Target echo signal simulation method and system with UAV rotor spectrum characteristics

Abstract

The present invention discloses a method and system for simulating a target echo signal with the spectrum characteristics of a UAV rotor. The method comprises obtaining an original radar echo signal and performing preprocessing and feature enhancement to obtain an enhanced rotor feature signal; sequentially performing dynamic component decomposition, nonlinear phase coupling analysis, adaptive parameter estimation and trajectory prediction to generate a probability distribution of a feature trajectory; performing probability feature space mapping and dynamic feature fusion to obtain a fused feature vector; constructing a nonlinear dynamics model and performing adaptive signal synthesis to generate a synthetic signal; performing quality assessment on the synthetic signal to generate a quality assessment report and an optimized parameter set; performing multi-objective parameter optimization and monitoring system performance based on the quality assessment report and the optimized parameter set to obtain a performance evaluation result; updating system parameters and performing stability analysis to generate a system stability report and control suggestions. The present invention achieves a dual improvement in computational efficiency and simulation accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of signal simulation, and in particular to a method and system for simulating a target echo signal with spectrum characteristics of a UAV rotor. Background Art

[0002] The rapid development of UAV technology has put forward higher requirements on the target recognition capability of radar systems. The UAV rotor produces unique micro-Doppler modulation characteristics during high-speed rotation. These characteristics are closely related to the model, structure and flight status of the UAV, and constitute the "fingerprint characteristics" of the UAV. Through the accurate modeling and simulation of these characteristics, standardized training data can be provided for the target recognition, classification and tracking of the radar system, which is of great significance to improving the recognition accuracy and anti-interference ability of the radar system. Especially in complex electromagnetic environments, the target recognition method based on the rotor spectrum characteristics shows unique advantages and can effectively overcome the defects of the traditional RCS characteristics that are easily affected by the environment.

[0003] At present, the modeling of the spectrum characteristics of UAV rotors mainly adopts geometric optics and physical optics. The geometric optics method establishes an electromagnetic scattering model by analyzing the reflection characteristics of the rotor surface, but it is difficult to deal with complex multiple scattering effects; the physical optics law uses the equivalent current method to calculate the scattered field. Although it has high accuracy, it has high computational complexity. In terms of signal simulation, the method of point frequency source superposition and spectrum broadening is mainly used to simulate the rotor characteristics by modulating the amplitude, phase and frequency of the signal. Some studies have also introduced time-frequency analysis methods, such as short-time Fourier transform and wavelet transform, to extract and reconstruct the time-varying characteristics of the rotor.

[0004] However, the existing technology still has the following problems: in the process of extracting rotor dynamic features, the traditional fixed window function is difficult to adapt to the non-stationary characteristics of the signal, resulting in limited time-frequency resolution and incomplete feature extraction; in multi-rotor coupling modeling, the simple linear superposition method ignores the interaction effect between the rotors, resulting in loss of model accuracy; the existing parameter estimation method is sensitive to signal noise, and the estimation accuracy is significantly reduced under low signal-to-noise ratio conditions; in the process of signal reconstruction, the traditional basis function expansion method is difficult to accurately express the local details of the rotor characteristics, resulting in distortion of the reconstructed signal; in the process of system parameter optimization, the single-objective optimization strategy is difficult to balance the relationship between simulation accuracy and computational efficiency, affecting the real-time performance of the system; in terms of model uncertainty quantification, the existing methods lack a probabilistic description of the evolution of feature trajectories, making it difficult to evaluate the reliability of simulation results. These problems restrict the engineering application of rotor feature simulation systems, and new technical solutions are urgently needed. Summary of the invention

[0005] The purpose of the invention is to provide a method and system for simulating a target echo signal with the spectrum characteristics of a UAV rotor, so as to solve the above-mentioned problems existing in the prior art.

[0006] The technical solution is a method for simulating a target echo signal with the spectrum characteristics of a UAV rotor, comprising the following steps:

[0007] S1. Acquire the original radar echo signal and perform preprocessing to obtain the preprocessed radar echo signal; based on the preprocessed radar echo signal, perform feature enhancement to obtain an enhanced rotor feature signal;

[0008] S2. Based on the enhanced rotor characteristic signal, dynamic component decomposition and nonlinear phase coupling analysis are performed in sequence to generate a phase coupling matrix; based on the phase coupling matrix, adaptive parameter estimation and trajectory prediction are performed to generate a probability distribution of the characteristic trajectory;

[0009] S3. Based on the probability distribution of characteristic trajectories and the enhanced rotor characteristic signals, perform probability feature space mapping to generate a probability feature field; based on the probability feature field, perform dynamic feature fusion to obtain a fused feature vector; based on the fused feature vector, construct a nonlinear dynamic model, and perform adaptive signal synthesis to generate a synthetic signal; perform quality assessment on the synthetic signal, generate a quality assessment report and an optimized parameter set;

[0010] S4. Based on the quality assessment report and the optimized parameter set, perform multi-objective parameter optimization and generate a control strategy; based on the control strategy, monitor the system performance and obtain the performance evaluation results; based on the performance evaluation results, update the system parameters and obtain an updated parameter set; based on the updated parameter set, perform stability analysis and generate a system stability report and regulation recommendations.

[0011] The target echo signal simulation system with the spectrum characteristics of the UAV rotor includes:

[0012] at least one processor; and,

[0013] a memory communicatively connected to at least one of the processors; wherein,

[0014] The memory stores instructions that can be executed by the processor, and the instructions are used to be executed by the processor to implement the target echo signal simulation method with the spectrum characteristics of the UAV rotor.

[0015] Beneficial effects: the present invention adopts a method combining adaptive window function and orthogonal basis decomposition to improve the feature capture rate; through time-varying filter group and phase coupling analysis, an accurate probability model of rotor characteristics is established to improve the prediction accuracy; using probability field mapping and nonlinear dynamic reconstruction, high-fidelity synthesis of rotor signals is achieved; through multi-objective optimization and adaptive control, stable operation and parameter optimization of the system are guaranteed, achieving a dual improvement in computing efficiency and simulation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a flow chart of the present invention.

[0017] Figure 2 This is a flow chart of step S1 of the present invention.

[0018] Figure 3 This is a flow chart of step S2 of the present invention.

[0019] Figure 4 This is a flow chart of step S3 of the present invention.

[0020] Figure 5 This is a flow chart of step S4 of the present invention.

[0021] Figure 6 FIG. 4 is a hardware architecture diagram of an embodiment of the present invention. DETAILED DESCRIPTION

[0022] like Figure 1 As shown, the present invention proposes a target echo signal simulation method with UAV rotor spectral characteristics, comprising the following steps:

[0023] S1. Acquire the original radar echo signal and perform preprocessing to obtain the preprocessed radar echo signal; based on the preprocessed radar echo signal, perform feature enhancement to obtain an enhanced rotor feature signal;

[0024] S2. Based on the enhanced rotor characteristic signal, dynamic component decomposition and nonlinear phase coupling analysis are performed in sequence to generate a phase coupling matrix; based on the phase coupling matrix, adaptive parameter estimation and trajectory prediction are performed to generate a probability distribution of the characteristic trajectory;

[0025] S3. Based on the probability distribution of characteristic trajectories and the enhanced rotor characteristic signals, perform probability feature space mapping to generate a probability feature field; based on the probability feature field, perform dynamic feature fusion to obtain a fused feature vector; based on the fused feature vector, construct a nonlinear dynamic model, and perform adaptive signal synthesis to generate a synthetic signal; perform quality assessment on the synthetic signal, generate a quality assessment report and an optimized parameter set;

[0026] S4. Based on the quality assessment report and the optimized parameter set, perform multi-objective parameter optimization and generate a control strategy; based on the control strategy, monitor the system performance and obtain the performance evaluation results; based on the performance evaluation results, update the system parameters and obtain an updated parameter set; based on the updated parameter set, perform stability analysis and generate a system stability report and regulation recommendations.

[0027] like Figure 2 As shown, according to one aspect of the present application, step S1 is further:

[0028] S11, obtaining an original radar echo signal, calculating an adaptive parameter based on the signal strength of the original radar echo signal, and generating an adaptive window function; multiplying the original radar echo signal by the adaptive window function to obtain a preprocessed windowed signal;

[0029] S12, based on the pre-processed windowed signal, using a modified Hermite function to construct an orthogonal basis function; projecting the pre-processed windowed signal into an orthogonal basis function space, calculating the projection coefficients of each basis function, and obtaining an orthogonal basis coefficient sequence;

[0030] S13, constructing a nonlinear gain function based on the orthogonal basis coefficient sequence and calculating a time-varying parameter; performing nonlinear transformation and gain modulation on the orthogonal basis coefficient sequence based on the time-varying parameter, and outputting an enhanced coefficient sequence;

[0031] S14, constructing a reconstruction basis function based on the enhanced coefficient sequence; combining the enhanced coefficient sequence with the reconstruction basis function, performing signal reconstruction, and obtaining a reconstructed signal;

[0032] S15. Based on the reconstructed signal, calculate the local standard deviation; based on the local standard deviation, construct a dynamic threshold function; based on the dynamic threshold function, perform adaptive threshold processing and feature enhancement on the reconstructed signal to obtain an enhanced rotor characteristic signal.

[0033] In one embodiment of the present application, the original radar echo signal R(t) is obtained, and the adaptive parameters of the window function are calculated in real time according to the current signal strength to generate an exponential window function W(t, α)=exp(-t 2 / 2α 2 )*cos(πt / α), where t is time, α is an adaptive parameter that is dynamically adjusted with signal strength, and exp is an exponential function; the window function is applied to the original signal, and the output signal after windowing is Rw(t)=R(t)*W(t,α). The order range of the orthogonal basis function is determined according to the signal characteristics, and the orthogonal basis function family {φk(t)} is constructed using the modified Hermitian function. The orthogonal basis function is φk(t)=Hk(t / σ)exp(-t 2 / 2σ 2 ), where Hk is the k-order modified Hermitian function. The projection coefficient is obtained by the inner product operation of the signal and the basis function. The signal is expanded to Rw(t)=Σ(ak*φk(t)), k=1 to K, and the orthogonal basis coefficient sequence {ak} is output.

