency features. Local time-frequency analysis techniques have strong local feature capture capabilities and high adaptability, but they also face challenges such as high computational complexity and difficulty in feature quantization.

[0005] Therefore, we developed a method for extracting micro-motion features of slow, small targets by combining SET and LTFAT, to achieve more accurate and efficient feature extraction. Summary of the Invention

[0006] To address the aforementioned problems in existing technologies, this invention proposes a method for extracting micro-motion features of slow, 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, this invention proposes a method for extracting micro-motion features of slow, small targets by combining SET and LTFAT, comprising:

[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: The synchronous extraction transformation and local time-frequency analysis fusion extraction algorithm is applied to extract time-frequency features from the preprocessed 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: The extracted features are subjected to correlation analysis and feature importance assessment. Redundant features are removed and effective parts are retained to 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 the synchronous extraction transformation and local time-frequency analysis fusion processing are as follows:

[0013] S21. Synchronous Extraction and Transform (SET) Processing: The Synchronous Extraction and Transform (SET) algorithm is applied to the preprocessed multi-band radar echo data signal to obtain the time-frequency distribution and energy characteristics of the signal. The correlation coefficient is obtained by using the instantaneous frequency position in the time spectrum, and key information including the instantaneous frequency, instantaneous amplitude, and time-frequency distribution of the signal is extracted.

[0014] S22. Local Time-Frequency Analysis (LTFAT) Processing: The LTFAT technique is applied to the signal after SET processing to extract local features. Adaptive processing is performed on the local features in the time-frequency domain, the location of the peak is recorded, time factors are combined, and the local frequency of the peak sequence is used to extract the local features of the signal.

[0015] S23. The processing results of synchronous extraction transformation and local time-frequency analysis techniques are integrated to construct a feature extraction fusion method.

[0016] Preferably, in S21, the specific steps of synchronous extraction transformation SET processing include:

[0017] S211. Construct a time-frequency spectrum function reflecting the time-frequency characteristics of the signal by convolving the signal with a window function and its frequency domain representation: Calculate the time-frequency spectrum function of the signal s(t). To analyze the time-frequency characteristics of a signal, the time-frequency spectrum function. The specific expression is:

[0018] ;

[0019] In the formula, It is a signal Obtained through Fourier transform The complex conjugate of the Fourier transform is ;

[0020] Among them, the standard expression of signal s(t) and its frequency domain expression obtained by Fourier transform are given. It was used to construct the time-spectrum function;

[0021] S212. Solving for the instantaneous frequency position: instantaneous frequency By solving the instantaneous frequency-correlated time-spectrum function The first derivative with respect to time t, combined with the synchronization extraction operator. The specific expression for the instantaneous frequency position is obtained as follows:

[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 the correlation coefficient: Through synchronous extraction transformation, the correlation coefficient is obtained using the instantaneous frequency position in the time spectrum, expressed as:

[0026] ;

[0027] In the formula, The synchronous extraction operator is used to extract coefficients corresponding to the instantaneous frequency position in the time spectrum.

[0028] Preferably, in S211, the time-frequency spectrum function G(t,ω) is used to construct the window function of the objective function in the frequency domain by solving for its existence in the frequency domain.

[0029] Preferably, in S22, the specific steps of the Local Time-Frequency Analysis (LTFAT) process include:

[0030] S221, For discrete time series , The peak time series was solved using LTFAT. , The peak time is expressed as:

[0031] ;

[0032] S222, Based on the peak time series Calculate the time scale T s and peak scale P s Record the location of the peak; where the time scale T s and peak scale P s The calculation formula is:

[0033] ;

[0034] ;

[0035] The location of the peak value is indicated as follows: ;

[0036] In the formula, 'a' represents the time scale factor. Represents the peak scaling factor. Represents the sampling frequency. Represents peak sequence The number of non-zero values;

[0037] S223, Discrete Sequence By combination Time factor, and utilize Peak sequence below Local frequency Extracting local features of the signal; among which, peak sequence Local frequency The calculation formula is:

[0038] ;

[0039] In the formula, It is the duration of the sequence; It is a peak sequence The number of non-zero peak values.

