EEMD-based radar signal feature extraction analysis optimization method and system

Abstract

The application provides an EEMD-based radar signal feature extraction analysis optimization method and system, and relates to the technical field of radar signal processing.The method comprises the following steps: receiving an original echo signal, performing analog-digital conversion and time series reconstruction, performing spectrum energy distribution analysis and local time-frequency density estimation, performing multiple non-uniform amplitude modulation random noise superposition processing, respectively performing empirical mode decomposition on multiple groups of perturbation signal sets, clustering, aligning and merging and reconstructing mode components of different perturbation signal decomposition results, establishing a multi-dimensional mode evaluation index, and performing feature extraction on a core mode component subset.The technical problems that the existing technology has serious mode aliasing, many false components, incomplete radar signal noise suppression and difficult target separation are solved.Through full-link optimization of the EEMD radar signal processing, accurate radar signal noise suppression and effective target separation are realized, and the technical effect of improving the target feature extraction precision is achieved.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing technology, and more specifically to a radar signal feature extraction, analysis and optimization method and system based on EEMD. Background Technology

[0002] In radar target detection and identification, echo signals often exhibit nonlinear and non-stationary time-varying characteristics. Especially in complex environments, target echoes, clutter, and noise highly overlap in the time and frequency domains. Traditional short-time Fourier transforms are constrained by the Heisenberg uncertainty principle and cannot simultaneously achieve time and frequency resolution. Although classical EMD can achieve adaptive signal decomposition, it is prone to mode mixing and generates a large number of spurious components without physical meaning, which seriously interferes with the extraction of true features.

[0003] To address the shortcomings of EMD, existing technologies have proposed using ensemble empirical mode decomposition (EEMD) by repeatedly adding white noise to the signal to be decomposed and performing ensemble averaging, leveraging the statistical properties of the noise to suppress mode aliasing. However, existing EEMD schemes, when applying fixed-amplitude global noise injection in actual radar signal processing, lack time-frequency adaptive capabilities, easily contaminate the target principal components, and fail to effectively fill spectral gaps. Furthermore, the IMFs across decompositions lack corresponding identification mechanisms, and the same physical mode is prone to order drift. The same physical mode is also prone to order drift under different noise implementations, ultimately leading to misjudgment of target components and incomplete noise suppression, affecting the overall accuracy of radar target feature extraction.

[0004] In summary, existing technologies suffer from severe mode aliasing and numerous false components, leading to incomplete noise suppression of radar signals, difficulty in target separation, and consequently affecting the accuracy of target feature extraction. Summary of the Invention

[0005] The purpose of this application is to provide a radar signal feature extraction and analysis optimization method and system based on EEMD, which can solve the technical problems of severe mode mixing and many false components in the existing technology, resulting in incomplete suppression of radar signal noise and difficulty in target separation, thus affecting the accuracy of target feature extraction.

[0006] In view of the above problems, this application provides a radar signal feature extraction, analysis and optimization method and system based on EEMD.

[0007] The first aspect of this application provides a radar signal feature extraction, analysis, and optimization method based on EEMD. The method includes: after receiving the original echo signal, performing analog-to-digital conversion and time-series reconstruction via an echo acquisition device to form a time-series signal to be processed; performing spectral energy distribution analysis and local time-frequency density estimation on the time-series signal to be processed to construct a spectral domain weighted mapping relationship; after receiving the spectral domain weighted mapping relationship, a noise injection controller performs multiple non-uniform amplitude modulation random noise superposition processes on the time-series signal to be processed to generate multiple sets of disturbance signals; and further optimizing the radar signal feature extraction, analysis, and optimization method based on EEMD. Multiple sets of perturbation signals are subjected to empirical mode decomposition (EMD) to establish intrinsic mode function (EMF) sequences. Based on the instantaneous frequency distribution and energy characteristics of each EMF, a modal similarity metric across perturbation sets is constructed. The modal components of different perturbation signal decomposition results are clustered, aligned, merged, and reconstructed using the modal similarity metric to generate a unified modal component set. A multidimensional modal evaluation index is established for the unified modal component set based on energy concentration, instantaneous frequency stability, time-frequency trajectory continuity, and matching deviation from clutter templates to locate the core modal component subset. Feature extraction of the core modal component subset is performed, and the feature extraction results are output.

[0008] Optionally, the subset of core modal components is input to the envelope demodulation unit and the phase tracking unit in the echo processing link, respectively, to extract the corresponding instantaneous amplitude sequence and instantaneous phase sequence. After phase expansion processing, an instantaneous frequency sequence is constructed. The pulse compression consistency correction is performed on the instantaneous frequency sequence by calling the transmitted signal reference template of the matched filter to extract the main feature of the target scattering intensity. Micro-Doppler perturbation separation is performed on the instantaneous frequency sequence to obtain the target motion frequency shift feature. Based on the spectral domain weight mapping relationship, the main feature of the target scattering intensity and the target motion frequency shift feature are weighted and coupled to construct a time-frequency joint constraint target feature vector. The target feature vector is output as the feature extraction result.

[0009] Optionally, the noise injection controller divides the time-series signal to be processed into multiple time-frequency local sub-intervals according to the spectral domain weight mapping relationship, and assigns a corresponding noise injection weight coefficient to each time-frequency local sub-interval. The noise injection weight coefficient is inversely correlated with the energy density and spectral sparsity of the corresponding time-frequency local sub-interval. After reading multiple sets of noise sequences with different random seeds and amplitude distribution parameters, the noise sequences are segmented and modulated according to the noise injection weight coefficients, so that the noise is injected in a restricted manner in high-energy concentrated areas and injected in a stronger manner in low-energy or spectral gap areas. The modulated noise sequence is superimposed on the time-series signal to be processed one after another, and the overall signal-to-noise ratio and local frequency band disturbance intensity of the superimposed signal are constrained and corrected in each superposition process to generate multiple sets of disturbance signals.

[0010] Optionally, using the generation order of the disturbance signal set as a constraint, the instantaneous frequency evolution trajectory and energy distribution sequence corresponding to the modal components of each intrinsic mode function are extracted, and a cross-disturbance modal candidate correspondence is established under a unified time index; the modal candidate correspondence is used to perform segmented trajectory alignment and energy distribution matching on the potential corresponding modal components in different disturbance results, calculate the local matching degree reflecting the consistency of frequency evolution and the consistency of energy concentration trend, and form a continuous matching response sequence along the time dimension; the continuous matching response sequence is integrated and fused in the entire time domain, and a modal similarity metric index characterizing the cross-disturbance consistency and existence stability of modal components is constructed by combining the occurrence frequency and stable duration interval of each modal component in multiple disturbances.

[0011] Optionally, a Hilbert transform is performed on each modal component in the unified modal component set to extract the component instantaneous amplitude sequence and the component instantaneous frequency sequence; the total energy of the modal component is calculated based on the component instantaneous amplitude sequence, and a time-frequency compact support region is defined based on the aggregation range of the component instantaneous frequency sequence, with the ratio of energy within the time-frequency compact support region to the total energy used as an energy concentration index; normalized local variance is calculated for the component instantaneous frequency sequence, and the calculation result is used as an instantaneous frequency stability index; time-frequency trajectory continuity is detected for the component instantaneous frequency sequence. The frequency difference between adjacent sampling times is calculated, and the positions where the absolute value of the difference exceeds the preset frequency continuity threshold are marked as breakpoints. A time-frequency trajectory continuity index is generated based on the ratio of the length of the maximum continuous unbroken segment to the total length of the sequence. A clutter time-frequency template corresponding to the typical clutter distribution characteristics in the current radar detection scenario is obtained, and the two-dimensional normalized cross-correlation coefficient between the time-frequency distribution of the modal components and the clutter time-frequency template is calculated to construct a matching deviation index. The energy concentration index, instantaneous frequency stability index, time-frequency trajectory continuity index, and matching deviation index are output as multi-dimensional modal evaluation indexes.

[0012] Optionally, the evaluation attention weight of the modal component in each time-frequency region is determined according to the spectral domain weight mapping relationship; the evaluation attention weight is used to weight and fuse the energy concentration index, instantaneous frequency stability index, time-frequency trajectory continuity index, and matching deviation index to establish a target confidence score for each modal component; the target confidence scores of all modal components in the unified modal component set are jointly judged with the modal similarity measurement index across the perturbation set, and modal components with target confidence scores higher than the adaptive threshold and modal similarity measurement index satisfying the preset stability criterion are selected to form the core modal component subset.

[0013] Optionally, the echo acquisition unit includes an analog-to-digital converter chip and a field-programmable gate array (FPGA) front-end preprocessing module. The analog-to-digital converter chip samples the original echo signal and transmits the sampled data stream to the FPGA front-end preprocessing module through a direct memory access channel. The FPGA front-end preprocessing module has built-in time series reconstruction logic to segment, buffer, and align the sampled data stream to generate the timing signal to be processed.

[0014] Optionally, the parallel computing array within the field-programmable gate array performs empirical mode decomposition on the multiple sets of disturbance signals respectively. The parallel computing array contains multiple independent empirical mode decomposition processing cores. Each empirical mode decomposition processing core shares the timing signal to be processed and the modulated noise sequence, performs superposition and decomposition operations in parallel, and writes the decomposed intrinsic mode function sequence into an off-chip double-rate synchronous dynamic random access memory.