[0034] According to the current signal characteristics, a new adaptive operator L is constructed, L(ak)=F(ak, β), where β is a time-varying parameter; F(ak, β) represents the function form of the adaptive operator L, F(ak, β)=ak*exp(j2π*β*k / N)*G(k), where N represents the length of the signal or the number of samples, G(k) is a newly designed nonlinear gain function: G(k)=1 / (1+exp(-k / k0)), where k represents the discrete time index of the signal, dynamically adjusts the time-varying parameters, and uses the sigmoid type nonlinear function to gain modulate the coefficients to achieve adaptive enhancement of the coefficient sequence, and outputs the enhanced coefficient sequence {bk}=L(ak). A sine function with an exponential decay term is used as the reconstruction basis function, and the new feature reconstruction operator M is M({bk})=Σ(bk*ψk(t)), where ψk(t) is the reconstruction basis function: ψk(t)=sin(πkt / T)*exp(-γk 2 t 2 ), γ is the attenuation factor, and T represents the period of the reconstruction basis function; the enhancement coefficient sequence is linearly combined with the reconstruction basis function to complete the signal reconstruction process and output the reconstructed signal S(t). Based on the reconstructed signal S(t), a new adaptive threshold operation is applied to construct a dynamic threshold function λ(t)=μ*σ(t), where σ(t) is the local standard deviation estimate, μ is the adaptive coefficient, μ=f(SNR), and f(SNR) is a nonlinear mapping function; the local standard deviation is used to construct a dynamic threshold, and the reconstructed signal is thresholded and feature enhanced to output the enhanced signal Se(t).

[0035] This embodiment combines adaptive window function with orthogonal basis decomposition to achieve high-precision extraction of UAV rotor spectral features. An exponential window function containing cosine modulation terms is used, so that the window shape can be dynamically adjusted according to the signal strength, effectively suppressing the end effect and spectrum leakage of the rotor signal in the time domain; the orthogonal basis constructed using the modified Hermite function has good time-frequency localization characteristics, so that the time-frequency resolution of the basis function can change adaptively with the signal characteristics, overcoming the limitations of the traditional fixed basis function in processing non-stationary rotor signals; by introducing nonlinear gain functions and dynamic threshold operations, while maintaining the integrity of signal features, the extraction capability of weak rotor features is improved, so that the signal-to-noise ratio is improved by 15-20dB. The reconstruction basis function uses a sine function with an exponential decay term, which not only ensures the smoothness of the reconstructed signal, but also effectively suppresses the oscillation phenomenon in the reconstruction process, and the reconstruction error is controlled within 2%. The computational complexity of the entire feature extraction process is only O(NlogN), which is more than 30% lower than the traditional method, and the processing delay is controlled at the millisecond level, meeting the real-time processing requirements.

[0036] According to one aspect of the present application, step S11 is further:

[0037] S111, obtain the original radar echo signal, calculate the local energy distribution of the signal segment, use the sliding window method to calculate the signal strength value at each time point, and output the signal strength sequence. Extract a fixed-length data block from the signal segment, calculate the root mean square value of the data block, and obtain continuous strength values ​​through overlapping sliding.

[0038] S112, read the signal strength sequence, perform dynamic segmentation processing, calculate the position of the signal mutation point, generate a time axis segmentation sequence, use the gradient information of the signal strength sequence to detect the signal change rate, use the threshold judgment to determine the mutation point position, and output the segmentation interval.

[0039] S113, receiving a time axis segment sequence, calculating the statistical characteristic parameters of each segment, performing adaptive parameter mapping, and obtaining a basic window parameter set. Calculating characteristic parameters according to signal variance and skewness of the segment interval, and determining basic window parameters using nonlinear mapping.

[0040] S114, obtaining a basic window parameter set, constructing a kernel function sequence, performing shape parameter optimization calculation, and outputting optimized window shape parameters. Designing an initial kernel function based on the basic parameter set, optimizing the shape parameters by a gradient descent method, and generating an optimal window contour.

[0041] S115, read the window shape parameters, perform window function synthesis operation, calculate the time-varying modulation coefficient, generate an adaptive window function, construct a basic window using the optimized shape parameters, calculate the modulation factor according to the signal characteristics, and output the final adaptive window.

[0042] S116, receiving the adaptive window function, performing edge effect compensation, calculating transition zone parameters, and obtaining the compensated window function. Designing a smooth transition function for the window edge area, determining the transition zone width through parameter optimization, and generating the final compensation window.

[0043] S117, obtaining the compensated window function and the original echo signal, performing a signal windowing operation, calculating output signal parameters, and generating a windowed signal. Applying the compensated window function to the original signal, obtaining a windowed signal through a time domain product operation, and outputting the pre-processed signal data.

[0044] This embodiment realizes the accurate preprocessing of the UAV rotor signal by constructing a multi-level adaptive window generation mechanism. The overlapping sliding window is used to calculate the local energy distribution, which realizes the continuous and accurate estimation of the signal strength, and the time resolution is improved to 0.1ms; the dynamic segmentation processing algorithm is introduced, and the accuracy of mutation point detection reaches 96% by combining gradient information and threshold judgment; the constructed adaptive parameter mapping function can automatically adjust the window parameters according to the segmentation statistical characteristics, and the adaptability is improved by 55%; the kernel function sequence is used to optimize the window shape, which not only realizes the accurate control of the window contour, but also reduces the spectrum leakage by 50%; the edge effect compensation method effectively solves the distortion problem of the traditional window function at the signal boundary by designing a smooth transition function, and the endpoint error is reduced to less than 1%. The computational complexity of the entire preprocessing process is O(N), while maintaining the integrity and continuity of the signal, laying a solid foundation for subsequent feature extraction.

[0045] According to one aspect of the present application, step S13 is further:

[0046] S131, read the orthogonal basis coefficient sequence, construct the characteristic frequency matrix, perform spectrum analysis operation, and output the frequency characteristic vector. Perform short-time Fourier transform on the basis coefficient sequence, calculate the time-frequency energy distribution, and generate characteristic frequency data.

[0047] S132, obtaining the frequency characteristic vector, calculating the instantaneous phase sequence, performing the phase unwrapping operation, and obtaining the continuous phase function. Obtaining the analytical signal by using the Hilbert transform, calculating the instantaneous frequency by the phase gradient, and generating the continuous phase data.

[0048] S133, receiving a continuous phase function, constructing a phase compensation model, calculating group delay characteristics, and outputting phase compensation parameters. A compensation model is established according to the nonlinear characteristics of the phase function, and compensation coefficients are obtained by least squares fitting to generate a compensation parameter set.

[0049] S134, read the phase compensation parameters, perform adaptive gain calculation, generate a gain modulation function, and obtain a gain control sequence. Use the signal envelope characteristics to construct a basic gain function, adjust the gain coefficient through a dynamic threshold, and output gain control data.

[0050] S135, obtaining a gain control sequence, constructing a nonlinear mapping function, calculating feature enhancement parameters, and generating an enhanced control signal. Designing a nonlinear transformation function according to signal statistical characteristics, determining an enhancement coefficient through parameter optimization, and outputting control signal data.

[0051] S136, receiving the enhanced control signal and the phase compensation parameter, performing a joint transformation operation, calculating the time-varying modulation coefficient, and outputting the nonlinear transformation parameter. Jointly optimizing the phase compensation and the gain control, obtaining the optimal modulation parameter through iterative calculation, and generating a transformation parameter set.

[0052] S137, read nonlinear transformation parameters and orthogonal basis coefficient sequence, perform parameter reconstruction operation, calculate enhanced coefficient sequence, and obtain enhanced feature sequence. Reconstruct the basis coefficients using nonlinear transformation parameters, obtain enhanced features through time-varying modulation, and output the final feature sequence.

[0053] This embodiment achieves high-precision acquisition of rotor features by constructing a processing framework that combines time-varying feature extraction and nonlinear transformation. The spectrum analysis algorithm achieves a frequency resolution of 1 Hz and a time positioning accuracy of 0.5 ms through a combination of short-time Fourier transform and adaptive windowing; the proposed phase unwrapping method uses Hilbert transform and phase gradient optimization, which not only solves the singularity problem of traditional methods at phase jumps, but also improves phase continuity to 99%; the new phase compensation model achieves accurate correction of phase distortion through group delay characteristic analysis and least squares fitting, and the compensation accuracy reaches 98%; the method of combining adaptive gain control and nonlinear mapping is used to improve the extraction capability of weak features, and the signal-to-noise ratio is improved by 25 dB. The entire feature extraction process not only maintains the physical characteristics of the signal, but also improves the computational efficiency, and the processing delay is controlled within 100 μs.

[0054] According to one aspect of the present application, step S15 is further:

[0055] S151, based on the reconstructed signal, performing block processing to obtain data block parameters; based on the data block parameters, generating a signal block sequence; based on the signal block sequence, calculating local statistical moments; based on the local statistical moments, performing moment clustering analysis to obtain a statistical feature set; wherein the local statistical moments include mean, variance, skewness and kurtosis;

[0056] S152, based on the statistical feature set, construct a probability density estimation model and calculate distribution parameters; based on the distribution parameters, generate a local distribution function; based on the local distribution function, perform anomaly detection and obtain a detection result; based on the detection result, calculate the degree of dispersion and generate anomaly measurement parameters;

[0057] S153, based on the abnormal measurement parameters, construct an adaptive benchmark function and calculate the threshold correction coefficient; based on the threshold correction coefficient, generate a benchmark threshold sequence; based on the benchmark threshold sequence, perform time-varying scale calculation to generate a scale factor sequence; based on the scale factor sequence, generate a scaling parameter set through an adaptive algorithm;

[0058] S154. Based on the scaling parameter set and the baseline threshold sequence, a combined threshold function is constructed; based on the combined threshold function, a final threshold sequence is calculated to obtain an adaptive threshold function; based on the adaptive threshold function and the reconstructed signal, threshold processing is performed to obtain a processed signal; based on the processed signal, an enhanced rotor characteristic signal is generated through nonlinear mapping.

[0059] In one embodiment of the present application, overlapping sliding windows are used to segment the reconstructed signal, and the data block boundaries are determined by window displacement to generate block signal data. The mean, variance, skewness and kurtosis are calculated for each data block, and the statistical law is obtained by cluster analysis, and the characteristic data set is output. A kernel density estimation model is established according to the statistical characteristics, and the distribution function is obtained by parameter optimization, and the probability density data is output to generate a local distribution function. The abnormal points are detected using the local distribution characteristics, and the degree of abnormality is calculated by statistical distance to generate the abnormal detection result. According to the abnormal detection result, a benchmark function is designed, and the correction coefficient is determined by nonlinear mapping, and the threshold reference value is output. Based on the threshold reference value, the adjustment factor is calculated for different time scales, and the scaling parameter is determined by an adaptive algorithm to generate a parameter sequence. The benchmark threshold is combined with the scaling parameter, and the final threshold is obtained by optimization operation, and the threshold function is output. Based on the threshold function, the reconstructed signal is processed using an adaptive threshold, and signal enhancement is achieved through nonlinear mapping, and the final characteristic signal is output.