[0040] Preferably, in S23, the specific steps for constructing the feature extraction fusion method by fusing the processing results of synchronous extraction transformation and local time-frequency analysis techniques include:

[0041] S231. Model the multi-band radar echo data as a function of instantaneous amplitude and instantaneous frequency. Transform the original signal and find its derivative. The expression is:

[0042] ;

[0043] In the formula, It is the derivative with respect to time. It is the result of the Fourier transform of the function;

[0044] S232. The relevant instantaneous frequency is calculated based on the transformation and differentiation formula of the original signal; where the relevant instantaneous frequency is:

[0045] ;

[0046] S233. Extract time-frequency domain energy features based on instantaneous frequency to obtain relevant synchronous extraction transform; wherein, the obtained relevant synchronous extraction transform is:

[0047] ;

[0048] S234, through relevant time points Applying Taylor expansion, the first Instantaneous amplitude of the component function and instantaneous phase IP function And instantaneous phase function expansion, reconstructing the signal And its local time-frequency analysis expression is derived; where, the local time-frequency analysis expression is:

[0049] ;

[0050] S235. Analyzing the spectral energy distribution, the expression for its spectral energy is as follows:

[0051] ;

[0052] S236. Design a frequency extraction operator to extract the time-frequency energy peak value. The expression for the frequency extraction operator is as follows:

[0053] .

[0054] Preferably, in S231, the multi-band radar echo signal is the original signal, which is represented as follows:

[0055] ;

[0056] In the formula, and These are instantaneous amplitude and instantaneous frequency, respectively.

[0057] Preferably, in S3, the extraction of the target blade micro-motion features specifically involves:

[0058] S31. Verify the pattern separation conditions and make the separability assumption;

[0059] S32. The instantaneous frequency and amplitude information corresponding to the maximum time-frequency energy value are directly obtained by using the frequency extraction operator to complete the extraction of blade micro-motion features.

[0060] Preferably, in S31, the spectral energy is concentrated on the instantaneous frequency trajectory with an ambiguous energy distribution.

[0061] Preferably, in S31, the specific steps of the separability assumption are as follows:

[0062] The frequency spacing between two arbitrary modes satisfies At that time, based on the zero-point characteristics of the Fourier transform of the window function... The reconstructed frequency extraction operator is used to verify mode separability; the expression for the reconstructed frequency extraction operator is as follows:

[0063] ;

[0064] In the formula, , This represents the distance between two patterns.

[0065] Therefore, this invention proposes a method for extracting micro-motion features of slow, small targets by combining SET and LTFAT, with the following beneficial effects:

[0066] (1) The fusion strategy of this invention combines the global time-frequency characteristics of SET with the local detail capture capability of LTFAT, effectively suppressing noise interference and improving the feature stability under complex signals;

[0067] (2) This invention uses local feature adaptive processing and frequency extraction operator to directly locate the maximum time-frequency energy, reduce redundant calculations, and at the same time ensure the accurate extraction of blade micro-motion features;

[0068] (3) This invention provides reliable technical support for low-altitude security and drone supervision, and its feature stability meets the needs of actual scenarios.

[0069] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0070] Figure 1 This is a flowchart of the extraction process for the low-speed, small-target micro-motion feature extraction method combining SET and LTFAT of the present invention.

[0071] Figure 2 These are processed images of DJI Mavic 2, DJI Phantom, DJI M350, and DJI Inspire 2. Among them, (a) is a processed image of DJI Mavic 2, (b) is a processed image of DJI Phantom, (c) is a processed image of DJI M350, and (d) is a processed image of DJI Inspire 2.

[0072] Figure 3 These are the energy distribution maps of DJI Mavic 2, DJI Phantom, DJI M350 and DJI Inspire 2 SET. Among them, (a) is the energy distribution map of DJI Mavic 2 SET, (b) is the energy distribution map of DJI Phantom SET, (c) is the energy distribution map of DJI M350 SET, and (d) is the energy distribution map of DJI Inspire 2 SET.

[0073] Figure 4 These are the SET-LTFAT power distribution maps for DJI Mavic 2, DJI Phantom, DJI M350, and DJI Inspire 2. Among them, (a) is the SET-LTFAT power distribution map for DJI Mavic 2, (b) is the SET-LTFAT power distribution map for DJI Phantom, (c) is the SET-LTFAT power distribution map for DJI M350, and (d) is the SET-LTFAT power distribution map for DJI Inspire 2. Detailed Implementation

[0074] To make the technical solutions, advantages, and objectives of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below. The described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without creative effort are within the protection scope of this application.

