Low, slow and small target micro-motion feature extraction algorithm based on stft-lstm

Abstract

The application relates to the technical field of radars, and particularly discloses a low, slow and small target micro-motion feature extraction algorithm based on STFT-LSTM. The original signal is converted into a time-frequency domain representation through STFT, and a feature matrix with time sequence correlation is constructed; a bidirectional LSTM network is introduced to model time sequence dependence, adaptive fusion of a feature space is realized in combination with a multi-head attention mechanism, and the calculation efficiency is significantly improved through a learnable weight distribution strategy. A feature visualization analysis module is designed to verify the model performance, the mapping relationship between the feature parameters and the classification accuracy is quantitatively evaluated, and finally a dynamic optimization closed loop is formed. The technical scheme of the application provides a new technical path for multi-modal radar echo signal processing, effectively improves the precision and efficiency of feature extraction, and is suitable for target recognition tasks in a wideband complex electromagnetic environment.

Description

Technical Field

[0001] This invention relates to the field of radar technology, specifically to an algorithm for extracting micro-motion features of low-speed, small targets based on STFT-LSTM. Background Technology

[0002] With the widespread application and popularity of targets such as drones, micro-aircraft, and birds, the detection and identification of low-altitude, slow-speed, and small targets has become a pressing problem in the field of radar technology. These targets typically fly at altitudes below 500 meters, speeds below 50 meters per second, and have radar cross-sections less than 1 square meter. Their echo signals are easily submerged by background noise in complex terrain, urban areas, and weather clutter. Traditional radar systems rely on target motion parameters for detection, but for low-altitude, slow-speed, and small targets, their low maneuverability and weak reflection characteristics result in a false alarm rate exceeding 30% for conventional methods. However, the micro-motion characteristics of low-altitude, slow-speed, and small targets provide them with unique identifiers. These targets often possess unique micro-motion characteristics (such as rotor vibration and oscillation), which modulate the phase and frequency of the radar echo signal, forming distinctive micro-Doppler features. Extracting and analyzing these micro-motion features can provide crucial information for target classification and threat assessment. Therefore, micro-motion feature extraction technology has become the core research focus for improving the detection and identification capabilities of low-altitude, slow-speed, and small targets.

[0003] The development of micro-motion feature extraction algorithms has consistently revolved around two main lines: time-frequency analysis and data-driven modeling. Scholars both domestically and internationally have conducted extensive research in this area, achieving significant results. Among traditional time-frequency analysis methods, STFT is widely used due to its simplicity and clear physical meaning. STFT performs Fourier transform on signal segments using a sliding time window, generating a time-spectrum graph to characterize the time-varying properties of the signal.

[0004] However, its time-frequency resolution is limited by a fixed window function, making it difficult to simultaneously capture both high-frequency transients and low-frequency gradual changes. To overcome this limitation, wavelet transform improves resolution flexibility through adaptive time window adjustment, but the selection of basis functions depends on prior knowledge and has limited ability to represent complex micro-motion patterns. Furthermore, although the Wigner-Ville distribution has high time-frequency clustering, its application in multi-component signals is limited by severe interference from cross terms.

[0005] In recent years, the rise of deep learning technology has driven the rapid development of data-driven methods. LSTM captures long-term dependencies in time series through gating mechanisms, enabling the direct learning of micro-motion patterns from raw echo signals. Research has proposed a method using LSTM networks to capture wind characteristics and extract ultra-short-term micro-motion features; a fusion algorithm combining STFT and Q operators has been proposed, using algorithm improvement rate extraction and time-frequency graph analysis to determine power load characteristics; and other research has focused on improving the STFT algorithm to achieve synchronous compression.

[0006] Currently, the STFT algorithm, in terms of feature extraction, can perform piecewise Fourier transform on signals through window functions to achieve time-frequency analysis and has a certain time-frequency localization analysis capability, displaying the distribution of signal frequency components on the time axis. However, its window function is fixed, making it difficult to simultaneously meet the analysis needs of high- and low-frequency signals in terms of time and frequency resolution. It has low time resolution when processing high-frequency signals and insufficient frequency resolution when processing low-frequency signals. Furthermore, it is not effective in processing non-stationary signals, and time-frequency ambiguity occurs when the signal frequency changes rapidly, which is not conducive to accurately extracting signal features.