[0015] Optionally, the noise injection controller is integrated within the field-programmable gate array and is configured with a hardware random number generation submodule for generating multiple sets of noise sequences with different random seeds.

[0016] A second aspect of this application provides a radar signal feature extraction, analysis, and optimization system based on EEMD. The system includes: a signal forming component, used to perform analog-to-digital conversion and time-series reconstruction on the received raw echo signal via an echo collector to form a time-series signal to be processed; a signal analysis component, used to perform spectral energy distribution analysis and local time-frequency density estimation on the time-series signal to be processed, and construct a spectral domain weighted mapping relationship; a disturbance signal generation component, used to perform multiple non-uniform amplitude modulation random noise superposition processing on the time-series signal to be processed after the noise injection controller receives the spectral domain weighted mapping relationship, generating multiple sets of disturbance signals; and a metric construction component. The system is used to perform empirical mode decomposition on the multiple sets of disturbance signals, establish an intrinsic mode function sequence, and construct a mode similarity metric across the disturbance sets based on the instantaneous frequency distribution and energy characteristics of each intrinsic mode function; a mode component processing component is used to cluster, align, merge, and reconstruct the mode components of different disturbance signal decomposition results using the mode similarity metric to generate a unified mode component set; an evaluation index establishment component is used to establish multi-dimensional mode evaluation indexes for the unified mode component set based on energy concentration, instantaneous frequency stability, time-frequency trajectory continuity, and matching deviation from clutter template, and locate the core mode component subset; a feature extraction component is used to perform feature extraction on the core mode component subset and output the feature extraction results.

[0017] One or more technical solutions provided in this application have at least the following technical effects or advantages: After receiving the original echo signal, the echo acquisition unit performs analog-to-digital conversion and time-series reconstruction to form a time-series signal to be processed. The time-series signal to be processed is then subjected to spectral energy distribution analysis and local time-frequency density estimation to construct a spectral domain weight mapping relationship. After receiving the spectral domain weight mapping relationship, the noise injection controller performs multiple non-uniform amplitude modulation random noise superposition processes on the time-series signal to be processed, generating multiple sets of disturbance signals. Empirical mode decomposition is performed on each of the multiple sets of disturbance signals to establish an intrinsic mode function sequence. Based on the instantaneous frequency distribution and energy characteristics of each intrinsic mode function, a modal similarity metric across disturbance sets is constructed. The modal components of different disturbance signal decomposition results are clustered, aligned, and reconstructed using the modal similarity metric to generate a unified modal component set. A multi-dimensional modal evaluation index is established for the unified modal component set based on energy concentration, instantaneous frequency stability, time-frequency trajectory continuity, and matching deviation from the clutter template to locate the core modal component subset. Feature extraction of the core modal component subset is performed, and the feature extraction results are output. The technology achieves the technical effect of improving the accuracy of target feature extraction by optimizing EEMD radar signal processing across the entire chain, thereby enabling precise suppression of radar signal noise and effective target separation.

[0018] The above description is merely an overview of the technical solution of this application. To better understand the technical means of this application and to facilitate its implementation according to the description, and to make the above and other objects, features, and advantages of this application more apparent, specific embodiments of this application are described below. It should be understood that the content described in this section is not intended to identify key or important features of the embodiments of this application, nor is it intended to limit the scope of this application. Other features of this application will become readily apparent through the following description. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely exemplary. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0020] Figure 1 A flowchart illustrating the radar signal feature extraction, analysis, and optimization method based on EEMD provided in this application.

[0021] Figure 2 The modal component joint discriminant analysis diagram in the radar signal feature extraction and analysis optimization method based on EEMD provided in this application.

[0022] Figure 3A schematic diagram of the structure of the radar signal feature extraction, analysis and optimization system based on EEMD provided in this application.

[0023] Explanation of reference numerals in the attached figures: Signal formation component 11, Signal analysis component 12, Disturbance signal generation component 13, Metric construction component 14, Modal component processing component 15, Evaluation metric establishment component 16, Feature extraction component 17. Detailed Implementation

[0024] This application provides a radar signal feature extraction and analysis optimization method and system based on EEMD, which addresses the technical problems of severe mode mixing and numerous false components in existing technologies, leading to incomplete radar signal noise suppression, difficulty in target separation, and consequently affecting the accuracy of target feature extraction. It achieves the technical effect of improving the accuracy of target feature extraction by optimizing EEMD radar signal processing across the entire chain, thereby realizing precise radar signal noise suppression and effective target separation.

[0025] The technical solutions of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. It should be understood that the present invention is not limited to the exemplary embodiments described herein. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention. It should also be noted that, for ease of description, only the parts related to the present invention are shown in the accompanying drawings, not all of them.

[0026] Example 1, as Figure 1 As shown, this application provides a radar signal feature extraction, analysis, and optimization method based on EEMD, which includes: After receiving the raw echo signal, the echo acquisition unit performs analog-to-digital conversion and time series reconstruction to form the timing signal to be processed.

[0027] Furthermore, the echo acquisition unit includes an analog-to-digital converter chip and a field-programmable gate array (FPGA) front-end preprocessing module. The analog-to-digital converter chip samples the original echo signal and transmits the sampled data stream to the FPGA front-end preprocessing module through a direct memory access channel. The FPGA front-end preprocessing module has built-in time series reconstruction logic to segment, buffer, and align the sampled data stream to generate the timing signal to be processed.

[0028] Specifically, after down-conversion processing is completed in the radar front-end RF receiving link, the RF signal is shifted to intermediate frequency (IF) or zero IF to acquire the original echo signal. This original echo signal is a continuous-time waveform in the form of analog voltage in the time domain, and its instantaneous amplitude is modulated by both the target scattered echo power and clutter fluctuations. The original echo signal is input to an echo acquisition unit, which includes an analog-to-digital converter (ADC) chip and a field-programmable gate array (FPGA) front-end preprocessing module. The ADC chip adopts a pipelined structure or a successive approximation register structure. The sampling clock is provided by the system's high-stability crystal oscillator after frequency multiplication via a phase-locked loop (PLL). The sampling frequency is set according to the bandwidth of the radar transmitted signal, following the Nyquist sampling theorem, i.e., the sampling frequency must be no less than twice the bandwidth of the transmitted signal.

[0029] The analog-to-digital converter (ADC) chip samples the input raw echo signal at equal time intervals, acquiring a digital quantized value at each sampling moment. The quantization bit depth is 12 or 14 bits, and the quantized value is represented in two's complement form, reflecting the instantaneous amplitude of the echo signal at that moment. The ADC chip completes one sampling and quantization operation on each rising edge of the sampling clock, forming a sampled data stream. The sampled data stream contains continuous sampled quantized values ​​and their corresponding sampling moments. The sampled data stream is transmitted directly to the field-programmable gate array (FPGA) front-end preprocessing module via a direct memory access channel using a high-speed serial or parallel interface protocol, such as JESD204B or LVDS. The FPGA internally configures data receive buffer logic, which includes a first-in-first-out (FIFO) buffer queue to eliminate the read / write rate mismatch caused by the slight frequency deviation between the ADC output data rate and the FPGA's internal processing clock domain.

[0030] The field-programmable gate array (FPGA) front-end preprocessing module incorporates time series reconstruction logic. After the FPGA reads the sampled data stream from the first-in-first-out (FIFO) buffer queue, the time series reconstruction logic performs segmented buffering and alignment stitching processing. Segmented buffering refers to dividing the continuous sampled data stream into fixed-length sampled data according to the radar's preset pulse repetition period (PRI). The number of sampling points in each sampled data is calculated by multiplying the sampling duration corresponding to the radar's maximum unambiguous range by the sampling rate. Alignment stitching refers to using the radar's transmitted pulse reference synchronization signal as a time zero-point reference, aligning and stitching the sampled data within each pulse repetition period in the segmented buffer according to the timestamp of the sampling moment, forming a continuous time sequence. Finally, after segmented buffering and alignment stitching processing, a time-series signal with continuous time index and equally spaced sampling points is generated for processing.

[0031] By using analog-to-digital conversion and employing direct memory access channels and field-programmable gate array (FPGA) front-end preprocessing, the real-time performance and integrity of the sampled data stream are ensured. Combined with time series reconstruction, potential timing errors during the transmission of the sampled data stream are avoided, providing a reliable and standard signal to be processed for subsequent signal analysis and optimization.

[0032] The spectral energy distribution analysis and local time-frequency density estimation are performed on the time-series signal to be processed, and a spectral domain weight mapping relationship is constructed.

[0033] Specifically, a windowed Discrete Fourier Transform (DFT) is employed to analyze the spectral energy distribution of the time-series signal to be processed. The Hanning window is preferred to suppress spectral leakage, with the window length set to 1 / 10 of the total number of sampling points in the signal and the overlap between windows set to 50%. After windowing, a Fourier Transform is performed to map the signal from the time domain to the frequency domain, outputting a complex spectral sequence. Then, the square of the magnitude is calculated for each frequency point of the complex spectral sequence, yielding multiple power spectral densities. These power spectral densities are then normalized by dividing the power spectral density value at each frequency point by the sum of all power spectral densities, resulting in a normalized spectral energy distribution.