[0075] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0076] like Figure 1 As shown, the present invention provides a method for extracting micro-motion features of slow, small targets by combining SET and LTFAT, comprising:

[0077] S1. Signal preprocessing: Preprocessing the input multi-band radar echo signal, including denoising and normalization.

[0078] S2. Synchronous Extraction Transformation and Local Time-Frequency Analysis Fusion Processing: The synchronous extraction transformation and local time-frequency analysis fusion extraction algorithm is applied to extract time-frequency features from the preprocessed multi-band radar echo signal, capturing key information including the instantaneous frequency, instantaneous amplitude, and time-frequency distribution of the signal;

[0079] In S2, the specific steps of synchronous extraction transformation and local time-frequency analysis fusion processing are as follows:

[0080] S21. Synchronous Extraction and Transform (SET) Processing: The Synchronous Extraction and Transform (SET) algorithm is applied to the preprocessed multi-band radar echo data signal to obtain the time-frequency distribution and energy characteristics of the signal. The correlation coefficient is obtained by using the instantaneous frequency position in the time spectrum, and key information including the instantaneous frequency, instantaneous amplitude, and time-frequency distribution of the signal is extracted.

[0081] In S21, the specific steps of the synchronous extraction transform SET processing include:

[0082] S211. Construct a time-frequency spectrum function reflecting the time-frequency characteristics of the signal by convolving the signal with a window function and its frequency domain representation: Calculate the time-frequency spectrum function of the signal s(t). To analyze the time-frequency characteristics of the signal;

[0083] Signal The standard expression is:

[0084] ;

[0085] In the formula, Represents the basic window function;

[0086] make The instantaneous frequency-correlated frequency spectrum function is obtained by Passevar's theorem. The expression for the time-frequency spectrum function is:

[0087] ;

[0088] In the formula, It is a signal Obtained through Fourier transform The complex conjugate of the Fourier transform is ;

[0089] The standard expression of signal s(t) and its frequency domain expression obtained by Fourier transform are used to construct the time-spectrum function;

[0090] In S211, the time-frequency spectrum function By solving for the existence in the frequency domain, the window function of the objective function is constructed in the frequency domain, specifically as follows:

[0091] make We can obtain:

[0092] ;

[0093] ;

[0094] make Introducing a signal frequency And indicate the relevant frequency domain By constructing the window function of the objective function in the frequency domain, the instantaneous frequency-correlated frequency spectrum function is obtained as follows:

[0095] ;

[0096] In the formula, when the instantaneous frequency is correlated, the spectrum function is... middle At that time, it achieves its maximum correlation amplitude. ;

[0097] S212. Solving for the instantaneous frequency position: instantaneous frequency By solving the instantaneous frequency-correlated time-spectrum function The first derivative with respect to time t, combined with the synchronization extraction operator. The specific expression for the instantaneous frequency position is obtained as follows:

[0098] ;

[0099] In the two-dimensional time-frequency plane, the instantaneous frequency is obtained by solving the limit, and the expression is:

[0100] ;

[0101] S213. Extracting the correlation coefficient: Through synchronous extraction transformation, the correlation coefficient is obtained using the instantaneous frequency position in the time spectrum, expressed as:

[0102] ;

[0103] In the formula, The synchronous extraction operator is used to extract coefficients corresponding to the instantaneous frequency position in the time spectrum.

[0104] S22. Local Time-Frequency Analysis (LTFAT) Processing: The LTFAT technique is applied to the signal after SET processing to extract local features. Adaptive processing is performed on the local features in the time-frequency domain, the location of the peak is recorded, time factors are combined, and the local frequency of the peak sequence is used to extract the local features of the signal.

[0105] In S22, the specific steps of the Local Time-Frequency Analysis (LTFAT) technique include:

[0106] S221, For discrete time series , The peak time series was solved using LTFAT. , The peak time is expressed as:

[0107] ;

[0108] S222, Based on the peak time series Calculate the time scale T s and peak scale P s Record the location of the peak; where the time scale T s and peak scale P s The calculation formula is:

[0109] ;

[0110] ;

[0111] In the peak sequence, The corresponding values ​​for local peak values, and the location of the peak value are represented as follows: ;

[0112] In the formula, 'a' represents the time scale factor. Represents the peak scaling factor. Represents the sampling frequency. Represents peak sequence The number of non-zero values;

[0113] Since there are time intervals between adjacent non-zero peaks, the number of time intervals is . This Each time interval can be combined to form a new sequence, the expression of which is:

[0114] ;

[0115] For peak sequences Time interval scale Defined as:

[0116] ;

[0117] S223, Discrete Sequence By combination Time factor, and utilize Peak sequence below Local frequency Extracting local features of the signal; among which, peak sequence Local frequency The calculation formula is:

[0118] ;

[0119] In the formula, It is the duration of the sequence; It is a peak sequence The number of non-zero peak values.