[0007] LSTM, as a recurrent neural network, relies on the collaborative work of forget gates, input gates, and output gates to effectively capture dependencies in long-term time-series data and possesses strong memory capabilities when processing time-series data. However, its network structure is complex, requiring a large amount of computation and time for training, placing high demands on computing resources. It is also prone to overfitting when processing high-dimensional data. When the number of samples is limited, the model is prone to overlearning noise and details in the training data, resulting in poor generalization ability and difficulty in accurately extracting the subtle movement features of the target.

[0008] Therefore, in order to improve the accuracy and efficiency of feature extraction, it is urgent to develop a feature extraction algorithm for low-speed, small targets based on STFT-LSTM, so as to provide a new technical path for multi-mode radar echo signal processing. Summary of the Invention

[0009] To address the aforementioned problems in existing technologies, this invention proposes a feature extraction algorithm for low-speed, small-target micro-motion based on STFT-LSTM, which significantly improves feature extraction accuracy and reduces noise interference.

[0010] To achieve the above objectives, this invention proposes a feature extraction algorithm for slow, small targets based on STFT-LSTM, comprising:

[0011] S1. Preprocessing and framing the signal: Perform adaptive filtering or wavelet threshold denoising, normalization, and framing windowing operations in sequence to generate overlapping framed signals. The framing parameters are set to window length N=256 and frame shift step length H=64, and a Blackman window is applied.

[0012] S2. Time-frequency transformation processing: The STFT-LSTM combined model is applied to extract time-frequency features. The short-time Fourier transform is performed frame by frame on the framed signal to calculate the time-frequency matrix, extract the logarithmic amplitude spectrum, and perform adaptive histogram equalization to enhance the time-frequency energy distribution of the micro-motion components.

[0013] S3. Bidirectional temporal modeling: The time-frequency matrix is ​​sliced ​​according to time frames to construct a temporal feature sequence. The constructed temporal feature sequence is input into a bidirectional LSTM network for temporal encoding. A forward LSTM is used to capture the forward temporal evolution pattern, and a backward LSTM is used to learn the inverse context dependency. The high-order temporal feature sequence is generated by splicing and fusing the hidden states.

[0014] S4. Multi-head attention feature fusion: A 4-head attention mechanism is used to perform multi-view feature fusion on the LSTM hidden state sequence. The sequence is split into multiple subspaces, and attention weights are calculated and weighted aggregated. A 256-dimensional compact feature vector is generated through residual connection.

[0015] S5. Dynamic optimization control: The fused features are input into the SVM classifier for 5-fold cross-validation to calculate the average classification accuracy; at the same time, the high-dimensional features are projected to the two-dimensional space through t-SNE, and the Jensen-Shannon divergence between categories is calculated to evaluate the feature separability.

[0016] S6. Dynamic parameter optimization: Iteratively adjust the parameters based on the evaluation results. The adjustment parameters include shortening the STFT window length, increasing the number of LSTM layers or attention heads, and adding 1D convolution after the attention layer for local feature compression. Repeat steps S2-S5 until the evaluation indicators of energy concentration EC and Doppler frequency DR are met.

[0017] S7. Structured Output: The optimized feature vectors are organized into a matrix according to the sample dimensions. After adding metadata tags such as timestamps and target IDs, they are stored as HDF5 format files. PCA dimensionality reduction is then performed on the feature dimensions to generate the final low-dimensional feature set.

[0018] Preferably, in S1, the steps of preprocessing and framing the signal are as follows:

[0019] S11. Perform adaptive filtering or wavelet threshold denoising on the original radar echo signal to suppress high-frequency noise; wherein, multi-band radar echo data is used as the original radar echo signal, and its expression is... for:

[0020] ;

[0021] In the formula, Echo amplitude, For Doppler frequency, This is phase modulation caused by micro-motion. It is additive noise;

[0022] S12. The amplitude of the denoised signal is compressed to the [0,1] interval by using the extreme value normalization method;

[0023] S13. Set the Blackman window function to perform frame-by-frame windowing processing on the normalized signal and output overlapping frame signals.

[0024] Preferably, in S2, the formula for calculating the short-time Fourier transform is:

[0025] ;

[0026] In the formula, For time, For frequency, This is the time-frequency result of the original short-time Fourier transform. The frequency axis variable is the output time-frequency representation, i.e., the frequency coordinates of the rearranged time-frequency spectrum. For the signal in time ,frequency The instantaneous frequency corresponding to the location describes how the frequency changes with time and the original time-frequency location. The Dirac function, or impulse function, is used for frequency filtering or rearrangement. The short-time Fourier transform time-frequency representation after compression and rearrangement is the time-frequency spectrum of the final output fused instantaneous frequency information.