[0034] Simultaneously, a smooth pseudo-Wigner-Vell distribution is used to estimate the local time-frequency density of the time-series signal to be processed. The time-frequency plane of the time-series signal to be processed is divided into local sub-grids of uniform size. The time dimension length of each sub-grid is set to 1 / 20 of the radar pulse repetition period, and the frequency dimension width is set to 1 / 10 of the Doppler frequency shift corresponding to the radar range resolution. Then, the sum of time-frequency energy in each sub-grid is calculated, and the ratio of the sum of time-frequency energy to the area of ​​the sub-grid is defined as the local time-frequency density of the sub-grid, which is used to reflect the degree of energy concentration in the local time-frequency region.

[0035] The local time-frequency density of each local subgrid is reverse normalized, that is, the region with higher local time-frequency density is assigned a smaller weight coefficient. The normalized spectral energy distribution and the local reverse normalized density weight are multiplied to obtain the spectral domain weight coefficient corresponding to each local time-frequency subgrid. Multiple spectral domain weight coefficients are integrated to form a spectral domain weight mapping relationship, which is then transmitted to the noise injection controller.

[0036] By using global spectrum analysis and high-resolution local time-frequency density estimation, the energy distribution characteristics of the radar echo to be processed are accurately reflected. The generated spectral domain weight mapping relationship provides a quantitative reference that is fully adapted to the current signal scenario for subsequent non-uniform noise injection, avoiding the poor adaptability problem that occurs when traditional EEMD processes signals in different scenarios with fixed parameters, thereby improving the mode mixing suppression effect.

[0037] After receiving the spectral domain weight mapping relationship, the noise injection controller performs multiple random noise superposition processes with non-uniform amplitude modulation on the timing signal to be processed, generating multiple sets of disturbance signals.

[0038] Furthermore, the noise injection controller is integrated within the field-programmable gate array and is equipped with a hardware random number generation submodule for generating multiple sets of noise sequences with different random seeds.

[0039] Furthermore, the time-series signal to be processed undergoes multiple random noise superposition processes with non-uniform amplitude modulation to generate multiple sets of disturbance signals. This includes: a noise injection controller dividing the time-series signal to be processed into multiple time-frequency local sub-intervals according to the spectral domain weight mapping relationship, and assigning a corresponding noise injection weight coefficient to each time-frequency local sub-interval, wherein the noise injection weight coefficient is inversely correlated with the energy density and spectral sparsity of the corresponding time-frequency local sub-interval; after reading multiple sets of noise sequences with different random seeds and amplitude distribution parameters, segmented amplitude modulation is performed on the noise sequences according to the noise injection weight coefficients, so that noise is restricted in high-energy concentrated areas and enhanced in low-energy or spectral gap areas; the modulated noise sequences are successively superimposed on the time-series signal to be processed, and the overall signal-to-noise ratio and local frequency band disturbance intensity of the superimposed signal are constrained and corrected during each superposition process to generate multiple sets of disturbance signals.

[0040] Specifically, the noise injection controller is integrated within a Field-Programmable Gate Array (FPGA) and is equipped with a hardware random number generation submodule. This submodule is a pseudo-random number generator implemented using the FPGA's internal logic resources. It generates multiple noise sequences with different random seeds, and the length of each noise sequence is perfectly aligned with the timing signal to be processed. After receiving the spectral domain weight mapping relationship, the noise injection controller divides the timing signal to be processed into multiple time-frequency local sub-intervals in the time domain according to the spectral domain weight mapping relationship. Each time-frequency local sub-interval corresponds to a specific time window and a specific frequency sub-band. The time window is determined by the starting position and length of the window in the short-time Fourier transform, and the frequency sub-band is formed by merging several consecutive frequency points in the spectral domain weight vector.

[0041] The noise injection controller assigns a corresponding noise injection weight coefficient to each time-frequency local sub-interval based on the spectral domain weight mapping relationship. This noise injection weight coefficient is inversely related to the energy density and spectral sparsity of the corresponding time-frequency local sub-interval: the higher the energy density and the denser the spectrum in the time-frequency local sub-interval, the smaller the noise injection weight coefficient; conversely, the sparser the spectrum in the low-energy clutter gap region, the larger the noise injection weight coefficient. After completing the noise injection weight coefficient allocation, the noise injection controller activates its internally configured hardware random number generation submodule. This hardware random number generation submodule can be a linear feedback shift register (LFSR), which generates random number sequences based on different random seeds. The random seed refers to the initial value used to initialize the pseudo-random number generator. For example, a 32-bit LFSR has a 32-bit binary value as its seed, such as 0x5A3F9C2E. Whenever a random number is needed, the LFSR performs a shift operation, shifting the feedback bit into the highest bit. The new register state is the output random number. Different seeds result in different initial states of the LFSR, leading to completely different subsequent shift state sequence paths, thus generating statistically independent noise sequences.

[0042] Multiple sets of different random seeds are loaded sequentially. Each set of random seeds generates a noise sequence of the same length as the time-series signal to be processed. The value of each sampling point in each noise sequence is an independent and identically distributed random variable. Its amplitude distribution parameter is preset according to the overall power level of the time-series signal to be processed. For example, the root mean square value of the noise sequence is set to be between 10% and 30% of the root mean square value of the time-series signal to be processed. After reading multiple sets of noise sequences with different random seeds and amplitude distribution parameters, the noise sequence is segmented and amplitude modulated according to the noise injection weight coefficient. The noise amplitude of each segment is multiplied by the noise injection weight coefficient of the corresponding time-frequency local sub-interval, resulting in a non-uniformly modulated noise sequence whose amplitude changes dynamically with the sub-interval. This achieves a differentiated injection effect, where noise is injected in a restricted manner in high-energy concentrated areas and injected in a stronger manner in low-energy or spectral gap areas.

[0043] Each modulated noise sequence is sequentially superimposed point-to-point with the original timing signal to be processed. Immediately after each superposition, a dual-constraint correction is performed: first, the overall signal-to-noise ratio (SNR) of the superimposed signal is checked by calculating the ratio of the overall power of the perturbation signal to the power of the timing signal to be processed. If this ratio deviates from the preset target SNR range (e.g., between 15dB and 25dB), the noise injection controller applies a global scaling factor to the entire perturbation signal, bringing its SNR back to the target range to ensure that different perturbation signal sets have a consistent overall noise intensity level. Then, the local frequency band perturbation intensity of each time-frequency sub-interval is checked segment by segment to ensure that the frequency band perturbation amplitude in the high-energy target area does not exceed 5% of the corresponding noise signal amplitude. If the actual perturbation power of a certain sub-interval exceeds the expected value, the noise injection controller applies a local fine-tuning scaling to the corresponding time-domain segment of that sub-interval, causing the actual perturbation intensity to converge to the target level indicated by the noise injection weighting coefficient. After all checks pass, the noise sequence is stored in the FPGA's parallel buffer array, generating a complete set of multiple perturbation signals.

[0044] For example, the timing signal to be processed has a length of 128 points and a root mean square (RMS) value of 1.0V. The preset noise injection multiplication factor is 16 times, and the seed list consists of 16 different 32-bit hexadecimal values. For example, the first seed is 0x5A3F9C2E, the second is 0x7B91D4A8, ..., and the 16th is 0xF8A3C07D. For the first noise injection: the noise injection controller writes the seed 0x5A3F9C2E into the 32-bit register of the LFSR as the initial state. The LFSR continuously performs 128 shift feedback operations, outputting 128 random numbers. The amplitude distribution of the noise sequence is set to a Gaussian distribution with a mean of 0 and a standard deviation of 0.2V, i.e., a RMS value of 0.2V, which is 20% of the RMS value of the signal to be processed (1.0V). The 128 values ​​of the noise sequence are generated independently and randomly, for example, the output is [0.15, -0.23, 0.08..., -0.11]. Then, the noise injection controller modulates the noise sequence in segments according to the spectral domain weight mapping relationship. If the spectrum is divided into 4 sub-bands, the weight of the low-frequency band corresponding to the first 32 points is 0.12. Then, the noise values ​​from the 1st to the 32nd are multiplied by 0.12, and the amplitude is compressed to about [0.018, -0.028, 0.010...]. The weight of the 33rd to the 64th points is 0.25, and the amplitude is adjusted to about [0.037, -0.055...]. The weight of the 65th to the 96th points is 0.70, and the amplitude is increased to about [0.105, -0.161...]. The weight of the 97th to the 128th points is 0.80, and the amplitude is increased to about [0.120, -0.184...]. The modulated noise sequence is weak in the low-frequency band and strong in the high-frequency band. After modulation, the modulated noise is added point-by-point to the original 128-point signal, and after constraint correction, the first set of perturbation signals is formed. The noise is then injected into the controller, and a second seed (0x7B91D4A8) is loaded. The above process is repeated to generate the second set of perturbation signals, and so on, until all 16 sets of perturbation signals are generated, resulting in a set of multiple perturbation signals. These 16 sets of perturbation signals share the same original signal body, but each is supplemented with noise of different random implementations and differentially modulated amplitudes, providing sufficient and statistically independent input data for subsequent parallel empirical mode decomposition.

[0045] Precise and differentiated noise injection is achieved through spectral domain weighting. This utilizes the uniform spectral characteristics of white noise to fill the time-frequency gaps in the signal, eliminating the core cause of mode aliasing in EMD decomposition at its root, while also preventing excessive noise contamination of effective features in high-energy target regions. A hardware random number generation submodule, combined with multiple sets of different random seeds, provides statistically independent and sufficiently diverse noise implementation samples, ensuring that multiple decomposition results can effectively offset random biases caused by noise. Furthermore, overall signal-to-noise ratio constraints and local frequency band perturbation intensity constraints ensure that the actual effect of each noise injection remains stable within the preset target range, enhancing the consistency and repeatability of EEMD decomposition across different noise implementations.