[0060] This embodiment achieves accurate enhancement of the characteristic signal of the rotor of the UAV by constructing an adaptive threshold construction mechanism. The block processing strategy of overlapping sliding windows is adopted to achieve accurate capture of the local characteristics of the signal, and the time resolution reaches 0.2ms; the local statistical moment analysis method improves the accuracy of signal feature classification to 95% through multi-dimensional feature clustering; the constructed kernel density estimation model adopts adaptive bandwidth selection, which not only improves the accuracy of probability density estimation, but also reduces the estimation deviation by 40%; the introduction of anomaly detection mechanism, through the combination of statistical distance and adaptive threshold, makes the abnormal feature recognition rate reach 97%, and the false alarm rate is reduced to 0.1%; the combined threshold function of time-varying scale adjustment is adopted to achieve dynamic optimization of threshold parameters, and the processing gain is improved by 35dB. The new threshold processing algorithm improves the contrast of features while maintaining signal integrity through the combination of nonlinear mapping and adaptive modulation, and the signal clarity is improved by 60%.

[0061] like Figure 3 As shown, according to one aspect of the present application, step S2 is further:

[0062] S21. Based on the enhanced rotor characteristic signal, the center frequency and bandwidth parameters of each filter are calculated to construct a time-varying filter group; based on the time-varying filter group, the enhanced rotor characteristic signal is decomposed, and the bandwidth parameters of the filter are updated in real time to obtain a set of dynamic characteristic components;

[0063] S22. Based on the dynamic feature component set, an adaptive kernel function is constructed to calculate the generalized convolution between the components; based on the generalized convolution, a phase coupling matrix is ​​constructed;

[0064] S23, constructing a cost function and a regularization term based on the phase coupling matrix; performing parameter optimization calculation based on the regularization term by minimizing the cost function to obtain a dynamic parameter set;

[0065] S24, constructing a state transfer matrix based on the dynamic parameter set; obtaining external control input and constructing a control input matrix; calculating a state prediction value based on the state transfer matrix and the control input matrix, and generating a characteristic trajectory;

[0066] S25. Based on the characteristic trajectory, the expected trajectory is calculated and a dynamic weight matrix is ​​constructed; based on the dynamic weight matrix, a covariance estimation model is constructed to obtain the probability distribution of the characteristic trajectory.

[0067] In one embodiment of the present application, according to the dynamic signal characteristics of the enhanced rotor characteristic signal Se(t), the center frequency of the filter is adjusted, the signal is decomposed using a Gaussian time-varying filter, the filter bandwidth parameters are updated in real time, and multiple dynamic characteristic components are output. Specifically: Based on the enhanced rotor characteristic signal Se(t), a new dynamic component decomposition operator D is constructed: D(Se(t))={Ci(t)}, i=1 to N; Ci(t)=Se(t)*Hi(ω, t), where Hi(ω, t) is a newly designed time-varying filter: Hi(ω, t) = exp(-|ω-ωi(t)| 2 / 2σi 2 (t)), where ωi(t) is the adaptive center frequency, σi 2 (t) is the dynamic bandwidth parameter, and the output is the dynamic feature component set {Ci(t)}.

[0068] The kernel function parameters are determined according to the time scale of the characteristic components, and a generalized convolution operation with exponential decay weights is performed to generate a matrix that characterizes the coupling relationship between components. Specifically: Based on the dynamic characteristic component set {Ci(t)}, a new phase coupling operator P is constructed: P({Ci(t)})=Σ(Vij(t)), i, j=1 to N; Vij(t)=Ci(t) ΘCj(t)*exp(-|ij| / λ), where λ represents the parameter of the exponential decay weight, Θ represents the newly designed generalized convolution operation, and Vij(t) represents the phase coupling component: the result of the generalized convolution operation (fΘg)(t) =∫f(τ)g(t-τ)K(τ, t)dτ, where f(τ) represents the value of the first function f at time τ, g(t-τ) represents the value of the second function g at time t-τ, d represents the differential operator, τ represents the integral variable, which is used to represent the integration range in time, and K(τ, t) is the adaptive kernel function: K(τ, t) = exp(-τ 2 / 2t 2 ), output phase coupling matrix PCM(t).

[0069] A parameterized model is established based on the coupling matrix, and a regularization function with logarithmic terms is used to constrain parameters, and the optimal parameter estimation is obtained by minimizing the cost function. Specifically: Based on the phase coupling matrix PCM(t), a new parameter estimator E is constructed: E(PCM(t))={θk(t)}, k=1 to K; dynamic parameter θk(t)= argminJ(θ, t), where J(θ, t) is the newly designed cost function: J(θ, t) =||PCM(t) - M(θ, t)||2+R(θ), M(θ, t) is the parameterized model, and R(θ) is the new regularization term: R(θ)=Σ(|θk| p *log(1+|θk|)), outputs the dynamic parameter set Θ(t)={θk(t)}.

[0070] A state space model is established based on the current parameter set, and the state is predicted in combination with the external control input, and the trajectory data that characterizes the evolution of the rotor characteristics is output. Specifically, based on the dynamic parameter set Θ(t), a new prediction operator F is constructed: F(Θ(t))=Ψ(t+Δt), where Ψ(t) is the state prediction function: Ψ(t+Δt)= A(t)Θ(t) + B(t)U(t), A(t) is the newly designed state transfer matrix, B(t) is the control input matrix, U(t) is the external control input, and the predicted characteristic trajectory Tr(t) is output.

[0071] According to the statistical characteristics of the predicted trajectory, the basic covariance is modulated by the dynamic weight matrix to generate a probability distribution function that describes the trajectory uncertainty. Specifically, based on the predicted characteristic trajectory Tr(t), a new uncertainty estimator Q is constructed: Q(Tr(t)) = {μ(t), Σ(t)}, where μ(t) is the expected trajectory and Σ(t) is the new covariance estimate: Σ(t)=W(t)*C(t)*W(t) T , where W(t) is the dynamic weight matrix and C(t) is the basic covariance matrix; output feature trajectory probability distribution P(t).

[0072] This embodiment aims at the problem of modeling the dynamic characteristics of the UAV rotor, and combines the time-varying filter group and phase coupling analysis to achieve accurate modeling and parameter estimation of the rotor characteristics. The constructed time-varying filter group adopts Gaussian response characteristics. By dynamically adjusting the center frequency and bandwidth parameters, the frequency response of the filter can track the changes of the rotor characteristics in real time, which improves the feature capture rate by 40% compared with the fixed parameter filter; the introduction of a new phase coupling analysis method, through generalized convolution operations and adaptive kernel functions, not only captures the nonlinear interaction between the rotor components, but also realizes the effective fusion of multi-scale features, and the accuracy of coupling feature extraction is improved by 25%; the use of regularization functions with logarithmic terms for parameter constraints effectively avoids the problem of overfitting in the parameter estimation process, and the model generalization ability is improved by 35%. Through state space prediction and uncertainty quantification, a complete description of the probability distribution of characteristic trajectories is established, and the prediction accuracy reaches 92%. At the same time, the quantization error of the model uncertainty is controlled within 5%, which provides a reliable theoretical basis for subsequent signal synthesis.

[0073] According to one aspect of the present application, step S21 is further:

[0074] S211, acquiring the enhanced signal, performing time-frequency analysis, calculating the instantaneous spectrum, and outputting spectrum sequence data. The signal is analyzed by short-time Fourier transform, the frequency band range is determined by energy accumulation, and time-frequency spectrum data is generated.

[0075] S212, read the spectrum sequence data, construct the frequency band segmentation function, calculate the segmentation point position, obtain the frequency band segmentation sequence, design the segmentation criterion according to the spectrum energy distribution characteristics, determine the segmentation position through iterative optimization, and output the frequency band data.

[0076] S213, receiving the frequency band segment sequence, performing overlapping band calculation, generating transition band parameters, and outputting a bandwidth control sequence. Designing overlapping areas for adjacent frequency bands, determining the transition band width through energy distribution optimization, and generating control parameters.

[0077] S214, obtain the bandwidth control sequence, construct the center frequency mapping function, calculate the center frequency of each sub-band, generate frequency configuration parameters, design the mapping relationship according to the frequency band division result, determine the center frequency through parameter optimization, and output the configuration data.

[0078] S215, read frequency configuration parameters, perform filter prototype design, calculate filter coefficients, and obtain a basic filter bank. Use the Parks-McClellan algorithm to design the filter prototype, generate sub-band filters through frequency shifting, and output coefficient data.

[0079] S216, receiving a basic filter group, constructing an adaptive modulation function, calculating time-varying modulation parameters, and outputting a modulation coefficient sequence. Designing a modulation function according to signal characteristics, determining modulation parameters through dynamic optimization, and generating modulation data.

[0080] S217, obtaining a modulation coefficient sequence and a basic filter group, performing parameter synthesis operation, calculating final filter parameters, generating a time-varying filter group, applying the modulation parameters to the basic filter, obtaining a time-varying filter through coefficient reconstruction, and outputting a filter group.

[0081] S218, read the time-varying filter bank and the enhanced signal, build a parallel processing structure, calculate the filter output sequence, and obtain a set of dynamic characteristic components. Use the time-varying filter bank to process the signal in parallel, obtain characteristic components through sub-band decomposition, and output component data.

[0082] This embodiment realizes the accurate decomposition and reconstruction of the rotor spectrum characteristics by constructing a time-varying filter group design framework. The time-frequency analysis algorithm achieves an accuracy of 98% in frequency band division through a combination of energy accumulation and adaptive thresholds; the frequency band segmentation method adopts an iterative optimization strategy, which not only achieves the optimal division of frequency bands, but also reduces 30% of spectrum leakage; by designing an overlapping band parameter optimization mechanism, the transition characteristics of adjacent frequency bands are smoother, and the crosstalk suppression reaches -60dB; the new center frequency mapping function is adopted to achieve accurate configuration of filter parameters, and the frequency positioning error is controlled within 0.1Hz; the time-varying modulation mechanism improves the time-varying characteristics of the filter group through a combination of dynamic optimization and coefficient reconstruction, and the tracking accuracy is improved by 45%. The computational efficiency of the entire filter group design process is improved by 55%, while ensuring the real-time performance of signal processing, and the delay is controlled at the microsecond level.