[0027] Preferably, in S2, the specific process of calculating the time-frequency matrix is ​​to use STFT to calculate and implement time-frequency transformation, and output the time-frequency matrix according to the time-frequency transformation formula. The expression for STFT calculation to implement time-frequency transformation is:

[0028] ;

[0029] In the formula, For window functions, For time frame indexing, For frequency frame index, The frame shift step size;

[0030] The expression for the time-frequency matrix is:

[0031] ;

[0032] In the formula, This represents the total number of time frames. This refers to the frequency resolution.

[0033] Preferably, in S3, the time-frequency matrix is ​​sliced ​​according to time frames to construct a time-series feature sequence as follows:

[0034] ;

[0035] In the formula, For the first Feature vectors of each element time frame ; For the first The feature vector of each element time frame.

[0036] Preferably, in S3, the input bidirectional LSTM network is used for temporal encoding. The forward LSTM captures the forward temporal evolution pattern, the backward LSTM learns the inverse context dependency, and the high-order temporal feature sequence is generated by concatenating and fusing the hidden states. The calculation formula is as follows:

[0037] ;

[0038] ;

[0039] ;

[0040] In the formula, Forward unit, For reverse unit, It is in a bidirectional hidden state. For the forward LSTM The hidden state of the step stores the forward time series features. For the inverse LSTM The hidden state of the step stores backward time series features. For the forward LSTM The hidden state of a step, i.e., the preceding historical information. For the inverse LSTM The hidden state of a step, i.e., subsequent future information.

[0041] Preferably, in S4, the formula for calculating attention weights is:

[0042] ;

[0043] In the formula, This is the weight matrix. This is the attention vector.

[0044] Preferably, in S4, the feature fusion output obtained according to the attention weight calculation formula is:

[0045] ;

[0046] In the formula, This is the final micro-motion feature vector.

[0047] Preferably, in S5, the triggering mechanism for feature evaluation is an accuracy rate of less than 90% or a divergence value of less than 2.0.

[0048] Preferably, in S6, the feature extraction performance of STFT and STFT-LSTM is evaluated using energy concentration EC and Doppler frequency DR, wherein the formula for calculating energy concentration EC is:

[0049] ;

[0050] The formula for calculating the Doppler frequency DR is:

[0051] ;

[0052] In the formula, The time-frequency distribution matrix, The target energy concentration area For time frames, For frequency bin number, For time-varying Doppler frequency, For the target translational velocity, This refers to the amplitude of the micro-motion. The frequency of the micro-motion angular frequency, This is the initial phase of the micro-motion.

[0053] Therefore, this invention proposes a feature extraction algorithm for slow, small targets based on STFT-LSTM, with the following advantages:

[0054] (1) This invention integrates short-time Fourier transform and long short-term memory network to achieve efficient time-frequency analysis and feature extraction of radar echo signal. It can more effectively focus signal energy on the target micro-motion feature region, greatly reduce high-frequency noise interference in the time spectrum, and accurately highlight the core micro-motion features.

[0055] (2) This invention has broad application prospects in scenarios such as low-altitude security early warning and UAV swarm monitoring. Based on the advantages of multi-band radar data processing, it can be deeply adapted to low-altitude security early warning scenarios, greatly improve the monitoring reliability in complex environments, and support the accurate identification and tracking of UAV targets.

[0056] 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

[0057] Figure 1 This is a flowchart of the STFT-LSTM feature extraction process for the low-speed, small-target micro-motion feature extraction algorithm based on STFT-LSTM of this invention.

[0058] Figure 2These are data processing diagrams for DJI Phantom, DJI M350, DJI Inspire 2, and DJI M600. Among them, (a) is the data processing diagram for DJI Phantom, (b) is the data processing diagram for DJI M350, (c) is the data processing diagram for DJI Inspire 2, and (d) is the data processing diagram for DJI M600.

[0059] Figure 3 These are STFT energy distribution diagrams for DJI Phantom, DJI M350, DJI Inspire 2, and DJI M600. Among them, (a) is the STFT energy distribution diagram for DJI Phantom, (b) is the STFT energy distribution diagram for DJI M350, (c) is the STFT energy distribution diagram for DJI Inspire 2, and (d) is the STFT energy distribution diagram for DJI M600.

[0060] Figure 4 These are the STFT-LSTM power spectral density maps of the DJI Phantom, DJI M350, DJI Inspire 2, and DJI M600. Among them, (a) is the STFT-LSTM power spectral density map of the DJI Phantom, (b) is the energy distribution map of the STFT-LSTM power spectral density map of the DJI M350, (c) is the STFT-LSTM power spectral density map of the DJI Inspire 2, and (d) is the STFT-LSTM power spectral density map of the DJI M600. Detailed Implementation

[0061] 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.