[0120] S23. The processing results of synchronous extraction transformation and local time-frequency analysis techniques are integrated to construct a feature extraction fusion method.

[0121] In S23, the specific steps for constructing a feature extraction fusion method by integrating the processing results of synchronous extraction transformation and local time-frequency analysis techniques include:

[0122] S231. Model the multi-band radar echo data as a function of instantaneous amplitude and instantaneous frequency. Transform the original signal and find its derivative. The expression is:

[0123] ;

[0124] In the formula, It is the derivative with respect to time. It is the result of the Fourier transform of the function;

[0125] In S231, the multi-band radar echo signal is the raw signal, which is represented as follows:

[0126] ;

[0127] In the formula, and These are instantaneous amplitude and instantaneous frequency, respectively.

[0128] S232. The relevant instantaneous frequency is calculated based on the transformation and differentiation formula of the original signal; where the relevant instantaneous frequency is:

[0129] ;

[0130] S233. Extract time-frequency domain energy features based on instantaneous frequency to obtain relevant synchronous extraction transform; wherein, the obtained relevant synchronous extraction transform is:

[0131] ;

[0132] S234, through relevant time points Applying Taylor expansion, the first Instantaneous amplitude of the component function and instantaneous phase IP function And instantaneous phase function expansion, reconstructing the signal And its local time-frequency analysis expression is derived; where, the local time-frequency analysis expression is:

[0133] ;

[0134] S235. Analyzing the spectral energy distribution, the expression for its spectral energy is as follows:

[0135] ;

[0136] S236. Design a frequency extraction operator to extract the time-frequency energy peak value. The expression for the frequency extraction operator is as follows:

[0137] .

[0138] S3. Feature selection and optimization: The extracted features are subjected to correlation analysis and feature importance assessment. Redundant features are removed and effective parts are retained to extract the target blade micro-motion features.

[0139] In S3, the specific extraction of the target's blade micro-motion features is as follows:

[0140] S31. Verify the pattern separation conditions and make the separability assumption;

[0141] S32. The instantaneous frequency and amplitude information corresponding to the maximum time-frequency energy value are directly obtained by using the frequency extraction operator to complete the extraction of blade micro-motion features.

[0142] In S31, the spectral energy is concentrated on the instantaneous frequency trajectory with an fuzzy energy distribution.

[0143] In S31, the specific steps of the separability assumption are as follows:

[0144] The frequency spacing between two arbitrary modes satisfies At that time, based on the zero-point characteristics of the Fourier transform of the window function... The reconstructed frequency extraction operator is used to verify mode separability; the expression for the reconstructed frequency extraction operator is as follows:

[0145] ;

[0146] In the formula, , This represents the distance between two patterns.

[0147] S4. Output Extracted Features: Output the selected and optimized blade micro-motion features.

[0148] Experiments and analysis were conducted on the proposed method for extracting micro-motion features of slow, small targets using a combination of SET and LTFAT.

[0149] The low-speed, small target detection dataset published in the Journal of Radar was used for simulation analysis, employing target data with a modulation bandwidth of 100MHz and a modulation period of 0.3ms in the Ku+L band. This dataset contains five types of low-speed, small targets, including the DJI Mavic 2, DJI Phantom, DJI M350, DJI Inspire 2, and DJI M600.

[0150] Simulation experiments were conducted using detection data from DJI Mavic 2, DJI Phantom, DJI M350, and DJI Inspire 2. Relevant information about the selected targets is shown in Table 1.

[0151] Table 1. Information related to the selected low-slow-speed small targets

[0152]

[0153] For the selected low-speed, small target, the data waveform after DC removal and range dimension processing is as follows: Figure 2 As shown.