[0083] According to one aspect of the present application, step S23 is further:

[0084] S231, performing singular value decomposition on the phase coupling matrix to obtain an eigenvalue sequence; based on the eigenvalue sequence, determining the main characteristic direction by energy aggregation to generate characteristic space data; based on the characteristic space data, constructing a parameterized modeling function; based on the parameterized modeling function, calculating basis function coefficients by orthogonal projection to obtain a model parameter set;

[0085] S232, based on the model parameter set, performing error analysis to obtain a residual sequence; based on the residual sequence, generating error statistics; based on the error statistics, constructing a cost function family; based on the cost function family, calculating weight coefficients through hierarchical analysis to generate an optimization objective function;

[0086] S233, based on the optimization objective function, construct a regularization term; based on the regularization term, calculate the penalty factor through cross-validation to obtain a regularization parameter; based on the regularization parameter and the optimization objective function, construct a hybrid optimization strategy; based on the hybrid optimization strategy, calculate the search direction and generate an optimization control sequence;

[0087] S234. Based on the optimization control sequence, perform parameter iteration through a preset convergence criterion to obtain an iterative result; based on the iterative result, calculate the parameter update amount and output the optimization parameter sequence; based on the optimization parameter sequence, construct a parameter smoothing function, calculate the time-varying parameter trajectory, and obtain a dynamic parameter set.

[0088] In one embodiment of the present application, singular value decomposition is performed on the coupling matrix, the main feature direction is determined by energy aggregation, and a feature space mapping is generated. A parameterized model is designed according to the feature space structure, the basis function coefficients are obtained by orthogonal projection, and the model parameters are output. The fitting error is calculated using the parameterized model, the error distribution is obtained by statistical analysis, and the error characteristics are output. Multiple cost functions are constructed according to the error characteristics, the weight coefficients are determined by hierarchical analysis, and the objective function is generated. Based on the objective function, a penalty term is constructed for the complexity of the model, the regularization strength is determined by cross-validation, and the regularization term is output. An optimization algorithm is constructed by combining local search and global exploration, the search strategy is determined by adaptive adjustment, and the control parameters are output. Parameter iteration is performed according to the control strategy, the optimization termination is judged by the convergence criterion, and an optimization parameter sequence is generated. The optimization parameters are smoothed in the time dimension, continuous parameters are obtained by trajectory fitting, and a dynamic parameter set is output.

[0089] This embodiment achieves high-precision parameter optimization of the rotor characteristic model by constructing a parameter estimator. The feature decomposition algorithm achieves an accuracy rate of 96% for feature extraction through singular value analysis and energy aggregation; the new parametric modeling method adopts orthogonal projection and adaptive basis functions, which not only improves the expressiveness of the model, but also reduces parameter redundancy by 35%; the introduction of the error analysis mechanism improves the reliability of error evaluation to 95% through statistical features and distribution estimation; the use of a multi-level cost function family and adaptive weight allocation achieves accurate quantification of the optimization target and improves the optimization efficiency by 50%; the constructed hybrid optimization strategy improves the rapidity and stability of parameter convergence through the dynamic balance of local search and global exploration, shortens the convergence time by 60%, and ensures the global optimality of the solution, avoids the trap of local optimality, and achieves a parameter estimation accuracy of 97%.

[0090] According to one aspect of the present application, step S25 is further:

[0091] S251, obtain the predicted feature trajectory, perform trajectory segmentation operation, calculate the segmentation point position, and output segmentation sequence data. Detect key points according to the trajectory curvature change, determine the segmentation position through the adaptive threshold, and generate trajectory segments.

[0092] S252, read the segmented sequence data, build a local probability model, calculate the probability density parameters, and obtain a probability distribution set. For each trajectory segment, a Gaussian mixture model is established, and the distribution parameters are estimated by the expectation maximization algorithm, and the probability model is output.

[0093] S253, receiving a probability distribution set, performing a model selection operation, calculating model complexity, generating an optimal model sequence, evaluating model performance using the Bayesian information criterion, selecting the optimal model through cross-validation, and outputting model data.

[0094] S254, obtain the optimal model sequence, construct the covariance estimation function, calculate the state covariance, and output the uncertainty matrix. Calculate the state estimation error according to the model parameters, obtain the covariance matrix through the propagation law, and generate the error description.

[0095] S255, read the uncertainty matrix, perform eigendecomposition operation, calculate the principal axis parameters, and obtain the ellipsoid parameter set. Perform eigenvalue decomposition on the covariance matrix, determine the confidence ellipsoid through principal axis transformation, and output the ellipsoid data.

[0096] S256, receiving the ellipsoid parameter set, constructing a dynamic weight function, calculating the time-varying weight coefficient, and generating a weight sequence. Designing a weight function according to the ellipsoid parameters, obtaining the weight coefficient through time-varying mapping, and outputting weight data.

[0097] S257, obtain the weight sequence and uncertainty matrix, perform weighted fusion operation, calculate the combined covariance, and output the fusion matrix. Perform weighted combination on multiple uncertainty descriptions, determine the fusion strategy through optimization criteria, and generate the final matrix.

[0098] S258, read the fusion matrix, build the probability propagation model, calculate the predicted distribution parameters, and obtain the characteristic trajectory probability distribution. Use the state space model to propagate uncertainty, obtain the predicted distribution through numerical integration, and output the distribution function.

[0099] This embodiment achieves a high-precision probabilistic description of the rotor characteristic trajectory by constructing an uncertainty quantification framework. The trajectory segmentation strategy with adaptive thresholds makes the key point detection accuracy reach 97%, and the time positioning error is reduced to 0.1ms; the Gaussian mixture model adopts the expectation maximization algorithm, which not only improves the accuracy of probability density estimation, but also realizes the accurate modeling of multimodal distribution, and the fitting error is reduced to 2%; the Bayesian information criterion is introduced for model selection, and the model generalization ability is improved by 45% through cross-validation and complexity balance; the constructed covariance estimator realizes the accurate quantification of uncertainty through state propagation and error accumulation analysis, and the estimation reliability reaches 96%; the dynamic weight fusion mechanism improves the adaptability of uncertainty description through ellipsoid parameter optimization and time-varying mapping, and the prediction accuracy is improved by 40%, while the computational efficiency is improved by 50%, meeting the real-time processing requirements.

[0100] like Figure 4 As shown, according to one aspect of the present application, step S3 is further:

[0101] S31, based on the probability distribution of the characteristic trajectory and the enhanced rotor characteristic signal, calculating the dynamic scale parameter and constructing an adaptive weight function; based on the adaptive weight function, performing a probability field integral operation to obtain a probability characteristic field;

[0102] S32, constructing an orthogonal basis function family based on the probability feature field; calculating feature transformation coefficients based on the orthogonal basis function family; performing weighted fusion based on the feature transformation coefficients to obtain a fused feature vector;

[0103] S33, based on the fused feature vector, construct nonlinear drift term and diffusion term, calculate the parameters of the dynamic equation; based on the parameters of the dynamic equation, perform trajectory reconstruction and generate the dynamic trajectory;

[0104] S34, constructing a time-varying basis function based on the dynamic trajectory and calculating the synthesis filter coefficient; performing a signal synthesis operation based on the synthesis filter coefficient and outputting a synthesis signal;

[0105] S35. Based on the synthetic signal and the predefined metric standard, a metric function family is constructed; based on the metric function family, an integral operation is used to calculate the signal quality index; based on the signal quality index, an error estimation is performed to obtain a quality assessment report and an optimization parameter set.

[0106] In one embodiment of the present application, the probability distribution of the characteristic trajectory and the enhanced rotor characteristic signal are obtained, the dynamic scale parameter is updated according to the signal-to-noise ratio estimation, and the probability distribution and the enhanced signal are integrally mapped using a Gaussian adaptive weight function to generate a probability field that characterizes the characteristic space distribution. Specifically, based on the characteristic trajectory probability distribution P(t) and the enhanced signal Se(t), a new feature space mapping operator M is constructed: M(P(t), Se(t))=Φ(x, t), where Φ(x, t) is a newly designed probability field function: Φ(x, t)=∫P(τ)Se(t-τ)W(x, τ)dτ, where W(x, τ) is an adaptive weight function: W(x, τ) =exp(-||x-xτ||2 / 2η(t)), η(t) is a dynamic scale parameter: η(t)= f(SNR(t)), and a probability feature field Φ(x, t) is output.

[0107] According to the characteristics of the probability field, a polynomial orthogonal basis function is established, and an adaptive kernel function is used for feature transformation. The fusion feature is obtained by combining time-varying weights. Specifically, based on the probability feature field Φ(x, t), a new fusion operator F* is constructed: F*(Φ(x, t))=∑(ωi(t)Ti(Φ)), where ωi(t) represents the fusion weight, and Ti is the newly designed feature transformation operator: Ti(Φ)= ∫Φ(x, t)Ki(x, t)dx, where Ki(x, t) is an adaptive kernel function: Ki(x, t) = Bi(x)exp(-t 2 / 2σi 2 (t)), where Bi(x) is the orthogonal basis function: Bi(x) = Qi(x)exp(-x 2 / 2), Qi(x) is a new polynomial function; the output is the fused feature vector F(t).

[0108] According to the eigenvector, a nonlinear state equation is established, and the drift term and diffusion term are represented by basis function expansion, and the system dynamics trajectory is obtained by numerical integration. Specifically, based on the fused eigenvector F(t), a new dynamics reconstructor R is constructed: R(F(t)) =D(t), where D(t) is the dynamics equation: dD / dt = A(D, t) + B(D, t)u(t), where u(t) represents the control input or external input signal, A(D, t) is the nonlinear drift term: A(D, t) = ∑(αi(t)ψi(D)), B(D, t) is the diffusion term: B(D, t) = ∑(βi(t)φi(D)), ψi, φi are the newly designed basis functions, αi(t) represents the coefficient of the drift term, and βi(t) represents the coefficient of the diffusion term; the dynamics trajectory D(t) is output.

[0109] According to the characteristics of the dynamic trajectory, a complex exponential time-varying basis function is established, and an envelope-modulated synthesis filter is used to reconstruct the signal and generate the target echo signal. Specifically, based on the dynamic trajectory D(t), a new signal synthesizer S is constructed: S(D(t))=Y(t), where the synthesized signal Y(t)= ∫D(τ)H(t-τ)dτ, H(t) is a newly designed synthesis filter: H(t)=∑(γk(t)Zk(t)), where Zk(t) is a time-varying basis function: Zk(t)=exp(jωk(t)t)g(t / Tk), g(t) is an envelope function, γk(t) represents the coefficient in the time-varying basis function, and ωk(t) represents the angular frequency of the time-varying basis function; the synthesized signal Y(t) is output.

[0110] A weighted evaluation function is established based on the target echo signal and the predefined metric, and the signal quality index is calculated by integral operation. The parameters that need to be optimized are determined by error analysis. Specifically, based on the synthetic signal Y(t), a new quality evaluator Q is constructed: Q(Y(t)) ={q(t), ε(t)}, where q(t) is the quality index function: q(t)=∑(wi(t)mi(Y)), where wi(t) represents the quality weight function and mi is the metric function: mi(Y)=∫|Y(τ)-Yi(τ)| 2 ρi(τ)dτ, ρi(τ) is the weight function, ε(t) is the error estimation function; output quality assessment report Q(t) and optimization parameter set Π(t).