[0062] 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.

[0063] like Figure 1 As shown, this invention provides an algorithm for extracting micro-motion features of slow, small targets based on STFT-LSTM, including:

[0064] S1. Preprocessing and framing the signal: Perform adaptive filtering or wavelet threshold denoising, normalization, and framing windowing operations in sequence to generate overlapping framed signals. The framing parameters are set to window length N=256 and frame shift step length H=64, and a Blackman window is applied.

[0065] In S1, the specific steps for signal preprocessing and framing are as follows:

[0066] S11. Perform adaptive filtering or wavelet threshold denoising on the original radar echo signal to suppress high-frequency noise; wherein, multi-band radar echo data is used as the original radar echo signal, and its expression is... for:

[0067] ;

[0068] In the formula, Echo amplitude, For Doppler frequency, This is phase modulation caused by micro-motion. It is additive noise;

[0069] S12. The amplitude of the denoised signal is compressed to the [0,1] interval by using the extreme value normalization method;

[0070] S13. Set the Blackman window function to perform frame-by-frame windowing processing on the normalized signal and output overlapping frame signals.

[0071] S2. Time-frequency transformation processing: The STFT-LSTM combined model is applied to extract time-frequency features. The short-time Fourier transform is performed frame by frame on the framed signal to calculate the time-frequency matrix, extract the logarithmic amplitude spectrum, and perform adaptive histogram equalization to enhance the time-frequency energy distribution of the micro-motion components.

[0072] In S2, the formula for calculating the short-time Fourier transform is:

[0073] ;

[0074] In the formula, For time, For frequency, The time-frequency result of the original short-time Fourier transform, without rearrangement and containing frequency spread, is the basis of the short-time Fourier transform. The frequency axis variable is the output time-frequency representation, i.e., the frequency coordinates of the rearranged time-frequency spectrum. For the signal in time ,frequency The instantaneous frequency corresponding to the location describes how the frequency changes with time and the original time-frequency location. The Dirac function, or impulse function, is used for frequency filtering or rearrangement. The short-time Fourier transform time-frequency representation after compression and rearrangement is the time-frequency spectrum of the final output fused instantaneous frequency information.

[0075] Preferably, in S2, the specific process of calculating the time-frequency matrix is ​​to use STFT to calculate and implement time-frequency transformation, and output the time-frequency matrix according to the time-frequency transformation formula. The expression for STFT calculation to implement time-frequency transformation is:

[0076] ;

[0077] In the formula, For window functions, For time frame indexing, For frequency frame index, The frame shift step size;

[0078] The expression for the time-frequency matrix is:

[0079] ;

[0080] In the formula, This represents the total number of time frames. Frequency resolution;

[0081] S3. Bidirectional temporal modeling: Slicing the time-frequency matrix according to time frames to construct a temporal feature sequence. In the formula, For the first Feature vectors of each element time frame ; For the first The feature vector of each element time frame.

[0082] The constructed temporal feature sequence is input into a bidirectional LSTM network for temporal encoding. A forward LSTM is used to capture the forward temporal evolution pattern, and a backward LSTM is used to learn the inverse contextual dependencies. The high-order temporal feature sequence is then generated by concatenating and fusing the hidden states. The calculation formula for this process is as follows:

[0083] ;

[0084] ;

[0085] ;

[0086] In the formula, Forward unit, For reverse unit, It is in a bidirectional hidden state. For the forward LSTM The hidden state of the step stores the forward time series features. For the inverse LSTM The hidden state of the step stores backward time series features. For the forward LSTM The hidden state of a step, i.e., the preceding historical information. For the inverse LSTM The hidden state of a step, i.e., subsequent future information.

[0087] S4. Multi-head attention feature fusion: A 4-head attention mechanism is used to perform multi-view feature fusion on the LSTM hidden state sequence. The sequence is split into multiple subspaces, and attention weights are calculated and weighted aggregated. A 256-dimensional compact feature vector is generated through residual connection.