[0154] The experiment used leaf length and rotational speed as evaluation indicators in the micro-motion characteristics of the blade to assess the feature extraction performance of the synchronous extraction transformation method and the fusion extraction method of synchronous extraction transformation and local time-frequency analysis. The formula for calculating leaf length is as follows:

[0155] ;

[0156] The formula for calculating rotational speed is:

[0157] ;

[0158] In the formula, It is the highest Doppler frequency. It's the wavelength. It is the flashing frequency of the blades. It's the rotational speed. It is the leaf that is long. This is the radar elevation angle.

[0159] The blade length and rotational speed parameters for these four types of low-speed, small targets are shown in Table 2:

[0160] Table 2 Technical parameters of UAVs

[0161]

[0162] The results of synchronous extraction and transformation, and the fusion extraction of synchronous extraction and transformation with local time-frequency analysis for four types of low, slow, and small targets are as follows: Figure 3 , Figure 4 As shown.

[0163] Figure 3 All synchronous extraction and transformation methods suffer from the same problem: energy distribution is relatively dispersed. This applies across the entire time period (0~8×10⁻⁶). 3s) exhibits a broad distribution, without forming a concentrated cluster targeting the signal; frequency dimension (0~4.5×10 3 At frequencies above 100 Hz, there is no obvious main energy peak, and at low frequencies (0~1.5×10⁻⁶), there is no significant main energy peak. 3 Hz) and high frequency (3×10 3 ~4.5×10 3 Scattered high-energy points appeared in the Hz region, but their distribution was chaotic, reflecting the insufficient ability of the synchronous extraction and transformation method to localize the signal in time and frequency, making it difficult to focus on the micro-motion characteristics of the target.

[0164] The color bars indicate a large dynamic range of energy, with continuous high-energy bands in the low-frequency range, which may be noise interference. Although there are local high-energy points in the high-frequency range, they are not clearly distinguishable from noise energy, and the micro-motion characteristics of the target are submerged. This indicates that the synchronous extraction and transformation method has weak noise resistance and cannot effectively separate the signal from the noise.

[0165] In the early stages of time (0~3×10) 3 In the later stages (5~8×10), low-frequency energy is diffused, with no clear characteristic frequency concentration; 3 The 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 features of low, slow, and small targets, thus affecting the accuracy of subsequent feature extraction.

[0166] Figure 4 The energy distribution advantage of the fusion extraction method combining synchronous extraction transformation and local time-frequency analysis is significant.

[0167] In terms of frequency, different models exhibit their own concentrated characteristics. The DJI Mavic 2's energy is highly focused on specific frequency bands, with lower energy around 20Hz and 80Hz, and higher energy in the adjacent 10-30Hz and 70-90Hz bands, precisely corresponding to key micro-motion characteristics such as blade rotation; the DJI Phantom's energy is concentrated in the 10Hz-20Hz and 30Hz-70Hz ranges, with lower energy around 20Hz-30Hz and 80Hz, highlighting rotor rotation characteristics; the DJI M350 has a low-energy band between 30Hz-60Hz and 80Hz-100Hz, with higher energy in the 10Hz-30Hz and 60Hz-80Hz regions on both sides, related to rotor rotation; the DJI Inspire 2 has lower energy around 20Hz, 50Hz, and 80Hz, and higher energy in the 30Hz-40Hz and 60Hz-70Hz regions, clearly showing the characteristic frequencies of rotor rotation.

[0168] In terms of time, all models demonstrated good stability. The DJI Mavic 2's performance improved from approximately 0.01 × 10⁻⁶ seconds. -1 ~0.05×10 -1Within the observation period of 0.01s to 0.05s, the energy distribution of each frequency remained stable for the DJI Phantom, M350, and DJI Inspire 2, unaffected by flight changes, interference, or attitude variations, enabling them to continuously and stably capture micro-motion information. Regarding noise suppression, the blue low-energy areas in the images of each aircraft played a crucial role, effectively shielding environmental noise and equipment interference, highlighting the true micro-motion energy characteristics, and providing strong support for accurate identification and tracking of each aircraft in low-altitude monitoring.