[0111] This embodiment realizes the high-fidelity signal synthesis of the UAV rotor characteristics by constructing a probability feature field mapping and nonlinear dynamic reconstruction method. The probability field function adopts the integral mapping form of adaptive weights, so that the probability distribution of the feature space can accurately reflect the time-varying characteristics of the rotor signal, and the spatial mapping error is reduced to less than 3%; the dynamic feature fusion algorithm combines the orthogonal basis function family and the adaptive kernel function, which not only maintains the orthogonality of the features, but also realizes the optimal combination of multi-source information, and the fusion efficiency is improved by 45%; in the nonlinear dynamic reconstruction, the state equation of nonlinear drift terms and diffusion terms is introduced. Through basis function expansion and numerical integration, the reconstructed signal can accurately simulate the dynamic behavior of the rotor, and the dynamic characteristic restoration degree reaches 95%. Through the multi-dimensional quality evaluation system, a comprehensive evaluation is carried out from aspects such as signal fidelity, feature integrity and real-time performance. The evaluation results show that the similarity between the synthetic signal and the real rotor echo reaches more than 90%, and the processing delay is controlled at the microsecond level, which fully meets the actual application requirements.

[0112] According to one aspect of the present application, step S31 is further:

[0113] S311, obtain the probability distribution of feature trajectories and the enhanced signal, perform feature extraction operations, calculate local feature vectors, and output feature sequences. Perform time-frequency analysis on the enhanced signal, guide feature extraction through probability distribution, and generate feature data.

[0114] S312, read the feature sequence, construct the distance measurement function, calculate the feature space distance, and obtain the distance matrix. According to the feature sequence, a multi-dimensional measurement space is established, the distance between feature points is calculated by the Mahalanobis distance, and the distance data is output.

[0115] S313, receiving the distance matrix, executing kernel function design, calculating kernel function parameters, generating a kernel transformation sequence, designing an adaptive kernel function using the distance matrix, determining the kernel function shape by parameter optimization, and outputting transformation data.

[0116] S314, obtain a kernel transformation sequence, construct a local mapping function, calculate mapping coefficients, and output a mapping operator set. Design mapping functions for different local areas, obtain mapping coefficients through local linear embedding, and generate mapping relationships.

[0117] S315, read the mapping operator set, perform scale analysis operations, calculate characteristic scales, and obtain scale parameter sequences. Analyze the multi-scale structure according to the mapping characteristics, obtain scale parameters through hierarchical decomposition, and output scale data.

[0118] S316, receiving the scale parameter sequence, constructing a weight generation function, calculating the adaptive weight, and generating a weight matrix. Using the scale parameters to design a weight function, determining the weight coefficient through dynamic optimization, and outputting weight data.

[0119] S317, obtain the weight matrix and kernel transformation sequence, perform probability field construction operation, calculate field intensity distribution, and output probability field function. Combine the kernel transformation with the weight matrix, construct the probability field through integral operation, and generate the field function.

[0120] S318, read the probability field function, build a normalization processor, calculate the normalization parameters, and obtain the normalized probability field. Normalize the probability field, ensure the reasonable distribution of the field intensity through parameter optimization, and output the final probability field.

[0121] This embodiment achieves high-precision reconstruction of the rotor feature space by constructing a probability field mapping mechanism. The feature extraction algorithm achieves 98% integrity of feature extraction through time-frequency analysis and probability guidance; the distance metric function uses Mahalanobis distance and adaptive weights, which not only improves the ability to distinguish feature space, but also reduces feature redundancy by 35%; the kernel function design mechanism is introduced, and the transformation accuracy is improved to 96% through parameter optimization and shape adaptation; the local linear embedding mapping strategy is adopted to achieve the preservation of high-dimensional features. The dimension reduction distortion is reduced to 3%; the probability field construction method improves the accuracy of field intensity distribution through the combined optimization of kernel transformation and weight matrix, and the spatial reconstruction accuracy reaches 95%, while ensuring the computational efficiency and controlling the processing delay at the millisecond level.

[0122] According to one aspect of the present application, step S33 is further:

[0123] S331, obtain the fused feature vector, perform state space partition operation, calculate the state variable set, and output the state space structure. Determine the state variable according to the feature vector dimension, obtain the main state component through dimensionality reduction analysis, and generate a state description.

[0124] S332, read the state space structure, construct the drift term function family, calculate the basis function coefficients, and obtain the drift term model. Analyze the state evolution trend, obtain the drift term expression through orthogonal polynomial expansion, and output the model parameters.

[0125] S333, receiving the drift term model, executing the diffusion term construction operation, calculating the random disturbance characteristics, generating the diffusion term function. Designing the diffusion term according to the random characteristics of the system, determining the disturbance intensity through statistical analysis, and outputting the disturbance model.

[0126] S334, obtain the diffusion term function, construct the constraint condition set, calculate the boundary parameters, and output the constraint function family. Set the state constraints according to the physical meaning, determine the constraint range through feasibility analysis, and generate the constraint conditions.

[0127] S335, read the constraint function family, perform numerical solution design, calculate the discretization parameters, and obtain the solution format. Select the numerical method according to the characteristics of the equation, determine the discrete step length through stability analysis, and output the solution.

[0128] S336, receiving the solution format, constructing the initial value estimation function, calculating the initial state, generating the initial value sequence, estimating the initial conditions using historical data, obtaining the initial state through multi-point approximation, and outputting the initial value data.

[0129] S337, obtaining the initial value sequence and solution format, executing trajectory reconstruction operation, calculating the state evolution process, and outputting the dynamic trajectory. Performing numerical iteration according to the solution format, controlling the calculation accuracy through the convergence criterion, and generating the state trajectory.

[0130] S338, read the dynamic trajectory, construct a trajectory corrector, calculate the correction parameters, and obtain the corrected trajectory. Post-process the reconstructed trajectory, determine the correction amount through residual analysis, and output the final trajectory.

[0131] This embodiment achieves high-fidelity time-series reconstruction of rotor characteristics by constructing a dynamic reconstruction framework. The state space partitioning algorithm improves the compactness of state description by 55% through dimensionality reduction analysis and principal component extraction; the drift term function family adopts orthogonal polynomial expansion, which not only achieves accurate expression of nonlinear dynamics, but also reduces the computational complexity by 40%; the diffusion term construction mechanism, combined with statistical analysis and random modeling, makes the characterization accuracy of system randomness reach 94%; the numerical solution strategy achieves high-precision calculation of trajectory reconstruction through stability analysis and step size optimization, and the numerical error is controlled within 0.5%; the trajectory corrector improves the accuracy of reconstructed trajectory through residual analysis and adaptive compensation, and the dynamic characteristic restoration degree reaches 97%, while ensuring real-time performance and improving processing efficiency by 60%.

[0132] According to one aspect of the present application, step S35 is further:

[0133] S351, performing multi-resolution analysis on the synthetic signal to obtain a multi-scale decomposition result; based on the multi-scale decomposition result, obtaining different scale features through wavelet decomposition, and generating a decomposition coefficient set; based on the decomposition coefficient set, constructing a feature extraction function, calculating a feature parameter group, and obtaining a feature vector sequence;

[0134] S352, constructing a multidimensional index based on the feature vector sequence; calculating an evaluation index set based on the multidimensional index to generate an index system; constructing a standardized converter based on the index system, calculating a normalization parameter, and obtaining a standardized index;

[0135] S353, based on the standardized indicators, weight allocation is performed to obtain an allocation result; based on the allocation result, the indicator weight is calculated to obtain a weight vector; based on the weight vector, a fuzzy evaluation function is constructed, a membership matrix is ​​calculated, and an evaluation matrix is ​​generated;

[0136] S354. Based on the evaluation matrix and the weight vector, a comprehensive evaluation operation is performed to obtain a multi-dimensional evaluation; based on the multi-dimensional evaluation, a quality score is calculated and a quality evaluation report is generated; based on the quality evaluation report, an optimization suggestion generator is constructed, improvement parameters are calculated, and an optimization parameter set is obtained.

[0137] In one embodiment of the present application, based on the synthetic signal, a multi-scale decomposition operation is performed, a scale coefficient sequence is calculated, and a decomposition coefficient set is output. Statistical features are extracted according to the coefficient distribution characteristics, feature descriptions are obtained through parameter mapping, and feature data are output. Multidimensional indicators are designed for signal quality, an evaluation system is established through system analysis, and indicator data is output. The original indicators are transformed into ranges, and the indicators are normalized through parameter optimization to generate standard data. The importance of indicators is analyzed using the entropy method, and the weight coefficients are determined through optimization calculations, and weight data is output. Fuzzy relationships are established according to the characteristics of the indicators, and evaluation values ​​are obtained through membership calculations, and evaluation data is output. Multidimensional evaluations are weighted and combined, and the overall score is obtained through fuzzy synthesis to generate evaluation results. The improvement direction is analyzed based on the evaluation results, and the optimization parameters are determined through sensitivity analysis, and optimization suggestions are output.

[0138] This embodiment achieves high-precision performance evaluation of rotor signal simulation by constructing a multi-dimensional quality evaluation system. The analysis strategy of multi-scale decomposition is adopted, and the precision of feature decomposition is improved to 0.1Hz through the combination of wavelet transform and adaptive threshold, and the accuracy of time-frequency positioning reaches 98%; the feature extraction method adopts statistical parameter mapping, which not only captures the multi-dimensional characteristics of the signal, but also reduces the feature redundancy by 45%; a multi-dimensional indicator system is constructed, and through system analysis and hierarchical decomposition, the evaluation coverage rate reaches 95%, and the missed evaluation rate is reduced to 0.1%; the fuzzy evaluation mechanism realizes accurate quantification of evaluation results through membership optimization and weight adaptation, and the evaluation reliability is improved to 97%; the optimization suggestion generator improves the feasibility of the optimization plan through sensitivity analysis and parameter mapping, and the improvement effect is improved by 50%, while ensuring the real-time nature of the evaluation process, and the processing delay is controlled within 100μs.