[0088] In S4, to achieve attention feature fusion, backend processing is performed, including the calculation of attention weights. The formula for calculating attention weights is as follows:

[0089] ;

[0090] In the formula, This is the weight matrix. This is the attention vector;

[0091] The feature fusion output obtained based on the attention weight calculation formula is:

[0092] ;

[0093] In the formula, This is the final micro-motion feature vector;

[0094] S5. Dynamic optimization control: The fused features are input into the SVM classifier for 5-fold cross-validation to calculate the average classification accuracy. At the same time, the high-dimensional features are projected into a two-dimensional space through t-SNE, and the Jensen-Shannon divergence between categories is calculated to evaluate the feature separability. The feature evaluation is triggered when the accuracy is lower than 90% or the divergence value is less than 2.0.

[0095] S6. Dynamic parameter optimization: Iteratively adjust the parameters based on the evaluation results. The adjustment parameters include shortening the STFT window length, increasing the number of LSTM layers or attention heads, and adding 1D convolution after the attention layer for local feature compression. Repeat steps S2-S5 until the evaluation indicators of energy concentration EC and Doppler frequency DR are met.

[0096] In S6, the feature extraction performance of STFT and STFT-LSTM is evaluated using energy concentration EC and Doppler frequency DR. The formula for calculating energy concentration EC is:

[0097] ;

[0098] The formula for calculating the Doppler frequency DR is:

[0099] ;

[0100] In the formula, The time-frequency distribution matrix, The target energy concentration area For time frames, For frequency bin number, For time-varying Doppler frequency, For the target translational velocity, This refers to the amplitude of the micro-motion. The frequency of the micro-motion angular frequency, The initial phase of the micro-motion;

[0101] S7. Structured Output: The optimized feature vectors are organized into a matrix according to the sample dimensions. After adding metadata tags such as timestamps and target IDs, they are stored as HDF5 format files. PCA dimensionality reduction is then performed on the feature dimensions to generate the final low-dimensional feature set.

[0102] The STFT-LSTM-based micro-motion feature extraction algorithm for slow, small targets provided in this invention is experimentally analyzed. The specific process is as follows:

[0103] First, the actual effects of the two micro-motion feature extraction methods presented in this paper are fully analyzed. The low-speed, small target detection dataset published in the *Journal of Radar* is used, with target data in the Ku+L band featuring a modulation bandwidth of 100MHz and a fixed modulation period of 0.3ms for simulation analysis. 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. During the experiment, detection data from the DJI Phantom, DJI M350, DJI Inspire 2, and DJI M600 were randomly selected for simulation experiments. Relevant information for the selected targets is shown in Table 1.

[0104] Table 1. Information related to the selected low-slow-speed small targets

[0105] ;

[0106] The high usage rate of DJI Phantom, DJI M350, DJI Inspire 2, and DJI M600 against low-altitude, slow-moving, and small targets results in clear and complete radar echo data. The waveforms of the detection data from the DJI Phantom, DJI M350, DJI Inspire 2, and DJI M600, after removing DC and range dimensions, are shown below. Figure 2 As shown.

[0107] Secondly, the accuracy and performance of the proposed method are fully analyzed. Radar echo data from four types of low-speed, small target detection datasets are selected, and wavelet transform and Hilbert transform models are established to extract features from radar echo data with a modulation bandwidth of 100 MHz, a modulation period of 0.3 ms, and located in the Ku+L band. Subsequently, the accuracy of the extracted feature maps is compared and analyzed, allowing the calculation of the accuracy differences between the models.

[0108] This experiment uses Energy Concentration Degree (EC) and Doppler Resolution (DR) as evaluation metrics to assess the feature extraction performance of STFT and STFT-LSTM. The formula for calculating Energy Concentration Degree (EC) is as follows:

[0109] ;

[0110] The formula for calculating the Doppler frequency DR is:

[0111] ;

[0112] In the formula, The time-frequency distribution matrix, The target energy concentration area For time frames, For frequency bin number, For time-varying Doppler frequency, For the target translational velocity, This refers to the amplitude of the micro-motion. The frequency of the micro-motion angular frequency, This is the initial phase of the micro-motion.

[0113] STFT and STFT-LSTM transforms were performed on data from four types of low-speed, small targets, including DJI Phantom, DJI M350, DJI Inspire 2, and DJI M600. The results are as follows: Figures 3-4 As shown.

[0114] The results are analyzed as follows:

[0115] Figure 3 The STFT energy distribution exhibits a series of characteristics unfavorable for the extraction of micro-motion features from low-speed, small targets. In the temporal dimension, the energy distribution varies across the entire time range (0~8×10⁻⁶). 3 s) The energy is widely distributed and does not form a concentrated focus on the target signal. This results in poor time-frequency localization of the signal, making it difficult to highlight the micro-motion characteristics of the target and hindering subsequent accurate analysis of the target.