[0046] Empirical mode decomposition is performed on the multiple sets of disturbance signals to establish an intrinsic mode function sequence. Based on the instantaneous frequency distribution and energy characteristics of each intrinsic mode function, a mode similarity metric for cross-disturbance sets is constructed.

[0047] Furthermore, the parallel computing array within the field-programmable gate array performs empirical mode decomposition on the multiple sets of disturbance signals respectively. The parallel computing array contains multiple independent empirical mode decomposition processing cores. Each empirical mode decomposition processing core shares the timing signal to be processed and the modulated noise sequence, performs superposition and decomposition operations in parallel, and writes the decomposed intrinsic mode function sequence into an off-chip double-rate synchronous dynamic random access memory.

[0048] Furthermore, a modal similarity metric for cross-disturbance sets is constructed based on the instantaneous frequency distribution and energy characteristics of each intrinsic mode function. This includes: extracting the instantaneous frequency evolution trajectory and energy distribution sequence corresponding to the modal components of each intrinsic mode function, constrained by the generation order of the disturbance signal set, and establishing cross-disturbance modal candidate correspondences under a unified time index; using the modal candidate correspondences to perform segmented trajectory alignment and energy distribution matching on the potential corresponding modal components in different disturbance results, calculating the local matching degree reflecting the consistency of frequency evolution and the consistency of energy concentration trend, and forming a continuous matching response sequence along the time dimension; performing full-time domain integral fusion on the continuous matching response sequence, and constructing a modal similarity metric that characterizes the consistency and stability of modal cross-disturbances by combining the occurrence frequency and stable duration interval of each modal component in multiple disturbances.

[0049] Specifically, after the noise injection controller performs multiple superpositions of non-uniform amplitude modulation noise and generates multiple sets of disturbance signals, it distributes these sets of disturbance signals to the parallel computing array within the FPGA for Empirical Mode Decomposition (EMD) processing. The parallel computing array within the FPGA consists of N independent EMD decomposition processing cores, where N equals a preset noise injection multiplicity, such as 16. Each processing core shares the original timing signal to be processed and each set of modulated noise sequences, performing superposition and decomposition operations in parallel. Furthermore, each processing core is structurally identical, containing extreme point detection logic, cubic spline interpolation logic, mean envelope calculation logic, and iteration termination judgment logic, thus realizing a complete EMD screening process.

[0050] During the Empirical Mode Decomposition (IMF) process, each processing core reads a corresponding set of perturbation signals from multiple sets of perturbation signals and independently executes the complete IMF process for each perturbation signal: Each processing core first locates all local maxima and local minima in the current perturbation signal sequence to be decomposed using extremum detection logic. Then, it uses cubic spline interpolation logic to fit the envelopes of the maxima and minima respectively, generating upper and lower envelopes. At each sampling time, it calculates the instantaneous mean of the upper and lower envelopes to form a mean envelope sequence. The mean envelope sequence is then subtracted from the time series signal sequence to be processed to obtain the first-order residual component. The iterative screening process of extremum detection, envelope fitting, and mean subtraction is repeated for the first-order residual component until the residual component meets the IMF criteria, i.e., the number of extrema in the entire time domain is equal to or differs from the number of zero-crossings by at most one, and the mean of the upper and lower envelopes is zero at any time. The residual component is then marked as a first-order intrinsic mode function (IMF) component and output. Then, the processing core subtracts all extracted IMF components from the original perturbation signal to obtain a new residual signal to be decomposed, and continues to perform the above screening iteration on it, extracting IMF2, IMF3, ... in order until the residual signal becomes a monotonic sequence or the amplitude is lower than a preset threshold, such as 0.2% to 0.5% of the maximum amplitude of the signal, at which point the decomposition is terminated, thereby outputting a set of intrinsic mode functions (IMF) sequences arranged from high to low frequency. All N processing cores execute the above process in parallel, and each writes the decomposed IMF sequence, the corresponding order label and the number of the perturbation group to the off-chip double rate synchronous dynamic random access memory to avoid on-chip buffer overflow, thus completing the parallel empirical mode decomposition of multiple sets of perturbation signals.

[0051] Constrained by the generation order of the perturbation signal set, i.e., in the order of group 1, group 2, ..., group N, the IMF component sequences obtained from each decomposition are read group by group. For each IMF component, a Hilbert transform is performed to obtain its instantaneous frequency and instantaneous amplitude. Then, under a unified time index, the instantaneous frequency value at each moment is recorded, forming a frequency-time curve, i.e., the instantaneous frequency evolution trajectory, reflecting the frequency drift and modulation characteristics of the mode component during the observation time. Simultaneously, based on the instantaneous amplitude sequence, the instantaneous energy at each moment is calculated, i.e., the square of the amplitude, forming an energy-time curve, i.e., the energy distribution sequence, reflecting the intensity fluctuations of the mode component at different moments. Under a unified time index, the instantaneous frequency evolution trajectories and energy distribution sequences of each IMF component extracted from different perturbation signal groups are traversed and compared. Mode components with similar scale ranges in different perturbation results are marked as mode candidate correspondences, establishing cross-perturbation mode candidate correspondences.

[0052] By utilizing modal candidate correspondences, segment-by-segment trajectory alignment and energy distribution matching are performed on the potential corresponding modal components in different perturbation results. For two candidate corresponding IMF components of different perturbation signal groups, the instantaneous frequency evolution trajectory sequences fA(t) and fB(t) of the two components are first extracted, and local alignment and matching are performed using sliding window correlation analysis: a fixed-length time window is set, for example, a window length of 16 sampling points and a sliding step size of 4 sampling points. The two instantaneous frequency evolution trajectory sequences are simultaneously divided into several overlapping or non-overlapping local segments according to the same time starting point. For two frequency segments within each time window, their Pearson correlation coefficient is calculated as a measure of frequency evolution consistency within that window. At the same time, the normalized cross-correlation coefficient of the two energy distribution sequences within the corresponding window is calculated as a measure of energy concentration trend consistency. The frequency evolution consistency measure and the trend consistency measure are weighted and fused, for example, each with a weight of 0.5, to obtain the local matching degree of the window, which reflects the consistency of frequency evolution and energy concentration trend. The above calculations are performed sequentially along all time windows and then spliced ​​along the time dimension to form a continuous matching response sequence. Each element in the matching response sequence corresponds to the local matching degree of a time window, recording the time-frequency similarity of the candidate corresponding mode in each observation period.

[0053] A full-time-domain integral fusion is performed on the continuous matching response sequence, that is, the local matching degrees of all time windows are accumulated and averaged to obtain the time-domain average matching degree. Simultaneously, the frequency of occurrence and stable duration interval of the candidate modal component in multiple perturbations are statistically analyzed. The frequency of occurrence is the number of times it is identified as having a candidate correspondence in all N sets of decomposition results. The stable duration interval is the ratio of the total length of intervals in the matching response sequence that continuously exceed a preset high similarity threshold, such as 0.75, to the total length of observations. The time-domain average matching degree, frequency of occurrence, and proportion of stable duration intervals are fused and calculated to construct the modal similarity metric S for the candidate modality. modal It is used to characterize modal consistency and existence stability across perturbations. ,in, F represents the time-domain average matching degree. o T is the total number of times this mode appears in all perturbation decomposition results. s To ensure the total length of the stable continuous interval, T total The total observation time is w1, w2, and w3 are preset weighting coefficients, such as 0.4, 0.3, and 0.3.

[0054] For example, the FPGA is configured with 16 parallel EMD decomposition processing cores. The decomposition result of the first disturbance signal is a 5th-order IMF component, including IMF1 to IMF5, plus a residual component; the decomposition result of the second decomposition is a 6th-order IMF component, including IMF1 to IMF6 plus a residual component; ...; the 16th decomposition result is also a 5th-order IMF component plus a residual component. Each processing core writes the decomposition result into an off-chip double-rate synchronous dynamic random access memory. Using the first set of decomposition results as a reference, the IMF3 component is extracted, and a Hilbert transform is performed on the IMF3 to obtain an instantaneous frequency evolution trajectory f3(t) of length 128 points and an energy distribution sequence E3(t) of the same length 128 points. Then, the instantaneous frequency evolution trajectories of IMF2, IMF3, and IMF4 in the second decomposition results were extracted, and segment-by-segment trajectory alignment and local matching degree calculation were performed with f3(t). The comparison revealed that the correlation coefficient between the instantaneous frequency evolution trajectories of IMF3 in the second group and IMF3 in the first group at 128 time points was 0.92, the energy distribution shape similarity was 0.88, and the average value of the weighted comprehensive local matching response sequence was 0.90. The matching degree of IMF2 in the second group was 0.35, and that of IMF4 was 0.28. Therefore, IMF3 in the second group and IMF3 in the first group were determined to be candidate corresponding modes. The same comparison was performed in the decomposition results of groups 3 to 16, and the frequency of occurrence of this candidate mode was counted: it appeared 13 times in groups 1, 2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, and 16, with a frequency of 13 / 16 = 0.8125. Meanwhile, among the 13 matching groups, the average length of intervals exceeding the high similarity threshold of 0.7 in the matched response sequences was 112 points, accounting for 87.5% of the total observed length of 128 points. Based on the above data, the average temporal matching degree of this candidate modality is 0.90, the frequency of occurrence is 0.8125, and the proportion of stable and persistent intervals is 0.875. Let the weight coefficients w1=0.4, w2=0.3, and w3=0.3, then the modality similarity metric is calculated as: S modal =0.4×0.90+0.3×0.8125+0.3×0.875=0.86625.