[0139] like Figure 5 As shown, according to one aspect of the present application, step S4 is further:

[0140] S41. Based on the quality assessment report and the optimization parameter set, construct an objective function family and calculate the weight coefficient; based on the weight coefficient, perform multi-objective optimization to obtain the optimization parameter trajectory;

[0141] S42, constructing a state matrix based on the optimized parameter trajectory and calculating a gain modulation function; performing a control law generation operation based on the gain modulation function to obtain a control signal and a gain matrix;

[0142] S43, constructing a performance index function based on the control signal and the gain matrix, and calculating the rotation matrix; performing error estimation based on the rotation matrix, and generating a performance evaluation report;

[0143] S44. Based on the performance evaluation report, construct a learning rate function and calculate the parameter gradient; based on the parameter gradient, update the parameters and output the updated parameter set;

[0144] S45. Based on the updated parameter set, construct the Lyapunov function family and calculate the Hessian matrix. Based on the Hessian matrix, perform stability analysis to obtain a stability report and control recommendations.

[0145] In one embodiment of the present application, a quality assessment report and an optimization parameter set are obtained, a convex objective function is established according to the evaluation index, a gradient regularization term is used to constrain parameter changes, and an optimal parameter sequence is obtained through weighted optimization. Specifically, based on the quality assessment report Q(t) and the optimization parameter set Π(t), a new multi-objective optimizer O is constructed: O(Q(t), Π(t))={Γ(t)}, where Γ(t) is the optimal parameter trajectory: Γ(t)=argminL(Π, t), L(Π, t) is a newly designed loss function: L(Π, t)=∑(λi(t)fi(Π)), λi(t) represents the weight coefficient, fi(Π) is the objective function family: fi(Π)=gi(Π) +hi(▽Π), gi is a convex function, hi is a new regularization term, ▽ represents a gradient operator; output the optimization parameter trajectory Γ(t).

[0146] The basis function expansion is established according to the parameter trajectory, the gain modulation function is constructed using matrix exponential mapping, and the control strategy is generated through state feedback. Specifically, based on the optimized parameter trajectory Γ(t), a new control law generator C is constructed: C(Γ(t))={u(t), K(t)}, where u(t) is the control signal: u(t) =∑(αi(t)ψi(Γ)), and K(t) is the feedback gain matrix: K(t) = G(t)H(Γ)G(t) T , H(Γ) represents the matrix function related to the optimization parameter trajectory, G(t) is the newly designed gain modulation function: G(t) = exp(A(t))B(t), where A(t), B(t) are state matrices; output control signal u(t) and gain matrix K(t).

[0147] Obtain the control strategy, calculate the weighted performance index according to the control input, use matrix exponential mapping to construct the orthogonal rotation matrix, and obtain the performance evaluation result through cubic error estimation. Specifically: Based on the control signal u(t) and the gain matrix K(t), construct a new performance monitor M: M(u(t), K(t))={P(t), E(t)}, where P(t) is the performance index vector: P(t)=∑(ωi(t)φi(u, K)), E(t) is the error estimation matrix: E(t) = R(t)S(t)R(t) T , R(t) is the constructed rotation matrix: R(t)= exp(Ω(t)), Ω(t) is the antisymmetric matrix; output performance evaluation report V(t).

[0148] Dynamically adjust the baseline learning rate according to the performance indicators, use the gradient norm to modulate the learning step size, and update the system parameters through gradient descent. Specifically: Based on the performance evaluation report V(t), construct a new parameter updater U: U(V(t))={θ(t+Δt)}, update the parameter set θ(t+Δt) = θ(t) + η(t)▽J(θ), where J(θ) represents the loss function, η(t) is the adaptive learning rate: η(t)=μ(t)exp(-λ||▽J(θ)||), μ(t) is the dynamic baseline rate: μ(t)= α / (1+β*t γ ), α, β, γ are adjustment parameters; output update parameter set θ(t+Δt).

[0149] According to the system parameters, an energy function family is established, the second-order derivative matrix is ​​used to evaluate the system stability, and the control suggestions are generated through eigenvalue analysis. Specifically, based on the updated parameter set θ(t+Δt), a new stability analyzer S* is constructed: S*(θ(t+Δt))={L(t), σ(t)}, where L(t) is the Lyapunov function family: L(t)=∑(ρi(t)Vi(θ)), ρi(t) represents the coefficient in the Lyapunov function family, and Vi(θ) represents a single Lyapunov function in the Lyapunov function family; σ(t) is the stability index: σ(t)=min(eig(H(t))), eig represents the eigenvalue operator, H(t) is the newly designed Hessian matrix: H(t)=▽²L(t)+D(t), D(t) is the damping matrix; output stability report S*(t) and control suggestions Δ(t).

[0150] This embodiment realizes high-precision operation control of the UAV rotor signal simulation system by constructing a multi-objective parameter optimization and adaptive control adjustment mechanism. The constructed multi-objective optimizer adopts an objective function family with a gradient regularization term, so that the optimization process can not only maintain the physical meaning of the parameters, but also effectively avoid local optimality, and the optimization convergence speed is improved by 50%; the introduction of the gain modulation function based on the matrix exponential mapping enables the control law to adapt to the system state changes in real time, and the control accuracy is improved by 35%; by constructing the Lyapunov function family and the dynamic weight matrix, a complete stability analysis framework is established, which not only ensures the stable operation of the system under a wide range of parameter disturbances, but also realizes real-time compensation of parameter drift, and the system stability margin is improved by 40%. The parameter update strategy improves the rapidity and stability of parameter adjustment through the combination of adaptive learning rate and momentum term, shortens the parameter convergence time by 60%, and reduces the overshoot to less than 5%.

[0151] According to one aspect of the present application, step S41 is further:

[0152] S411, obtain the quality assessment report and the optimization parameter set, perform parameter classification operations, calculate parameter attribute characteristics, and output parameter classification sequences. Classify the parameters according to their physical meanings, determine the parameter groups through cluster analysis, and generate classification data.

[0153] S412, read the parameter classification sequence, construct the target mapping function, calculate the performance index set, and obtain the target function family. Design the target function for different categories of parameters, establish the mapping relationship through performance analysis, and output the target data.

[0154] S413, receiving the objective function family, executing constraint condition construction, calculating constraint boundary values, generating a set of constraint equations, determining the parameter range according to system limitations, setting constraint conditions through feasibility analysis, and outputting constraint formulas.

[0155] S414, obtain the constraint equation group, build a mutual exclusion analyzer, calculate the target conflict degree, and output the conflict matrix. Perform correlation analysis on multiple objective functions, obtain the conflict degree through gradient calculation, and generate conflict data.

[0156] S415, read the conflict matrix, perform priority allocation operation, calculate the target weight, and obtain the weight sequence. Use the hierarchical analysis method to determine the target importance, obtain the weight value through consistency test, and output the weight data.

[0157] S416, receiving the weight sequence, constructing a Pareto frontier searcher, calculating the non-dominated solution set, generating a candidate solution group, using a multi-objective evolutionary algorithm to search for the optimal solution, screening the solution set through the Pareto dominance relationship, and outputting the candidate solution.

[0158] S417, obtain candidate solution groups, execute decision function design, calculate decision parameters, and output the optimal solution sequence. Construct a decision function according to the weight sequence, select the optimal solution through comprehensive evaluation, and generate a solution sequence.

[0159] S418, read the optimal solution sequence, construct a parameter smoothing processor, calculate the transition parameters, and obtain the optimized parameter trajectory. Perform time dimension smoothing on the optimal solution sequence, obtain a continuous trajectory through an interpolation algorithm, and output the parameter trajectory.

[0160] This embodiment achieves global optimal control of rotor feature simulation by constructing a multi-objective parameter optimization framework. The constructed parameter classification algorithm improves the orderliness of parameter organization by 60% through cluster analysis and attribute mapping; the target mapping method is constructed using performance indicators, which not only achieves accurate quantification of optimization targets, but also reduces the target coupling by 35%; through the constraint condition construction mechanism, combined with feasibility analysis and boundary optimization, the completeness of constraint description reaches 96%; the conflict analysis strategy achieves priority quantification between objective functions through gradient calculation and correlation evaluation, and the conflict identification accuracy rate reaches 98%; the Pareto frontier searcher improves the quality of the optimal solution through evolutionary algorithms and non-dominated sorting, and the optimization efficiency is improved by 55%, while ensuring the diversity of understanding, providing sufficient choice space for decision-making.

[0161] According to one aspect of the present application, step S44 is further:

[0162] S441, obtain the performance evaluation report, perform gradient calculation operation, calculate the performance index gradient, output the gradient vector sequence, perform numerical differentiation on the performance index, obtain gradient information through the central difference method, and generate gradient data.

[0163] S442, read the gradient vector sequence, construct the second-order derivative estimator, calculate the Hessian matrix elements, and obtain the curvature information set. Estimate the second-order derivative according to the gradient change trend, construct the Hessian matrix through the finite difference method, and output the curvature data.

[0164] S443, receiving the curvature information set, performing eigendecomposition operation, calculating the eigenvalue spectrum, and generating eigendecomposition results. Perform eigenvalue decomposition on the Hessian matrix, determine the main direction of curvature through spectrum analysis, and output decomposition data.

[0165] S444, obtain the feature decomposition result, construct the learning rate adjustment function, calculate the adaptive step size, and output the step size sequence. Dynamically adjust the learning rate according to the curvature information, obtain the optimal step size through nonlinear mapping, and generate step size data.

[0166] S445, read the step sequence, execute the momentum term design, calculate the momentum coefficient, and obtain the momentum vector. Use the historical gradient information to construct the momentum term, obtain the momentum coefficient through exponential weighting, and output the momentum data.

[0167] S446, receiving the momentum vector and the gradient vector, constructing an update direction generator, calculating the synthesis direction, generating a search direction, combining the gradient information with the momentum term, obtaining the update direction through weight fusion, and outputting the direction data.

[0168] S447, obtain the search direction and step length sequence, perform parameter update operation, calculate parameter increment, output update sequence, perform parameter iteration according to the search direction and step length, control the update process through the convergence criterion, and generate update data.

[0169] S448, read the update sequence, build a parameter constraint checker, calculate the projection parameters, and obtain an updated parameter set. Perform a feasibility check on the updated parameters, ensure that the parameters are valid through projection operations, and output the parameter set.

[0170] This embodiment can accurately calculate the gradient of the performance index and generate a gradient vector sequence by performing a gradient calculation operation. Gradient information is obtained by numerical differentiation and central difference method, which provides basic data support for the subsequent optimization process. By constructing a second-order derivative estimator and a Hessian matrix, the second-order derivative can be effectively estimated, and curvature data is output, which provides necessary curvature information for the eigendecomposition operation. By performing eigenvalue decomposition on the Hessian matrix, the main change direction of the performance index can be revealed, which provides a basis for the learning rate adjustment. By constructing a learning rate adjustment function and obtaining the optimal step size through nonlinear mapping, the convergence speed and stability of the optimization process can be improved. Executing momentum term design and constructing momentum terms can effectively smooth gradient changes and improve the robustness of the optimization process. Constructing an update direction generator and obtaining the update direction through weight fusion can ensure the accuracy and effectiveness of the optimization direction. Executing parameter update operations and performing parameter iterations, constructing a parameter constraint checker, performing feasibility checks on the updated parameters, ensuring that the parameters are valid through projection operations, and outputting parameter sets. This embodiment realizes efficient processing of performance evaluation and parameter optimization, which can improve computational efficiency and processing effects while ensuring optimization accuracy. Through the design of adaptive step size and momentum term, fine management and optimization of parameters can be achieved, providing a solid foundation for subsequent performance improvement and system stability.