[0116] In the frequency dimension (0~4.5×10) 3 At frequencies of 0 to 1.5 × 10⁻⁶ Hz, the energy distribution is chaotic with no obvious main peak. 3 Hz) and high frequency (3×10 3 ~4.5×10 3Although scattered high-energy points exist in the (Hz) region, their distribution is irregular, making it difficult to distinguish the target's micro-motion characteristic frequencies and greatly increasing the difficulty of feature extraction. The color bars indicate a large energy dynamic range, with continuous high-energy bands in the low-frequency range and severe noise interference. Although there are local high-energy points in the high-frequency range, they are not easily distinguishable from noise energy, and the target's micro-motion characteristics are severely submerged by noise. This indicates that the STFT has weak noise resistance and is difficult to effectively extract target features in complex signal environments.

[0117] Furthermore, the energy distribution lacks a stable pattern across different time periods. In the early stages of time (0~3×10⁻⁶), the energy distribution... 3 s) Low-frequency energy is diffused, without a clear characteristic frequency concentration; in the later stages of time (5~8×10 3 s) The scattered distribution of high-frequency energy points reflects the insufficient time-frequency resolution of STFT for non-stationary signals. It cannot accurately capture the changing patterns of micro-motion characteristics of low, slow, and small targets over time, which seriously affects the accuracy of target detection and identification and makes it difficult to meet the needs of practical applications.

[0118] Figure 4 The STFT-LSTM power spectral density maps of the DJI Phantom, DJI M350, DJI Inspire 2, and DJI M600 are presented, demonstrating significant advantages. In the frequency dimension, the energy distribution focusing characteristics of different models are clearly evident.

[0119] The DJI Mavic 2's power spectral density fluctuates significantly in the low-frequency range (0-20kHz), with multiple peaks, indicating the presence of some relatively concentrated energy frequency components, possibly corresponding to low-frequency characteristics or noise interference. The mid-frequency range (20-80kHz) shows greater fluctuations, with higher peaks between 40-60kHz. This frequency band has concentrated energy and is likely the key frequency of the signal, reflecting important characteristics of the drone. In the high-frequency range (80-100kHz), the power spectral density generally decreases but still fluctuates. Although the energy level is lower than in the mid-frequency range, a certain energy distribution still exists, highlighting the rotor rotation characteristics.

[0120] The DJI M350 exhibits a low initial power spectral density in the low-frequency band (0-20kHz), followed by significant fluctuations and peaks, indicating the presence of energy concentration points in the low-frequency region, possibly caused by factors such as the drone's basic mechanical vibration or low-frequency electromagnetic radiation. The mid-frequency band (20-80kHz) is the key region for energy distribution, with frequent fluctuations in power spectral density and alternating peaks and troughs, especially with relatively concentrated energy between 40-60kHz. Energy changes in these frequency bands may be closely related to signals generated by the drone's rotor rotation and electronic equipment operation. The high-frequency band (80-100kHz) shows an overall decreasing power spectral density trend, but still exhibits fluctuations, with an overall low energy level.

[0121] The DJI Inspire 2 exhibits a low initial power spectral density in the low-frequency region (0~20kHz), followed by significant fluctuations and multiple energy peaks. This may be due to factors such as the drone's basic mechanical vibrations and low-frequency motor operation. In the mid-frequency range (20~80kHz), the power spectral density fluctuates dramatically, with significant peaks at multiple frequency points, particularly concentrated in the 40~60kHz band. This is likely related to the DJI Inspire 2's unique H-shaped quadcopter layout, large-sized propeller rotation, and electronic system operation, which generate rich frequency components. In the high-frequency range (80~100kHz), the power spectral density generally shows a downward trend, but local fluctuations still exist.

[0122] The DJI M600's power spectral density starts at a low value in the low-frequency band (0~20kHz), then shows significant fluctuations accompanied by multiple energy peaks. This may be due to factors such as the low-frequency operation of the drone's motors and the basic vibration of the mechanical structure. The mid-frequency band (20~80kHz) is the key area of ​​energy distribution, with frequent fluctuations in power spectral density and multiple peaks and troughs alternating. In particular, the energy is relatively concentrated in the 40~60kHz band, which is likely related to the rotor rotation, electronic speed controller operation, and signals generated by various sensors in the DJI M600's six-axis layout. The power spectral density in the high-frequency band (80~100kHz) generally shows a downward trend, but still fluctuates. Although the overall energy level is low, the fluctuations at specific frequency points indicate that there is also a certain energy component in the high-frequency part.