[0169] The extraction effect was analyzed and judged by extracting indicators of its micro-motion characteristics. The results are shown in Table 3:

[0170] Table 3 Statistical Results of Model Extracted Indicators

[0171]

[0172] according to Figure 3 and Figure 4 The analysis results and the statistical results in Table 3 show that the average leaf length error of the synchronous extraction and transformation method is 2.32 cm, with the maximum error reaching 2.70 cm on the DJI M350, and an average error rate of approximately 20.11%. The average rotational speed error is 468.84 r / min, with the maximum error reaching 1296.88 r / min on the DJI M350, and an average error rate of approximately 30.98%. This indicates that the synchronous extraction and transformation method is susceptible to mode mixing and noise interference in complex signals, leading to significant feature extraction deviations. In contrast, the average leaf length error of the fusion extraction method combining synchronous extraction and transformation with local time-frequency analysis is 0.87 cm, with the maximum error of 1.72 cm on the DJI Mavic 2, and an average error rate of approximately 7.50%. The standard deviation of the leaf length error of the fusion extraction method combining synchronous extraction and transformation with local time-frequency analysis is significantly lower than that of the synchronous extraction and transformation method, indicating that it performs more stably across different data batches. The average rotational speed error was 27.04 r / min, with the largest error being 126.47 r / min for the DJI Inspire 2, and the average error rate was 4.64%. This demonstrates the advantages of the fusion extraction method of synchronous extraction transformation and local time-frequency analysis in separating high-frequency noise from the target signal, especially for the DJI M350, where the rotational speed error rate was reduced from 74.11% to 6.04%, showing a particularly significant improvement.

[0173] The average leaf length error of the fusion extraction method combining synchronous extraction transformation and local time-frequency analysis was reduced by 12.61% compared with that of the synchronous extraction transformation method, and the average rotational speed error of the fusion extraction method was reduced by 26.34% compared with that of the synchronous extraction transformation method. This fully verifies the extraction capability of the fusion extraction method combining synchronous extraction transformation and local time-frequency analysis for complex micro-motion features.

[0174] Therefore, this invention provides a method for extracting micro-motion features of low-altitude, slow-moving, small targets by combining SET and LTFAT. The fusion extraction method of synchronous extraction transformation and local time-frequency analysis significantly outperforms single methods in terms of blade length and rotational speed, verifying its high-precision extraction capability for complex micro-motion features. This method is applicable to scenarios such as low-altitude security and UAV surveillance, improving monitoring reliability under complex environments and electromagnetic interference through multi-band radar data processing. Compared with traditional methods, SET-LTFAT performs better in time-frequency resolution, noise resistance, and multi-modal feature separation efficiency, providing technical support for complex radar signal processing.

[0175] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions 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, small targets by combining SET and LTFAT, characterized in that, 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: The synchronous extraction transformation and local time-frequency analysis fusion extraction algorithm is applied to extract time-frequency features from the preprocessed 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: The extracted features are subjected to correlation analysis and feature importance assessment. Redundant features are removed and effective parts are retained to extract the target blade micro-motion features. S4. Output Extracted Features: Output the selected and optimized blade micro-motion features; In S2, the specific steps of synchronous extraction transformation and local time-frequency analysis fusion processing are as follows: S21. Synchronous Extraction and Transform (SET) Processing: The Synchronous Extraction and Transform (SET) algorithm is applied to the preprocessed multi-band radar echo data signal to obtain the time-frequency distribution and energy characteristics of the signal. The correlation coefficient is obtained by using the instantaneous frequency position in the time spectrum, and key information including the instantaneous frequency, instantaneous amplitude, and time-frequency distribution of the signal is extracted. S22. Local Time-Frequency Analysis (LTFAT) Processing: The LTFAT technique is applied to the signal after SET processing to extract local features. Adaptive processing is performed on the local features in the time-frequency domain, the location of the peak is recorded, time factors are combined, and the local frequency of the peak sequence is used to extract the local features of the signal. S23. The processing results of synchronous extraction transformation and local time-frequency analysis techniques are integrated to construct a feature extraction fusion method.

2. The method for extracting micro-motion features of slow, small targets by combining SET and LTFAT according to claim 1, characterized in that, In S21, the specific steps of the synchronous extraction transform SET processing include: S211. Construct a time-frequency spectrum function reflecting the time-frequency characteristics of the signal by convolving the signal with a window function and its frequency domain representation: Calculate the time-frequency spectrum function of the signal s(t). To analyze the time-frequency characteristics of a signal, the time-frequency spectrum function. The specific expression is: ； In the formula, It is a signal Obtained through Fourier transform The complex conjugate of the Fourier transform is ; Among them, the standard expression of signal s(t) and its frequency domain expression obtained by Fourier transform are given. It was used to construct the time-spectrum function; S212. Solving for the instantaneous frequency position: instantaneous frequency By solving the instantaneous frequency-correlated time-spectrum function The first derivative with respect to time t, combined with the synchronization extraction operator. The specific expression for the instantaneous frequency position is obtained as follows: ； In the two-dimensional time-frequency plane, the instantaneous frequency is obtained by solving the limit, and the expression is: ； S213. Extracting the correlation coefficient: Through synchronous extraction transformation, the correlation coefficient is obtained using the instantaneous frequency position in the time spectrum, expressed as: ； In the formula, The synchronous extraction operator is used to extract coefficients corresponding to the instantaneous frequency position in the time spectrum.