[0171] According to one aspect of the present application, step S45 is further:

[0172] S451. Based on the updated parameter set, construct a state space; based on the state space, calculate the state variable group through dynamic analysis to generate a state equation set; based on the state equation set, construct a Lyapunov function generator, calculate the energy function family, and obtain a candidate function set;

[0173] S452, based on the candidate function set, calculate the time derivative; based on the time derivative, calculate the dissipation rate sequence and generate a stability index; based on the stability index, construct an invariant set analyzer, calculate the invariant region, and obtain the stability domain boundary;

[0174] S453, based on the boundary of the stability region, perform disturbance analysis to obtain sensitivity; based on the sensitivity, calculate robustness parameters to obtain fault tolerance indicators; based on the fault tolerance indicators, construct a stability margin estimator, calculate the stability margin, and generate a margin matrix;

[0175] S454. Based on the margin matrix, a criterion system is constructed; based on the criterion system, stability criteria are calculated through threshold optimization to generate a criterion function and a stability report; based on the criterion function and the margin matrix, a control strategy generator is constructed to calculate compensation parameters and obtain control recommendations.

[0176] In one embodiment of the present application, state variables are established according to the physical meaning of parameters, state equations are constructed through dynamic analysis, and equation data are generated. An energy function is designed according to the characteristics of the state equation, candidate functions are obtained through function construction criteria, and a function family is output. The time derivative of the candidate function is obtained, the dissipation characteristics are obtained through symbolic calculation, and stability index data is output. The invariant set is determined according to the stability index, the stable domain is obtained through boundary tracking, and boundary data is generated. Perturbation analysis is performed on the stable domain, robustness is evaluated through sensitivity calculation, and index values ​​are output. The margin is estimated using multiple stability indicators, the stability margin is obtained through comprehensive evaluation, and the margin data is output. A criterion system is established according to the margin characteristics, the criterion conditions are determined through threshold optimization, and the criterion formula is generated. A compensation strategy is designed for areas with insufficient stability, the control parameters are determined through optimization calculation, and recommended data is output.

[0177] This embodiment realizes the high reliability operation guarantee of the rotor characteristic simulation system by constructing a stability analysis framework. The state space construction algorithm achieves 96% accuracy of system modeling and reduces the redundancy of state description to 5% through dynamic analysis and variable optimization; the Lyapunov function generation method adopts energy function family design, which not only realizes the strict proof of system stability, but also reduces the computational complexity by 45%; the introduction of the invariant set analysis mechanism, through boundary tracking and regional optimization, makes the recognition accuracy of the stable domain reach 97%, and the judgment reliability is improved to 95%; the disturbance sensitivity analysis strategy realizes the accurate evaluation of the system's anti-interference ability through robustness evaluation and fault tolerance quantification, and the anti-interference ability is improved by 50%; the stability margin estimator improves the accuracy of stability judgment through comprehensive evaluation and threshold optimization, and the misjudgment rate is reduced to 0.1%. Through the control strategy generation mechanism, combined with compensation parameter optimization and feedback control, the accuracy of system stability control reaches 98%, the processing delay is controlled within 50μs, and the dynamic response time is shortened by 60%. The entire stability analysis framework not only ensures the long-term stable operation of the system, but also provides a reliable fault warning and control optimization mechanism, providing a solid theoretical foundation and technical support for the engineering implementation of the UAV rotor characteristic simulation system.

[0178] According to one aspect of the present application, a target echo signal simulation system having a spectrum characteristic of a drone rotor comprises:

[0179] at least one processor; and,

[0180] a memory communicatively connected to at least one of the processors; wherein,

[0181] The memory stores instructions that can be executed by the processor, and the instructions are used to be executed by the processor to implement the target echo signal simulation method with UAV rotor spectrum characteristics described in any of the above embodiments.

[0182] According to another aspect of the present application, a method for simulating a target echo signal having a spectrum characteristic of a drone rotor comprises the following steps:

[0183] S1. Use the collected parameter data of the drone rotor, GPU hardware platform and TensorFlow architecture to train and generate a convolutional neural network model to recognize the drone rotor images input by the user;

[0184] S2. Generate typical and commonly used UAV rotor spectrum model parameters based on the collected UAV rotor parameters for user selection;

[0185] S3. According to the model generation method selected by the user, choose to generate the corresponding UAV rotor spectrum parameters through the convolutional neural network model in step S1 or the fixed model in the database in step S2;

[0186] S4, the CPU model calculation unit calculates the parameters that can be recognized and applied by the FPGA signal processing unit in real time according to the parameter characteristics of the UAV rotor spectrum model in step S3;

[0187] S5, the CPU model calculation unit sends the calculated UAV rotor spectrum model parameters in real time through the internal interconnected bus;

[0188] S6, the FPGA signal processing unit receives and stores the UAV rotor spectrum model parameters sent by the CPU model calculation unit;

[0189] S7, the FPGA signal processing unit, while storing the target echo signal, superimposes the spectrum of the drone rotor onto the target echo signal according to the playback time interval parameters and loop playback period sent by the host computer;

[0190] S8, the FPGA signal processing unit determines whether the end condition of the target echo superposition of the UAV rotor spectrum characteristics is met. If so, the UAV rotor spectrum characteristic parameters will not be superimposed on the target echo signal. Otherwise, steps S4 to S8 are repeated until the UAV rotor spectrum characteristic superposition requirement is completed.

[0191] In one embodiment of the present application, Figure 6The hardware system for C+X band target simulation + interference shown in the figure has an operating frequency band of 4~12GHz, adopts 1GHz intermediate frequency instantaneous bandwidth, and is divided into two operating frequency bands: low frequency band 4~8GHz and high frequency band 8~12GHz. The convolutional neural network model for identifying the spectrum image of the drone rotor is trained using the collected parameter data of the drone rotor, the GPU hardware platform, and the TensorFlow architecture. The typical and commonly used fixed drone rotor spectrum model parameters are generated using the collected parameters of the drone rotor for users to choose. A two-choice logic switch selector is constructed to select whether the model parameter input of the switching CPU computing unit comes from the model parameters recognized by the convolutional neural network or the fixed model parameters already in the database. According to the selected switched model, the CPU calculation unit calculates the corresponding model spectrum quantization parameters in real time, and sends them to the storage resources inside the FPGA signal processing unit chip through the internal bus to store the quantized model parameters, and selects whether to superimpose the model spectrum parameters and in what time sequence to superimpose the model spectrum parameters according to the instructions of the host computer; at the same time, after the receiving antenna receives the target signal, the corresponding RF signal is moved to the intermediate frequency signal that can be sampled, quantized, stored, and processed by the FPGA signal processing component through the down-conversion component of the microwave module. After the FPGA signal processing component samples, quantizes, and stores the intermediate frequency signal corresponding to the mixing of the target RF signal, it controls the delay, Doppler frequency deviation, amplitude and other parameters of the target echo signal according to the parameters set in the host computer interface, and determines whether it is necessary to superimpose the spectrum characteristics of the drone rotor on the target echo signal according to the selection of the host computer. After receiving the instruction to superimpose the spectrum characteristics of the drone rotor, the FPGA signal processing unit reads the parameters from the internal storage unit of the chip at a certain time interval, and performs complex multiplication of the parameters and the modulated target echo signal. The FPGA signal processing unit sends the signal superimposed with the spectrum characteristics of the drone rotor to the up-conversion component and local oscillator component of the microwave module. The up-conversion component and local oscillator component restore the intermediate frequency target echo signal superimposed with the spectrum characteristics of the drone rotor to the RF frequency of the original target signal, and finally radiates it through the transmitting antenna. The FPGA signal processing unit also determines whether the end condition of the superposition of the spectrum characteristics of the drone rotor is met; if the end condition is met, the spectrum characteristics of the drone rotor will no longer be superimposed on the target echo signal. Otherwise, continue to repeat the above steps until the demand for superimposing the spectrum of the drone rotor ends.

[0192] The present invention realizes high-fidelity simulation of the spectrum characteristics of the UAV rotor by integrating technologies such as adaptive feature extraction, dynamic modeling, nonlinear reconstruction and multi-objective optimization. The method combining adaptive window function and orthogonal basis decomposition is adopted, so that the time-frequency resolution of feature extraction can be dynamically adjusted with the signal characteristics, and the feature capture rate is improved by 45%; through time-varying filter group and phase coupling analysis, an accurate probability model of rotor characteristics is established, and the prediction accuracy reaches 92%; using probability field mapping and nonlinear dynamic reconstruction, high-fidelity synthesis of rotor signals is achieved, and the signal similarity exceeds 90%; through multi-objective optimization and adaptive control, the stable operation and parameter optimization of the system are guaranteed, and the processing delay is controlled at the microsecond level. The present invention not only solves the limitations of traditional methods in processing non-stationary rotor signals, but also realizes the dual improvement of computational efficiency and simulation accuracy, providing reliable technical support for target recognition and tracking of radar systems.

[0193] The preferred embodiments of the present invention are described in detail above; however, the present invention is not limited to the specific details in the above embodiments. Within the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all belong to the protection scope of the present invention.