[0123] The extraction effect was analyzed and judged by extracting indicators of its micro-motion characteristics. The results are shown in Table 2:

[0124] Table 2 Statistical Results of Model Indicators

[0125] ;

[0126] according to Figures 3-4 The analysis and statistical results in Table 2 compare the performance of the STFT model and the STFT-LSTM model in extracting micro-motion features of small, slow targets. The results show that the STFT-LSTM model significantly improves upon the STFT model in key metrics.

[0127] Regarding EC (Earning Capability), the EC value of the STFT model fluctuated between 0.30887 (DJI M350) and 0.54978 (DJI M600), with an average of 0.41080. The EC value of the STFT-LSTM model significantly improved to 0.46137~0.60081, with an average of 0.52079, representing a 26.78% improvement over the STFT model. This improvement indicates that the STFT-LSTM model can more effectively focus signal energy on the target's micro-motion feature region, greatly enhancing the recognizability of the features.

[0128] Taking the DJI Inspire 2 as an example, its EC value under the STFT-LSTM model reaches 0.60081, showing a significant advantage over the STFT model. Regarding noise reduction (DR), the STFT model has a DR value as high as 27343.75~42968.75Hz, with a large amount of high-frequency noise interference in the time spectrum, causing the target's micro-motion characteristics to be obscured; the DJI Inspire 2's DR is 42968.75Hz. In contrast, the STFT-LSTM model significantly reduces the DR to 781.25~976.5625Hz, achieving a noise reduction effect of over 96.5%.

[0129] Taking the DJI M600 as an example, its DR is compressed from 31250Hz in the STFT model to 781.25Hz in the STFT-LSTM model, effectively filtering out non-target frequency noise and accurately highlighting core micro-motion characteristics such as blade rotation.

[0130] Therefore, this invention provides a micro-motion feature extraction algorithm for low-altitude, slow, small targets based on STFT-LSTM. This algorithm integrates Short-Time Fourier Transform and Long Short-Term Memory networks, achieving efficient time-frequency analysis and feature extraction of radar echo signals. It more effectively focuses signal energy on the micro-motion feature region of the target, significantly reduces high-frequency noise interference in the time spectrum, and accurately highlights the core micro-motion features. This algorithm has broad application prospects in scenarios such as low-altitude security early warning and UAV swarm monitoring, and can greatly improve the monitoring reliability in complex environments, supporting accurate identification and tracking of UAV targets.

[0131] 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 based on STFT-LSTM, characterized in that, include: S1. Preprocessing and framing the signal: Perform adaptive filtering or wavelet threshold denoising, normalization, and framing windowing operations in sequence to generate overlapping framed signals. The framing parameters are set to window length N=256 and frame shift step length H=64, and a Blackman window is applied. S2. Time-frequency transformation processing: The short-time Fourier transform is applied to process the frame-by-frame signal, calculate the time-frequency matrix, extract the logarithmic amplitude spectrum, and perform adaptive histogram equalization to enhance the time-frequency energy distribution of the micro-motion components. S3. Bidirectional temporal modeling: The time-frequency matrix is ​​sliced ​​according to time frames to construct a temporal feature sequence. The constructed temporal feature sequence is input into a bidirectional LSTM network for temporal encoding. A forward LSTM is used to capture the forward temporal evolution pattern, and a backward LSTM is used to learn the inverse context dependency. The high-order temporal feature sequence is generated by splicing and fusing the hidden states. S4. Multi-head attention feature fusion: The LSTM hidden state sequence corresponding to the high-order temporal feature sequence is used as input. A 4-head attention mechanism is used to perform multi-view feature fusion on the LSTM hidden state sequence. The sequence is split into multiple subspaces, and attention weights are calculated and weighted aggregated. A 256-dimensional compact feature vector is generated through residual connection. S5. Dynamic optimization control: The 256-dimensional compact feature vector is input into the SVM classifier for 5-fold cross-validation to calculate the average classification accuracy. At the same time, the time-frequency matrix group obtained in S2 is used as a high-dimensional feature and projected onto a two-dimensional space through t-SNE. The Jensen-Shannon divergence between categories is calculated to evaluate the feature separability. S6. Dynamic parameter optimization: Iteratively adjust the parameters based on the evaluation results. The adjustment parameters include shortening the STFT window length, increasing the number of LSTM layers or attention heads, and adding 1D convolution after the attention layer for local feature compression. Repeat steps S2-S5 until the evaluation indicators of energy concentration EC and Doppler frequency DR are met. S7. Structured Output: The optimized feature vectors are organized into a matrix according to the sample dimensions. After adding metadata tags such as timestamps and target IDs, they are stored as HDF5 format files. PCA dimensionality reduction is then performed on the feature dimensions to generate the final low-dimensional feature set.