[0055] By using multi-core parallel EMD decomposition of FPGA parallel computing array, data processing efficiency is improved. Through similarity index constructed by cross-disturbance trajectory matching and multi-dimensional feature fusion, the physical authenticity of each modal component is accurately quantified, providing a quantifiable objective basis for subsequent modal merging and reconstruction.

[0056] Modal similarity metrics are used to cluster, align, merge, and reconstruct modal components from different perturbation signal decomposition results, generating a unified set of modal components.

[0057] Specifically, all IMF components obtained from the decomposition of all N groups of perturbation signals and their corresponding modal similarity metrics are obtained. IMF components with modal similarity metrics below a preset confirmation threshold, such as 0.5, are marked as noise-induced spurious components and removed from the subsequent clustering and alignment process. Through threshold filtering, the remaining IMF components are considered candidate real modes, and a modal similarity graph is constructed: each node in the modal similarity graph represents a candidate IMF component, accompanied by its perturbation signal group number and order label. The edge weight between nodes is the modal similarity metric value between the two components. The modal similarity graph is a sparse graph based on threshold pruning. For any two candidate IMF components, if the similarity metric between them is higher than a preset clustering threshold, such as 0.65, a connection edge is established between them, with the edge weight being the similarity metric value. If it is lower than the clustering threshold, they are considered not to belong to the same physical mode, and no connection is established.

[0058] Breadth-first search is used to perform connected component analysis on the constructed modal similarity graph. All interconnected node groups are found within the graph, where any two nodes within a connected group are connected by an edge, and there are no connecting edges between groups. Each connected component represents a cluster, and all IMF components within each cluster exhibit high similarity under perturbation conditions, representing the same physical mode in different noise implementations. For example, if IMF3 from group 1, IMF4 from group 2, IMF3 from group 5, and IMF2 from group 7 are grouped into the same connected component, it indicates that although these four IMF components have different orders in their respective decomposition results, their time-frequency evolution characteristics and energy distribution are highly consistent, essentially representing multiple different manifestations of the same real physical mode.

[0059] After clustering, fine alignment and merging reconstruction of time-frequency trajectories are performed on all IMF components within each cluster. First, the component with the highest modal similarity metric within the cluster is selected as the reference baseline component for that cluster. Using the time axis of this reference baseline component as a benchmark, dynamic time warping (DTW) alignment is performed on the other IMF components within the cluster to eliminate minor time offsets or phase differences caused by noise injection, ensuring comparability of all components under a unified time index. After alignment, all aligned IMF components within the cluster are weighted and fused. The fusion weights are determined by normalizing the modal similarity metric values ​​of each component; components with higher metrics are assigned higher weights in the fusion. The instantaneous amplitudes of each component within the cluster are then weighted and averaged according to the normalized weights to obtain the unified modal component value for that cluster. After performing the above weighted fusion on each cluster, a unified modal component set is obtained. Each component in the unified modal component set is a pure estimate that best represents a certain true oscillation mode in the signal, obtained by statistical fusion of multiple sets of perturbation decompositions after excluding the random influence of a single noise injection.

[0060] By constructing modal similarity graphs and performing connected component analysis, automatic identification and clustering of corresponding modal components in different perturbation decomposition results are achieved. Through weighted fusion within clusters, components corresponding to the same physical mode in multiple decomposition results are statistically synthesized, resulting in a unified modal component with a lower noise floor and a higher signal-to-noise ratio in the final output, while preserving the true time-frequency structure of the signal, further improving the accuracy and efficiency of radar signal feature extraction.

[0061] A multidimensional modal evaluation index is established for the unified modal component set based on energy concentration, instantaneous frequency stability, time-frequency trajectory continuity, and matching deviation from clutter template, and the core modal component subset is located.

[0062] Furthermore, a multi-dimensional modal evaluation index is established for the unified modal component set based on energy concentration, instantaneous frequency stability, time-frequency trajectory continuity, and matching deviation from clutter template. This includes: performing a Hilbert transform on each modal component in the unified modal component set to extract the component's instantaneous amplitude sequence and instantaneous frequency sequence; calculating the total energy of the modal component based on the component's instantaneous amplitude sequence, defining a time-frequency compact support region based on the aggregation range of the component's instantaneous frequency sequence, and using the ratio of energy within the time-frequency compact support region to the total energy as the energy concentration index; calculating the normalized local variance of the component's instantaneous frequency sequence, and using the calculation result as the instantaneous frequency... Rate stability index; perform time-frequency trajectory continuity detection on the instantaneous frequency sequence of the components, calculate the frequency difference between adjacent sampling times, mark the position where the absolute value of the difference exceeds the preset frequency continuity threshold as the break point, and generate a time-frequency trajectory continuity index based on the ratio of the length of the maximum continuous unbroken segment to the total length of the sequence; obtain the clutter time-frequency template corresponding to the typical clutter distribution characteristics in the current radar detection scenario, calculate the two-dimensional normalized cross-correlation coefficient between the time-frequency distribution of the modal components and the clutter time-frequency template, and construct the matching deviation index; output the energy concentration index, instantaneous frequency stability index, time-frequency trajectory continuity index, and matching deviation index as multi-dimensional modal evaluation indexes.

[0063] Furthermore, locating the core modal component subset includes: determining the evaluation attention weight of the modal component in each time-frequency region based on the spectral domain weight mapping relationship; using the evaluation attention weight to perform weighted fusion of the energy concentration index, instantaneous frequency stability index, time-frequency trajectory continuity index, and matching deviation index to establish a target confidence score for each modal component; jointly judging the target confidence scores of all modal components in the unified modal component set with the modal similarity measurement index across the perturbation set, and selecting modal components whose target confidence scores are higher than an adaptive threshold and whose modal similarity measurement index meets the preset stability criterion to constitute the core modal component subset.

[0064] Specifically, a Hilbert transform is performed on each modal component ck(t) in the unified modal component set to construct an analytic signal z. k (t) = ck(t) + j·H[ck(t)], where H[·] represents the Hilbert transform operator, and j is the imaginary unit. The instantaneous amplitude sequence A of the components is extracted from the magnitude of the analytic signal |zk(t)|. k (t), derived from the phase of the analytic signal derivative with respect to time Extracting the instantaneous frequency sequence f of the components k (t). Based on the component instantaneous amplitude sequence A k (t) Calculate the total energy of the modal components And analyze the instantaneous frequency sequence f of the components. k The aggregation range of (t) is defined by centering on the mean of the instantaneous frequency sequence of the component, thus establishing a time-frequency compact support region. This region is the set of moments where the instantaneous frequency value falls within the range of [mean instantaneous frequency - standard deviation of instantaneous frequency sequence, mean instantaneous frequency + standard deviation of instantaneous frequency sequence]. This represents the time-domain interval where the energy of this modal component is most concentrated and the frequency is most stable. The sum of the instantaneous energy at each moment within this time-frequency compact support region is calculated, and its ratio to the total energy is used to obtain the energy concentration index C. energy .

[0065] For the component instantaneous frequency sequence f k (t) To calculate the normalized local variance, first calculate the global variance of the component instantaneous frequency sequence as the normalization benchmark. Then, slide a preset sliding window along the time axis window by window. The preset sliding window is used to divide the component instantaneous frequency sequence into multiple local segments along the time axis. For example, the window length of the preset sliding window is 16 sampling points, and the sliding step size is 4 sampling points. Calculate the local variance of the component instantaneous frequency value within each sliding window. Divide the local variance of the window by the global variance to calculate the normalized local variance. Then, calculate the time average of the normalized local variances of all sliding windows to obtain the instantaneous frequency stability index S. freq S freq The smaller the value, the smaller the fluctuation amplitude of the instantaneous frequency within the observation time compared to the global fluctuation, the more stable the frequency, and the more consistent it is with the constant Doppler frequency characteristics of the echo of a uniform linear motion or stationary target. The larger the value, the more drastic the frequency fluctuation.

[0066] For the component instantaneous frequency sequence f k (t) Perform time-frequency trajectory continuity detection, calculate the frequency difference between adjacent sampling times, and obtain the absolute value of the difference between adjacent sampling times Δf(t)=|f k (t+1)-f k (t)∣。A preset frequency continuity threshold θf is set, for example, to 0.5 times the global standard deviation of the component instantaneous frequency sequence. The absolute value of the difference is compared with the preset frequency continuity threshold θf. When Δf(t)>θf, the position is marked as a breakpoint, indicating that the frequency trajectory has discontinuously jumped at this point. When Δf(t)≤θf, the position is marked as a continuity point, that is, the frequency trajectory continues smoothly at this point. The length of the longest continuous unbroken segment formed by all adjacent continuity points is counted, that is, the number of sampling points L contained in the longest continuous unbroken segment. max And calculate the time-frequency trajectory continuity index T. continuity =L max / T, where T is the total sequence length, i.e., the total number of sampling points corresponding to the total observation duration. T continuityA value closer to 1 indicates that the frequency trajectory of this modal component remains continuous and smooth during the observation time, conforming to the inertial constraints of the motion of a real physical target. continuity The smaller the value, the more frequently the frequency trajectory breaks.