3. The method for extracting micro-motion features of slow, small targets by combining SET and LTFAT according to claim 2, characterized in that, In S211, the time-frequency spectrum function G(t,ω) is used to construct the window function of the objective function in the frequency domain by solving for its existence in the frequency domain.

4. The method for extracting micro-motion features of slow, small targets by combining SET and LTFAT according to claim 1, characterized in that, In S22, the specific steps of the Local Time-Frequency Analysis (LTFAT) technique include: S221, For discrete time series , The peak time series was solved using LTFAT. , The peak time is expressed as: ； S222, Based on the peak time series Calculate the time scale T s and peak scale P s Record the location of the peak; where the time scale T s and peak scale P s The calculation formula is: ； ； The location of the peak value is indicated as follows: ; In the formula, 'a' represents the time scale factor. Represents the peak scaling factor. Represents the sampling frequency. Represents peak sequence The number of non-zero values; S223, Discrete Sequence By combination Time factor, and utilize Peak sequence below Local frequency Extracting local features of the signal; among which, peak sequence Local frequency The calculation formula is: ； In the formula, It is the duration of the sequence; It is a peak sequence The number of non-zero peak values.

5. The method for extracting micro-motion features of slow, small targets by combining SET and LTFAT according to claim 1, characterized in that, In S23, the specific steps for constructing a feature extraction fusion method by integrating the processing results of synchronous extraction transformation and local time-frequency analysis techniques include: S231. Model the multi-band radar echo data as a function of instantaneous amplitude and instantaneous frequency. Transform the original signal and find its derivative. The expression is: ； In the formula, It is the derivative with respect to time. It is the result of the Fourier transform of the function; S232. The relevant instantaneous frequency is calculated based on the transformation and differentiation formula of the original signal; where the relevant instantaneous frequency is: ； S233. Extract time-frequency domain energy features based on instantaneous frequency to obtain relevant synchronous extraction transform; wherein, the obtained relevant synchronous extraction transform is: ； S234, through relevant time points Applying Taylor expansion, the first Instantaneous amplitude of the component function and instantaneous phase IP function And instantaneous phase function expansion, reconstructing the signal And its local time-frequency analysis expression is derived; where, the local time-frequency analysis expression is: ； S235. Analyzing the spectral energy distribution, the expression for its spectral energy is as follows: ； S236. Design a frequency extraction operator to extract the time-frequency energy peak value. The expression for the frequency extraction operator is as follows: 。 6. The method for extracting micro-motion features of slow, small targets by combining SET and LTFAT according to claim 5, characterized in that, In S231, the multi-band radar echo signal is the raw signal, which is represented as follows: ； In the formula, and These are instantaneous amplitude and instantaneous frequency, respectively.

7. The method for extracting micro-motion features of slow, small targets by combining SET and LTFAT according to claim 1, characterized in that, In S3, the specific extraction of the target's blade micro-motion features is as follows: S31. Verify the pattern separation conditions and make the separability assumption; S32. The instantaneous frequency and amplitude information corresponding to the maximum time-frequency energy value are directly obtained by using the frequency extraction operator to complete the extraction of blade micro-motion features.

8. The method for extracting micro-motion features of slow, small targets by combining SET and LTFAT according to claim 7, characterized in that, In S31, the spectral energy is concentrated on the instantaneous frequency trajectory with an fuzzy energy distribution.

9. The method for extracting micro-motion features of slow, small targets by combining SET and LTFAT according to claim 7, characterized in that, In S31, the specific steps of the separability assumption are as follows: The frequency spacing between two arbitrary modes satisfies At that time, based on the zero-point characteristics of the Fourier transform of the window function... The reconstructed frequency extraction operator is used to verify mode separability; the expression for the reconstructed frequency extraction operator is as follows: ； In the formula, , This represents the distance between two patterns.

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