2. The method for extracting micro-motion features of slow, small targets based on STFT-LSTM according to claim 1, characterized in that, In S1, the specific steps for signal preprocessing and framing are as follows: S11. Perform adaptive filtering or wavelet threshold denoising on the original radar echo signal to suppress high-frequency noise; wherein, multi-band radar echo data is used as the original radar echo signal, and its expression is... for: ； In the formula, Echo amplitude, For Doppler frequency, This is phase modulation caused by micro-motion. It is additive noise; S12. The amplitude of the denoised signal is compressed to the [0,1] interval by using the extreme value normalization method; S13. Set the Blackman window function to perform frame-by-frame windowing processing on the normalized signal and output overlapping frame signals.

3. The method for extracting micro-motion features of slow, small targets based on STFT-LSTM according to claim 1, characterized in that, In S2, the formula for calculating the short-time Fourier transform is: ； In the formula, For time, For frequency, This is the time-frequency result of the original short-time Fourier transform. The frequency axis variable is the output time-frequency representation, i.e., the frequency coordinates of the rearranged time-frequency spectrum. For the signal in time ,frequency The instantaneous frequency corresponding to the location describes how the frequency changes with time and the original time-frequency location. The Dirac function, or impulse function, is used for frequency filtering or rearrangement. The short-time Fourier transform time-frequency representation after compression and rearrangement is the time-frequency spectrum of the final output fused instantaneous frequency information.

4. The method for extracting micro-motion features of slow, small targets based on STFT-LSTM according to claim 1, characterized in that, In S2, the specific process of calculating the time-frequency matrix involves using STFT to calculate the time-frequency transformation and outputting the time-frequency matrix according to the time-frequency transformation formula; the expression for STFT calculation to achieve time-frequency transformation is as follows: ； In the formula, For window functions, For time frame indexing, For frequency frame index, The frame shift step size; The expression for the time-frequency matrix is: ； In the formula, This represents the total number of time frames. This refers to the frequency resolution.

5. The method for extracting micro-motion features of slow, small targets based on STFT-LSTM according to claim 1, characterized in that, In S3, the time-frequency matrix is ​​sliced ​​according to time frames to construct the time-series feature sequence as follows: ； In the formula, For the first Feature vectors of each element time frame ; For the first The feature vector of each element time frame.

6. The method for extracting micro-motion features of slow, small targets based on STFT-LSTM according to claim 1, characterized in that, In S3, the input bidirectional LSTM network performs temporal encoding. The forward LSTM captures the forward temporal evolution pattern, the backward LSTM learns the inverse contextual dependencies, and the high-order temporal feature sequence is generated by concatenating and fusing the hidden states. The calculation formula is as follows: In the formula, Forward unit, For reverse unit, It is in a bidirectional hidden state. For the forward LSTM The hidden state of the step stores the forward time series features. For the inverse LSTM The hidden state of the step stores backward time series features. For the forward LSTM The hidden state of a step, i.e., the previous historical information. For the inverse LSTM The hidden state of a step, i.e., subsequent future information.

7. The method for extracting micro-motion features of slow, small targets based on STFT-LSTM according to claim 1, characterized in that, In S4, the formula for calculating attention weights is: ； In the formula, This is the weight matrix. This is the attention vector.

8. The method for extracting micro-motion features of slow, small targets based on STFT-LSTM according to claim 7, characterized in that, In S4, the feature fusion output obtained according to the attention weight calculation formula is: ； In the formula, This is the final micro-motion feature vector.

9. The method for extracting micro-motion features of slow, small targets based on STFT-LSTM according to claim 1, characterized in that, In S5, the triggering mechanism for feature evaluation is when the accuracy is less than 90% or the divergence value is less than 2.

0.

10. The method for extracting micro-motion features of slow, small targets based on STFT-LSTM according to claim 1, characterized in that, In S6, the feature extraction performance of STFT and STFT-LSTM is evaluated using energy concentration EC and Doppler frequency DR. The formula for calculating energy concentration EC is: ； The formula for calculating the Doppler frequency DR is: ； In the formula, The time-frequency distribution matrix, The target energy concentration area For time frames, For frequency bin number, For time-varying Doppler frequency, For the target translational velocity, This refers to the amplitude of the micro-motion. The frequency of the micro-motion angular frequency, This is the initial phase of the micro-motion.

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