[0067] The clutter time-frequency template, corresponding to the typical clutter distribution characteristics in the current radar detection scenario, is obtained from the radar database or scenario configuration parameters. This template describes the time-frequency distribution characteristics of typical clutter in a specific scenario, such as sea clutter, ground clutter, and meteorological clutter. The clutter time-frequency template is stored in a two-dimensional matrix, with rows representing the time axis and columns representing the frequency axis. Matrix element values ​​are clutter power reference values ​​for the corresponding time-frequency units. The time-frequency distribution of the current modal component is obtained through short-time Fourier transform. The two-dimensional normalized cross-correlation coefficient ρ between the time-frequency distribution of the current modal component and the clutter template is then calculated. Where P(i,j) is the time-frequency power value of the modal component, and Q(i,j) is the reference value of the clutter template. , These are the means of both. The two-dimensional normalized cross-correlation coefficient ρ ranges from [-1, 1]. The closer ρ is to 1, the more similar the time-frequency distribution of the modal component is to the clutter template; the closer ρ is to 0 or a negative value, the more significant the difference between the component and the clutter template. The matching deviation index is defined as M. deviation =1-∣ρ∣, so that the larger the value, the farther away from clutter and the stronger the target attribute.

[0068] Furthermore, the energy concentration index, instantaneous frequency stability index, time-frequency trajectory continuity index, and matching deviation index are output as multi-dimensional modal evaluation indicators.

[0069] Based on the spectral domain weight mapping relationship, the spectral domain weight coefficients of all time-frequency local sub-intervals covered by each modal component are accumulated and normalized to obtain the evaluation attention weight of the modal component in each time-frequency region. Then, the evaluation attention weight is used to weight and fuse the energy concentration index, instantaneous frequency stability index, time-frequency trajectory continuity index, and matching deviation index to establish a target confidence score Score for each unified modal component, Score = a1 × C. energy +a2×(1-S freq )+a3×T continuity +a4×M deviation a1, a2, a3, and a4 are the evaluation attention weights dynamically determined by the spectral domain weight mapping relationship. The higher the target confidence score, the stronger the target attribute of the modal component, that is, the energy is concentrated, the frequency is stable, and the trajectory is continuous.

[0070] Calculate the mean and standard deviation of the target confidence scores for all uniform modal components. Set the adaptive threshold to mean ± β × standard deviation, where β is a preset adjustment coefficient, preferably between 0.5 and 1.0. Jointly discriminate the target confidence scores of all modal components in the uniform modal component set with the modal similarity metric across the perturbation set. Select modal components whose target confidence scores are greater than or equal to the adaptive threshold and whose modal similarity metric meets the preset stability criterion (e.g., 0.6) to form the core modal component subset.

[0071] For example, such as Figure 2 As shown, a joint discriminant analysis graph of modal components was constructed. The horizontal axis represents the sequence number of the modal components, and the vertical axis represents the normalized index value of the target confidence score and modal similarity metric for the corresponding modal component. The unified modal component set contains 12 components, labeled as U1 to U12. Taking component U1 as an example, the energy concentration index C is calculated. energy =0.82, the instantaneous frequency stability index S of the instantaneous frequency sequence freq =0.012. There are 3 locations where the absolute value of the frequency difference between adjacent sampling points exceeds the preset threshold of 50Hz. The longest continuous unbroken segment is 112 points, and the total length is 128 points. The time-frequency trajectory continuity index T continuity =112 / 128=0.875. The two-dimensional normalized cross-correlation coefficient between this modal component and the sea clutter template is 0.12, and the matching deviation M deviation =1-0.12=0.88. According to the spectral domain weight mapping relationship, the frequency band 120-150Hz where U1 is located corresponds to the medium energy concentration region in the original signal, and the spectral domain weight coefficient is 0.25. The evaluation attention weight of this region is set to 0.7, and the weighted fusion weights of the four-dimensional indicators are 0.3, 0.2, 0.2, and 0.3, respectively. Then, the target confidence score of U1 is: Score=0.3×0.82+0.2×(1-0.012)+0.2×0.875+0.3×0.88=0.8826.

[0072] Target confidence scores were calculated for all 12 components, yielding μ=0.52, σ=0.28, and β=0.8, with an adaptive threshold of 0.744. U1's score of 0.8826 is greater than 0.744, and its modal similarity metric is 0.866, higher than the stability threshold of 0.6; therefore, U1 is selected for the core modal component subset. Following the same discrimination process, U2's target confidence score of 0.81 and modal similarity metric of 0.79, and U3's target confidence score of 0.76 and modal similarity metric of 0.71 also meet the joint discrimination criteria and are included in the core modal component subset. U4's target confidence score of 0.75 is slightly higher than the adaptive threshold, but its modal similarity metric of 0.48 is less than the stability criterion of 0.6, therefore it is excluded. The scores of U5 to U12 are all below 0.744, indicating they are clutter or noise-dominated components, and are also excluded from the core subset.

[0073] By establishing a four-dimensional evaluation index of energy concentration, instantaneous frequency stability, time-frequency trajectory continuity, and clutter matching deviation, each modal component is quantitatively evaluated from a physical mechanism perspective. This ensures that the selection criteria are deeply coupled with the physical laws of radar target detection. By constructing an adaptive selection system adapted to the current scenario, the system avoids the crude mode of traditional EEMD that relies on manual experience to select effective IMF components. Through four-dimensional weighted evaluation guided by spectral domain weights, combined with stability verification of modal similarity, clutter components and spurious components are eliminated, achieving effective separation from clutter and noise backgrounds and improving the credibility and reliability of core components.

[0074] Perform feature extraction on a subset of the core modal components and output the feature extraction results.

[0075] Furthermore, feature extraction of the core modal component subset is performed, and the feature extraction results are output, including: inputting the core modal component subset to the envelope demodulation unit and the phase tracking unit in the echo processing link respectively, extracting the corresponding instantaneous amplitude sequence and instantaneous phase sequence, and constructing an instantaneous frequency sequence through phase expansion processing; calling the transmitted signal reference template of the matched filter to perform pulse compression consistency correction on the instantaneous frequency sequence, extracting the main feature of target scattering intensity, and performing micro-Doppler perturbation separation on the instantaneous frequency sequence to obtain the target motion frequency shift feature; weighting and coupling the main feature of target scattering intensity and the target motion frequency shift feature based on the spectral domain weight mapping relationship to construct a time-frequency jointly constrained target feature vector, and outputting the target feature vector as the feature extraction result.

[0076] Specifically, a subset of core mode components is input to the envelope demodulation unit and the phase tracking unit in the echo processing link, respectively. The envelope demodulation unit extracts the instantaneous amplitude sequence by performing a Hilbert transform on the mode components and taking their magnitudes. This sequence reflects the signal intensity fluctuations of the mode component at different times, directly corresponding to the fluctuations in the target's cross-sectional area (RCS) during the observation time. The phase tracking unit extracts the instantaneous phase sequence V. k (t), used to reflect the phase evolution of this modal component at different times, instantaneous phase sequence V k (t) is output in the form of the main value interval (-π, π], meaning all phase values ​​are folded into this interval, resulting in discontinuous phase transitions. Phase unrolling is performed on the instantaneous phase sequence by detecting the phase difference between adjacent sampling points: if the phase difference between two adjacent points is greater than +π, then 2π is subtracted from all subsequent phase values; if the phase difference is less than -π, then 2π is added to all subsequent phase values, thus restoring the folded phase to a continuously changing unrolled phase sequence W. k (t). Taking the central difference derivative of the expanded phase sequence, we obtain the instantaneous frequency sequence: ,in, The sampling period is the time difference between two adjacent sampling points, and its value is equal to the reciprocal of the sampling frequency.

[0077] The transmitted signal reference template of the matched filter is invoked to perform pulse compression consistency correction on the instantaneous frequency sequence. Specifically, the time-frequency characteristics of the transmitted signal reference template, i.e., the variation law of the instantaneous frequency of the transmitted signal over time, are deconvolved with the instantaneous frequency sequence of the current mode component in the frequency domain. That is, the instantaneous frequency sequence of the mode component is multiplied with the transmitted reference template of the matched filter in the frequency domain using complex conjugate multiplication. This cancels the phase distortion introduced by the modulation of the transmitted waveform, enabling the echo energy of each range cell to achieve coherent accumulation in the slow time dimension. After pulse compression consistency correction, the main feature of the target scattering intensity is extracted from the correction result. The main feature of the target scattering intensity is the peak energy amplitude of the corrected signal and its corresponding time delay position, which quantitatively reflects the radar cross section (RCS) intensity of the target scattering point corresponding to the core mode component. The larger the value of the main feature of the target scattering intensity, the stronger the electromagnetic scattering capability of the target and the more significant the back reflection of radar waves.