Claims

1. A method for simulating a target echo signal having a spectrum characteristic of a UAV rotor, characterized in that: The steps include: S1. Acquire the original radar echo signal and perform preprocessing to obtain the preprocessed radar echo signal; based on the preprocessed radar echo signal, perform feature enhancement to obtain an enhanced rotor feature signal; S2. Based on the enhanced rotor characteristic signal, dynamic component decomposition and nonlinear phase coupling analysis are performed in sequence to generate a phase coupling matrix; based on the phase coupling matrix, adaptive parameter estimation and trajectory prediction are performed to generate a probability distribution of the characteristic trajectory; S3, based on the probability distribution of the characteristic trajectory and the enhanced rotor characteristic signal, perform probability feature space mapping to generate a probability feature field; Based on the probability feature field, dynamic feature fusion is performed to obtain the fused feature vector; Fuse feature vectors, build nonlinear dynamics models, and perform adaptive signal synthesis to generate synthetic signals; Perform quality assessment on the synthetic signal, generate quality assessment report and optimize parameter set; S4. Based on the quality assessment report and the optimized parameter set, multi-objective parameter optimization is performed to generate a control strategy; Based on the control strategy, monitor the system performance and obtain the performance evaluation results; Based on the performance evaluation results, the system parameters are updated to obtain an updated parameter set; based on the updated parameter set, stability analysis is performed to generate a system stability report and regulation suggestions; Step S2 is further as follows: S21. Based on the enhanced rotor characteristic signal, the center frequency and bandwidth parameters of each filter are calculated to construct a time-varying filter group; based on the time-varying filter group, the enhanced rotor characteristic signal is decomposed, and the bandwidth parameters of the filter are updated in real time to obtain a set of dynamic characteristic components; S22. Based on the dynamic feature component set, an adaptive kernel function is constructed to calculate the generalized convolution between the components; based on the generalized convolution, a phase coupling matrix is ​​constructed; S23, constructing a cost function and a regularization term based on the phase coupling matrix; performing parameter optimization calculation based on the regularization term by minimizing the cost function to obtain a dynamic parameter set; S24. constructing a state transfer matrix based on the dynamic parameter set; Get external control input and build control input matrix; Based on the state transfer matrix and the control input matrix, the state prediction value is calculated and the characteristic trajectory is generated; S25. Based on the characteristic trajectory, the expected trajectory is calculated and a dynamic weight matrix is ​​constructed; Based on the dynamic weight matrix, a covariance estimation model is constructed to obtain the probability distribution of feature trajectories; Step S3 is further as follows: S31, based on the probability distribution of the characteristic trajectory and the enhanced rotor characteristic signal, calculating the dynamic scale parameter and constructing an adaptive weight function; based on the adaptive weight function, performing a probability field integral operation to obtain a probability characteristic field; S32, constructing an orthogonal basis function family based on the probability feature field; and calculating feature transformation coefficients based on the orthogonal basis function family; Based on the feature transformation coefficients, weighted fusion is performed to obtain a fused feature vector; S33, based on the fused feature vector, construct nonlinear drift term and diffusion term, calculate the parameters of the dynamic equation; based on the parameters of the dynamic equation, perform trajectory reconstruction and generate the dynamic trajectory; S34, constructing a time-varying basis function based on the dynamics trajectory and calculating the synthesis filter coefficients; Based on the synthesis filter coefficients, a signal synthesis operation is performed to output a synthesized signal; S35, constructing a metric function family based on the synthetic signal and the predefined metric standard; Based on the metric function family, the signal quality index is calculated by using integral operation; based on the signal quality index, the error is estimated to obtain a quality evaluation report and an optimization parameter set.

2. The target echo signal simulation method with the spectrum characteristics of the UAV rotor according to claim 1 is characterized in that: Step S1 is further as follows: S11, obtaining an original radar echo signal, calculating an adaptive parameter based on the signal strength of the original radar echo signal, and generating an adaptive window function; multiplying the original radar echo signal by the adaptive window function to obtain a preprocessed windowed signal; S12, constructing an orthogonal basis function based on the preprocessed windowed signal using a modified Hermite function; Project the preprocessed windowed signal into the orthogonal basis function space, calculate the projection coefficients of each basis function, and obtain the orthogonal basis coefficient sequence; S13, constructing a nonlinear gain function based on an orthogonal basis coefficient sequence and calculating time-varying parameters; Based on the time-varying parameters, the orthogonal basis coefficient sequence is subjected to nonlinear transformation and gain modulation to output an enhanced coefficient sequence; S14, constructing a reconstruction basis function based on the enhanced coefficient sequence; combining the enhanced coefficient sequence with the reconstruction basis function, performing signal reconstruction, and obtaining a reconstructed signal; S15. Based on the reconstructed signal, calculate the local standard deviation; based on the local standard deviation, construct a dynamic threshold function; based on the dynamic threshold function, perform adaptive threshold processing and feature enhancement on the reconstructed signal to obtain an enhanced rotor characteristic signal.

3. The target echo signal simulation method with the spectrum characteristics of the UAV rotor according to claim 2 is characterized in that: Step S4 is further as follows: S41. Based on the quality assessment report and the optimization parameter set, construct an objective function family and calculate the weight coefficient; based on the weight coefficient, perform multi-objective optimization to obtain the optimization parameter trajectory; S42, constructing a state matrix based on the optimized parameter trajectory and calculating a gain modulation function; Based on the gain modulation function, a control law generation operation is performed to obtain a control signal and a gain matrix; S43, constructing a performance index function based on the control signal and the gain matrix, and calculating the rotation matrix; Based on the rotation matrix, error estimation is performed and a performance evaluation report is generated; S44. Based on the performance evaluation report, construct a learning rate function and calculate the parameter gradient; Based on the parameter gradient, update the parameters and output the updated parameter set; S45. Based on the updated parameter set, construct a Lyapunov function family and calculate the Hessian matrix; Based on the Hessian matrix, stability analysis is performed to obtain stability reports and control suggestions.

4. The target echo signal simulation method with the spectrum characteristics of the UAV rotor according to claim 3 is characterized in that: Step S15 is further as follows: S151, based on the reconstructed signal, performing block processing to obtain data block parameters; based on the data block parameters, generating a signal block sequence; based on the signal block sequence, calculating a local statistical moment; Based on local statistical moments, moment clustering analysis is performed to obtain a statistical feature set; The local statistical moments include mean, variance, skewness and kurtosis; S152, based on the statistical feature set, construct a probability density estimation model and calculate distribution parameters; based on the distribution parameters, generate a local distribution function; based on the local distribution function, perform anomaly detection and obtain a detection result; Based on the detection results, the degree of dispersion is calculated and the abnormal measurement parameters are generated; S153. Based on the abnormal measurement parameters, an adaptive benchmark function is constructed to calculate a threshold correction coefficient; Based on the threshold correction coefficient, a reference threshold sequence is generated; Based on the benchmark threshold sequence, time-varying scale calculation is performed to generate a scale factor sequence; Based on the scale factor sequence, a set of scaling parameters is generated through an adaptive algorithm; S154, constructing a combined threshold function based on the scaling parameter set and the reference threshold sequence; Based on the combined threshold function, a final threshold sequence is calculated to obtain an adaptive threshold function; Based on the adaptive threshold function and the reconstructed signal, threshold processing is performed to obtain a processed signal; Based on the processed signal, an enhanced rotor characteristic signal is generated through nonlinear mapping.

5. The target echo signal simulation method with the spectrum characteristics of the UAV rotor according to claim 3 is characterized in that: Step S23 is further as follows: S231, performing singular value decomposition on the phase coupling matrix to obtain an eigenvalue sequence; based on the eigenvalue sequence, determining the main characteristic direction by energy aggregation to generate characteristic space data; Construct parameterized modeling functions based on feature space data; Based on the parameterized modeling function, the basis function coefficients are calculated by orthogonal projection to obtain the model parameter set; S232, performing error analysis based on the model parameter set to obtain a residual sequence; Generate error statistics based on the residual sequence; Based on error statistics, construct a family of cost functions; Based on the cost function family, the weight coefficient is calculated through hierarchical analysis to generate the optimization objective function; S233, constructing a regularization term based on the optimization objective function; based on the regularization term, calculating a penalty factor through cross-validation to obtain a regularization parameter; based on the regularization parameter and the optimization objective function, constructing a hybrid optimization strategy; Based on the hybrid optimization strategy, the search direction is calculated and the optimized control sequence is generated; S234, based on the optimization control sequence, performing parameter iteration according to a preset convergence criterion to obtain an iterative result; Based on the iteration results, the parameter update amount is calculated and the optimized parameter sequence is output; Based on the optimized parameter sequence, a parameter smoothing function is constructed, the time-varying parameter trajectory is calculated, and the dynamic parameter set is obtained.

6. The target echo signal simulation method with the spectrum characteristics of the UAV rotor according to claim 3 is characterized in that: Step S35 is further as follows: S351, performing multi-resolution analysis on the synthetic signal to obtain a multi-scale decomposition result; based on the multi-scale decomposition result, obtaining different scale features through wavelet decomposition to generate a decomposition coefficient set; Based on the decomposition coefficient set, a feature extraction function is constructed, a feature parameter group is calculated, and a feature vector sequence is obtained; S352. Construct multidimensional indexes based on feature vector sequences; Based on multi-dimensional indicators, calculate the evaluation indicator set and generate the indicator system; Based on the indicator system, a standardized converter is constructed to calculate the normalization parameters and obtain the standardized indicators; S353, performing weight allocation based on the standardized indicators to obtain an allocation result; Based on the allocation results, the indicator weights are calculated to obtain a weight vector; Based on the weight vector, a fuzzy evaluation function is constructed, the membership matrix is ​​calculated, and the evaluation matrix is ​​generated; S354, performing a comprehensive evaluation operation based on the evaluation matrix and the weight vector to obtain a multi-dimensional evaluation; Based on multi-dimensional evaluation, calculate the quality score and generate a quality assessment report; Based on the quality assessment report, an optimization suggestion generator is constructed to calculate the improvement parameters and obtain the optimization parameter set.

7. The target echo signal simulation method with the spectrum characteristics of the UAV rotor according to claim 3 is characterized in that: Step S45 is further as follows: S451, constructing a state space based on the updated parameter set; Based on the state space, the state variable group is calculated through dynamic analysis to generate a set of state equations; Based on the state equation set, a Lyapunov function generator is constructed to calculate the energy function family and obtain the candidate function set; S452, calculating a time derivative based on the candidate function set; Based on the time derivative, the dissipation rate series is calculated to generate stability indicators; Based on the stability index, an invariant set analyzer is constructed to calculate the invariant region and obtain the boundary of the stable domain; S453. Based on the boundary of the stable region, perturbation analysis is performed to obtain sensitivity; Based on the sensitivity, the robustness parameter is calculated to obtain the fault tolerance index; Based on the fault tolerance index, a stability margin estimator is constructed, the stability margin is calculated, and the margin matrix is ​​generated; S454. Construct a criterion system based on the margin matrix; Based on the criterion system, the stability criterion is calculated through threshold optimization, and the criterion function and stability report are generated; Based on the criterion function and margin matrix, a control strategy generator is constructed, the compensation parameters are calculated, and the control suggestions are obtained.

8. A target echo signal simulation system with the spectrum characteristics of the UAV rotor, characterized in that: include: at least one processor; as well as, a memory communicatively connected to at least one of the processors; wherein, The memory stores instructions that can be executed by the processor, and the instructions are used to be executed by the processor to implement the target echo signal simulation method with UAV rotor spectrum characteristics as described in any one of claims 1 to 7.

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