[0078] Micro-Doppler perturbation separation is performed on the instantaneous frequency sequence, specifically by performing a short-time Fourier transform to obtain its time-frequency spectrum. Energy centroid tracking is then performed on the time-frequency spectrum to obtain the baseline of the main Doppler frequency, which is the frequency value corresponding to the maximum energy value at each instant in the time spectrum. This value is then smoothed and filtered to obtain the main Doppler frequency shift estimate. Subtracting the main Doppler frequency shift estimate from the instantaneous frequency sequence yields the micro-Doppler perturbation component sequence. Time-varying characteristics, such as modulation amplitude and modulation period, are extracted from this micro-Doppler perturbation component sequence to obtain the target motion frequency shift characteristics, quantitatively describing the target's micro-motion characteristics.

[0079] The main feature of target scattering intensity is scaled according to the weight coefficients in the corresponding frequency band based on the spectral domain weight mapping relationship. The target motion frequency shift features, such as modulation amplitude and modulation period, are synchronously scaled with the same weight. Then, the two sets of scaled features are concatenated and spliced ​​according to the frequency dimension to form a target feature vector with joint time and frequency constraints. This target feature vector is output as the feature extraction result for use by the target classification, recognition and tracking modules, thereby improving the radar's target recognition accuracy and tracking stability in complex and cluttered environments.

[0080] By extracting the main scattering intensity features reflecting the target's electromagnetic scattering capability and size attributes through pulse compression consistency correction, and extracting the motion frequency shift features reflecting the target's translational velocity and micro-motion characteristics through micro-Doppler perturbation separation, the static structure and dynamic behavior of the target are decoupled and complementary. Then, the above features are weighted and coupled based on the spectral domain weight mapping relationship, ultimately achieving effective noise suppression of radar signals, accurate separation of targets and clutter, and complete mining and characterization of multi-dimensional fine features of targets, thereby improving the overall reliability and feature output accuracy of radar target detection in complex and cluttered scenarios.

[0081] Example 2 is based on the same inventive concept as the radar signal feature extraction, analysis and optimization method based on EEMD in the previous examples, such as... Figure 3 As shown, this application provides a radar signal feature extraction, analysis, and optimization system based on EEMD, wherein the radar signal feature extraction, analysis, and optimization system based on EEMD includes: The signal forming component 11 is used to perform analog-to-digital conversion and time-series reconstruction on the received raw echo signal via an echo acquisition unit to form a time-series signal to be processed. The signal analysis component 12 is used to perform spectral energy distribution analysis and local time-frequency density estimation on the time-series signal to be processed, and to construct a spectral domain weight mapping relationship. The disturbance signal generation component 13 is used to perform multiple non-uniform amplitude modulation random noise superposition processing on the time-series signal to be processed after the noise injection controller receives the spectral domain weight mapping relationship, and to generate multiple sets of disturbance signals. The metric construction component 14 is used to perform empirical mode decomposition on the multiple sets of disturbance signals respectively to establish intrinsic modes. The system comprises: a mode function sequence, which constructs a mode similarity metric for cross-disturbance sets based on the instantaneous frequency distribution and energy characteristics of each intrinsic mode function; a mode component processing component 15, which uses the mode similarity metric to cluster, align, merge, and reconstruct mode components from different disturbance signal decomposition results to generate a unified mode component set; an evaluation index establishment component 16, which establishes multi-dimensional mode evaluation indices for the unified mode component set based on energy concentration, instantaneous frequency stability, time-frequency trajectory continuity, and matching deviation from clutter templates to locate the core mode component subset; and a feature extraction component 17, which performs feature extraction on the core mode component subset and outputs the feature extraction results.

[0082] Furthermore, the feature extraction component 17 is also used to: input the subset of core modal components to the envelope demodulation unit and the phase tracking unit in the echo processing link respectively, extract the corresponding instantaneous amplitude sequence and instantaneous phase sequence, and construct an instantaneous frequency sequence after phase expansion processing; call the transmitted signal reference template of the matched filter to perform pulse compression consistency correction on the instantaneous frequency sequence, extract the main feature of target scattering intensity, and perform micro-Doppler perturbation separation on the instantaneous frequency sequence to obtain the target motion frequency shift feature; perform weighted coupling of the main feature of target scattering intensity and the target motion frequency shift feature based on the spectral domain weight mapping relationship to construct a target feature vector with time-frequency joint constraints, and output the target feature vector as the feature extraction result.

[0083] Furthermore, the disturbance signal generation component 13 is also used for: dividing the time-series signal to be processed into multiple time-frequency local sub-intervals according to the spectral domain weight mapping relationship, and assigning a corresponding noise injection weight coefficient to each time-frequency local sub-interval, wherein the noise injection weight coefficient is inversely correlated with the energy density and spectral sparsity of the corresponding time-frequency local sub-interval; after reading multiple sets of noise sequences with different random seeds and amplitude distribution parameters, performing segmented amplitude modulation on the noise sequences according to the noise injection weight coefficient, so that the noise is restricted in the high-energy concentrated region and enhanced in the low-energy or spectral gap region; successively superimposing the modulated noise sequence with the time-series signal to be processed, and constraining and correcting the overall signal-to-noise ratio and local frequency band disturbance intensity of the superimposed signal in each superposition process, generating multiple sets of disturbance signals.

[0084] Furthermore, the metric construction component 14 is also used to: extract the instantaneous frequency evolution trajectory and energy distribution sequence corresponding to the modal components of each intrinsic mode function, constrained by the generation order of the disturbance signal set, and establish cross-disturbance modal candidate correspondence under a unified time index; use the modal candidate correspondence to perform segmented trajectory alignment and energy distribution matching on the potential corresponding modal components in different disturbance results, calculate the local matching degree reflecting the consistency of frequency evolution and the consistency of energy concentration trend, and form a continuous matching response sequence along the time dimension; perform full-time domain integral fusion on the continuous matching response sequence, and construct a modal similarity metric that characterizes the consistency and stability of modal cross-disturbance based on the occurrence frequency and stable duration interval of each modal component in multiple disturbances.

[0085] Furthermore, the evaluation index establishment component 16 is also used for: performing a Hilbert transform on each modal component in the unified modal component set to extract the component instantaneous amplitude sequence and the component instantaneous frequency sequence; calculating the total energy of the modal component based on the component instantaneous amplitude sequence, and defining a time-frequency compact support region based on the aggregation range of the component instantaneous frequency sequence, using the ratio of energy within the time-frequency compact support region to the total energy as an energy concentration index; calculating the normalized local variance of the component instantaneous frequency sequence, and using the calculation result as an instantaneous frequency stability index; and performing time-frequency analysis on the component instantaneous frequency sequence. Frequency trajectory continuity detection involves calculating the frequency difference between adjacent sampling times, marking the locations where the absolute value of the difference exceeds a preset frequency continuity threshold as breakpoints, and generating a time-frequency trajectory continuity index based on the ratio of the length of the maximum continuous unbroken segment to the total sequence length. A clutter time-frequency template corresponding to the typical clutter distribution characteristics in the current radar detection scenario is obtained, and the two-dimensional normalized cross-correlation coefficient between the time-frequency distribution of the modal components and the clutter time-frequency template is calculated to construct a matching deviation index. The energy concentration index, instantaneous frequency stability index, time-frequency trajectory continuity index, and matching deviation index are output as multi-dimensional modal evaluation indicators.

[0086] Furthermore, the evaluation index establishment component 16 is also used to: determine the evaluation attention weight of the modal component in each time-frequency region based on the spectral domain weight mapping relationship; use the evaluation attention weight to perform weighted fusion of the energy concentration index, instantaneous frequency stability index, time-frequency trajectory continuity index and matching deviation index to establish a target confidence score for each modal component; jointly discriminate the target confidence scores of all modal components in the unified modal component set with the modal similarity measurement index across the perturbation set, and select modal components whose target confidence scores are higher than the adaptive threshold and whose modal similarity measurement index meets the preset stability criterion to constitute the core modal component subset.

[0087] Furthermore, the signal forming component 11 is also used for: the echo acquisition unit includes an analog-to-digital converter chip and a field-programmable gate array (FPGA) front-end preprocessing module, the analog-to-digital converter chip samples the original echo signal and transmits the sampled data stream to the FPGA front-end preprocessing module through a direct memory access channel, wherein the FPGA front-end preprocessing module has built-in time series reconstruction logic, and performs segmented buffering and alignment splicing of the sampled data stream to generate the timing signal to be processed.

[0088] Furthermore, the parallel computing array within the field-programmable gate array performs empirical mode decomposition on the multiple sets of disturbance signals respectively. The parallel computing array contains multiple independent empirical mode decomposition processing cores. Each empirical mode decomposition processing core shares the timing signal to be processed and the modulated noise sequence, performs superposition and decomposition operations in parallel, and writes the decomposed intrinsic mode function sequence into an off-chip double-rate synchronous dynamic random access memory.

[0089] Furthermore, the noise injection controller is integrated within the field-programmable gate array and is equipped with a hardware random number generation submodule for generating multiple sets of noise sequences with different random seeds.

[0090] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The radar signal feature extraction, analysis and optimization method and specific examples based on EEMD in the aforementioned embodiment 1 are also applicable to the radar signal feature extraction, analysis and optimization system based on EEMD in this embodiment. Through the foregoing detailed description of the radar signal feature extraction, analysis and optimization method based on EEMD, those skilled in the art can clearly understand the radar signal feature extraction, analysis and optimization system based on EEMD in this embodiment. Therefore, for the sake of brevity, it will not be described in detail here.

[0091] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0092] Obviously, those skilled in the art can make several improvements and modifications to this application without departing from the principles of this application, and these improvements and modifications also fall within the protection scope of this application.

Claims

1. A radar signal feature extraction, analysis, and optimization method based on EEMD, characterized in that, The method includes: After receiving the raw echo signal, the echo acquisition unit performs analog-to-digital conversion and time series reconstruction to form the timing signal to be processed. Spectral energy distribution analysis and local time-frequency density estimation are performed on the time-series signal to be processed to construct a spectral domain weight mapping relationship; After the noise injection controller receives the spectral domain weight mapping relationship, it performs multiple non-uniform amplitude modulation random noise superposition processing on the time sequence signal to be processed to generate multiple sets of disturbance signals. Empirical mode decomposition is performed on the multiple sets of disturbance signals to establish an intrinsic mode function sequence. Based on the instantaneous frequency distribution and energy characteristics of each intrinsic mode function, a mode similarity metric index across disturbance sets is constructed. Modal similarity metrics are used to cluster, align, merge, and reconstruct modal components from different perturbation signal decomposition results, generating a unified set of modal components. A multidimensional modal evaluation index is established for the unified modal component set based on energy concentration, instantaneous frequency stability, time-frequency trajectory continuity, and matching deviation from clutter template, and the core modal component subset is located. Perform feature extraction on a subset of the core modal components and output the feature extraction results.

2. The radar signal feature extraction, analysis, and optimization method based on EEMD as described in claim 1, characterized in that, Perform feature extraction on a subset of the core modal components and output the feature extraction results, including: The core modal component subsets are respectively input to the envelope demodulation unit and the phase tracking unit in the echo processing link to extract the corresponding instantaneous amplitude sequence and instantaneous phase sequence, and then construct the instantaneous frequency sequence through phase expansion processing; The pulse compression consistency correction is performed on the instantaneous frequency sequence by calling the transmitted signal reference template of the matched filter, the main feature of the target scattering intensity is extracted, and the micro-Doppler perturbation separation is performed on the instantaneous frequency sequence to obtain the target motion frequency shift feature; Based on the spectral domain weight mapping relationship, the main feature of the target scattering intensity and the frequency shift feature of the target motion are weighted and coupled to construct a target feature vector with joint time and frequency constraints, and the target feature vector is output as the feature extraction result.

3. The radar signal feature extraction, analysis, and optimization method based on EEMD as described in claim 1, characterized in that, Multiple random noise superposition processes with non-uniform amplitude modulation are performed on the timing signal to be processed to generate multiple sets of disturbance signals, including: The noise injection controller divides the time-series signal to be processed into multiple time-frequency local sub-intervals according to the spectral domain weight mapping relationship, and assigns a corresponding noise injection weight coefficient to each time-frequency local sub-interval. The noise injection weight coefficient is inversely related to the energy density and spectral sparsity of the corresponding time-frequency local sub-interval. After reading multiple noise sequences with different random seeds and amplitude distribution parameters, the noise sequences are segmented and amplitude modulated according to the noise injection weighting coefficient, so that the noise is restricted in the high-energy concentrated region and enhanced in the low-energy or spectral gap region. The modulated noise sequence is superimposed on the timing signal to be processed one after another, and the overall signal-to-noise ratio and local frequency band disturbance intensity of the superimposed signal are constrained and corrected during each superposition process to generate multiple sets of disturbance signals.

4. The radar signal feature extraction, analysis, and optimization method based on EEMD as described in claim 1, characterized in that, Modal similarity metrics across perturbation sets are constructed based on the instantaneous frequency distribution and energy characteristics of each intrinsic mode function, including: Using the generation order of the disturbance signal set as a constraint, the instantaneous frequency evolution trajectory and energy distribution sequence corresponding to the modal components of each intrinsic mode function are extracted, and a cross-disturbance modal candidate correspondence is established under a unified time index; Using the modal candidate correspondence, segment-by-segment trajectory alignment and energy distribution matching are performed on the potential corresponding modal components in different perturbation results. The local matching degree, which reflects the consistency of frequency evolution and energy concentration trend, is calculated, and a continuous matching response sequence is formed along the time dimension. The continuous matching response sequence is integrated and fused in the entire time domain. By combining the occurrence frequency of each modal component in multiple perturbations and the stable duration interval, a modal similarity metric index is constructed to characterize the consistency and stability of modes across perturbations.

5. The radar signal feature extraction, analysis, and optimization method based on EEMD as described in claim 1, characterized in that, A multidimensional modal evaluation index is established for the unified modal component set based on energy concentration, instantaneous frequency stability, time-frequency trajectory continuity, and matching deviation from clutter templates, including: Perform a Hilbert transform on each modal component in the unified modal component set to extract the component's instantaneous amplitude sequence and instantaneous frequency sequence; The total energy of the modal components is calculated based on the instantaneous amplitude sequence of the components, and the time-frequency compact support region is defined based on the aggregation range of the instantaneous frequency sequence of the components. The ratio of the energy in the time-frequency compact support region to the total energy is used as an energy concentration index. The normalized local variance is calculated for the instantaneous frequency sequence of the component, and the calculation result is used as an index of instantaneous frequency stability. The instantaneous frequency sequence of the component is subjected to time-frequency trajectory continuity detection. The frequency difference between adjacent sampling times is calculated. The position where the absolute value of the difference exceeds the preset frequency continuity threshold is marked as the break point. The time-frequency trajectory continuity index is generated based on the ratio of the length of the maximum continuous unbroken segment to the total length of the sequence. Obtain the clutter time-frequency template corresponding to the typical clutter distribution characteristics in the current radar detection scenario, calculate the two-dimensional normalized cross-correlation coefficient between the time-frequency distribution of the modal components and the clutter time-frequency template, and construct a matching deviation index. The energy concentration index, instantaneous frequency stability index, time-frequency trajectory continuity index, and matching deviation index are output as multi-dimensional modal evaluation indicators.

6. The radar signal feature extraction, analysis, and optimization method based on EEMD as described in claim 5, characterized in that, Locate the core modal component subset, including: The evaluation attention weight of the modal components in each time-frequency region is determined based on the aforementioned spectral domain weight mapping relationship; The energy concentration index, instantaneous frequency stability index, time-frequency trajectory continuity index, and matching deviation index are weighted and fused using evaluation attention weights to establish a target confidence score for each modal component; The target confidence scores of all modal components in the unified modal component set are jointly judged with the modal similarity metric of the cross-perturbation set. Modal components with target confidence scores higher than the adaptive threshold and modal similarity metrics that meet the preset stability criteria are selected to form the core modal component subset.

7. The radar signal feature extraction, analysis, and optimization method based on EEMD as described in claim 1, characterized in that, The echo acquisition unit includes an analog-to-digital converter chip and a field-programmable gate array (FPGA) front-end preprocessing module. The analog-to-digital converter chip samples the original echo signal and transmits the sampled data stream to the FPGA front-end preprocessing module through a direct memory access channel. The FPGA front-end preprocessing module has built-in time series reconstruction logic, which segments, buffers, aligns, and splices the sampled data stream to generate the timing signal to be processed.

8. The radar signal feature extraction, analysis, and optimization method based on EEMD as described in claim 7, characterized in that, The parallel computing array within the field-programmable gate array performs empirical mode decomposition on the multiple sets of disturbance signals. The parallel computing array contains multiple independent empirical mode decomposition processing cores. Each empirical mode decomposition processing core shares the timing signal to be processed and the modulated noise sequence, performs superposition and decomposition operations in parallel, and writes the decomposed intrinsic mode function sequence into an off-chip double-rate synchronous dynamic random access memory.

9. The radar signal feature extraction, analysis, and optimization method based on EEMD as described in claim 8, characterized in that, The noise injection controller is integrated within the field-programmable gate array and is equipped with a hardware random number generation submodule for generating multiple noise sequences with different random seeds.

10. A radar signal feature extraction, analysis, and optimization system based on EEMD, characterized in that, The step of implementing the radar signal feature extraction, analysis and optimization method based on EEMD according to any one of claims 1 to 9, wherein the radar signal feature extraction, analysis and optimization system based on EEMD comprises: The signal forming component is used to perform analog-to-digital conversion and time series reconstruction after receiving the raw echo signal, and form a timing signal to be processed. The signal analysis component is used to perform spectral energy distribution analysis and local time-frequency density estimation on the time-series signal to be processed, and to construct a spectral domain weight mapping relationship. The disturbance signal generation component is used to perform multiple non-uniform amplitude modulation random noise superposition processing on the time sequence signal to be processed after the noise injection controller receives the spectral domain weight mapping relationship, thereby generating multiple sets of disturbance signals. The metric construction component is used to perform empirical mode decomposition on the multiple sets of disturbance signals, establish an intrinsic mode function sequence, and construct a mode similarity metric across the disturbance set based on the instantaneous frequency distribution and energy characteristics of each intrinsic mode function. The modal component processing component is used to cluster, align, merge, and reconstruct modal components from different perturbation signal decomposition results using modal similarity metrics, generating a unified set of modal components. The evaluation index establishment component is used to establish multi-dimensional modal evaluation indices for a unified modal component set based on energy concentration, instantaneous frequency stability, time-frequency trajectory continuity, and matching deviation from clutter template, and to locate the core modal component subset. The feature extraction component is used to perform feature extraction on a subset of the core modal components and output the feature extraction results.

Images