Real data driven radar and electronic warfare model dynamic correction method and system

Abstract

The application discloses a kind of measured data driven radar and electronic warfare model dynamic correction method and system, belong to radar detection and electronic countermeasure technical field.For the problem that existing simulation model relies on ideal mathematical formula, ignores hardware nonlinear distortion and environmental dynamic characteristics, leading to insufficient simulation fidelity, the application proposes a kind of grey box hybrid modeling scheme that retains physical mechanism framework, relies on measured data correction parameter and compensates residual error using neural network.The method comprises: establishing a radar and electronic warfare reference mathematical model containing a set of parameters to be corrected;Collecting measured countermeasure data and defining a multi-dimensional feature residual error objective function;Offline correction of time-invariant parameters, real-time tracking of time-varying parameters using extended Kalman filter;Finally, compensate residual nonlinear error using the Transformer model.The application significantly improves model fidelity and electronic warfare evaluation credibility, with physical interpretability and data-driven accuracy.

Description

Technical Field

[0001] This invention relates to the fields of radar detection and electronic countermeasures, and more specifically, to a method and system for dynamic correction of radar and electronic warfare models driven by measured data. Background Technology

[0002] In modern information warfare, radar and electronic warfare systems constitute the core equipment for seizing electromagnetic dominance. To evaluate the anti-jamming performance of radar and the jamming effectiveness of electronic warfare systems in a laboratory environment, it is typically necessary to construct simulation models of radar and electronic warfare systems. High-fidelity simulation models can not only significantly reduce the cost and risk of actual flight testing, but also provide a reliable digital verification environment for the research and iteration of radar anti-jamming algorithms and the effectiveness evaluation of electronic warfare tactics and methods.

[0003] Currently, the industry widely adopts the "mechanism modeling based on theoretical formulas" approach. Typical practices include: using ideal linear frequency modulation (LFM) or phase coding formulas to describe radar transmitted signals; using the Swerling model and ideal radar cross section (RCS) formulas to characterize target echoes; and using ideal delay and Doppler shift formulas to construct electronic warfare models based on digital radio frequency memory (DRFM), such as range gate dragging (RGPO), velocity gate dragging (VGPO), and coherent decoy jamming. The advantages of this type of mechanism modeling method are: simple mathematical form, high computational efficiency, clear physical meaning, and no reliance on large amounts of measured data.

[0004] However, those skilled in the art have discovered through long-term engineering practice that mechanism modeling relying purely on mathematical formulas deviates significantly from actual flight or field testing conditions, i.e., there is a substantial "gap between simulation and reality." The fundamental reason for this is: (1) Hardware nonlinearity and distortion are not fully characterized. Actual radar transmitters, receivers, analog-to-digital converter (ADC) sampling circuits, and DRFM jammers not only have random phase noise, but also nonlinear amplitude distortion and processing delay drift that fluctuate with temperature and supply voltage. Theoretical formulas often simplify them to ideal Gaussian white noise or constant delay, which is seriously inconsistent with the actual situation. For example, the nonlinear saturation characteristics of the transmitter power amplifier under high power output state will cause significant distortion in the pulse envelope, which will directly affect the radar's pulse compression gain and sidelobe suppression performance.

[0005] (2) Complex dynamic environmental characteristics. When radar platforms (especially airborne platforms) are maneuvering at high speeds, the antenna array will undergo slight deformation, resulting in dynamic changes in the antenna pattern; in addition, the changes in water vapor content, air pressure gradient, and fuselage multipath effect in the actual atmospheric environment will lead to extremely complex phase modulation. These phenomena are difficult to accurately derive and characterize using definite analytical formulas.

[0006] (3) Fixed formula parameters cannot adapt to actual combat. Existing model parameters are usually set by design specifications or factory calibration values ​​at the beginning of model establishment. However, in actual combat, the equipment's working status parameters, environmental coupling parameters, and the tactical parameters of both sides are all dynamically changing. If simulation is still carried out according to the factory theoretical parameters, the evaluation results are often blindly optimistic or seriously distorted, making it difficult to serve as an effective basis for equipment development and tactical decision-making.

[0007] To address the discrepancy between theoretical formulas and actual data, data-driven methods have been introduced into radar signal processing and electronic warfare modeling in recent years. Pure data-driven "black box" models, such as those based on deep learning, can fit the statistical characteristics of measured data to some extent, but they lack clear physical meaning, have poor generalization ability, and are prone to failure in unfamiliar battlefield situations. Furthermore, training pure data-driven models heavily relies on large-scale, high-quality labeled data, while acquiring electronic warfare adversarial data is prohibitively expensive, making it difficult to meet the needs of model training.

[0008] Therefore, how to effectively combine existing physical formula mechanism models (white box) and utilize valuable measured adversarial data to dynamically correct model parameters, thereby enabling the simulation model to infinitely approximate the performance of real equipment, is a pressing technical challenge in the field of radar and electronic warfare digital twins. To address this, this invention proposes a measured data-driven method and system for dynamic correction of radar and electronic warfare models. Summary of the Invention

[0009] This invention aims to address the technical problems in existing radar and electronic warfare simulation modeling methods, such as insufficient simulation fidelity due to the lack of consideration for hardware nonlinear distortion, dynamic environmental characteristics, and time-varying parameter properties in pure mechanistic models, and the lack of physical interpretability and poor generalization ability in pure data-driven models. This invention provides a method and system for dynamic correction of radar and electronic warfare models driven by measured data.

[0010] The present invention addresses the following specific technical problems: (1) how to reverse correct the key parameters in the mechanism model based on measured data so that the model output closely resembles the characteristics of the measured data; (2) how to adopt appropriate correction strategies for the parameters that change slowly and the parameters that change rapidly over time in the model; and (3) how to use neural networks to compensate for residual nonlinear errors that cannot be represented by analytical formulas while preserving the physical mechanism framework.

[0011] To achieve the above objectives, this invention proposes a method and system for dynamic correction of radar and electronic warfare models driven by measured data.

[0012] Firstly, this application provides a method for dynamic correction of radar and electronic warfare models driven by measured data, including: Step S1: Establish a baseline mathematical mechanism model for airborne radar and electronic warfare. The baseline mathematical mechanism model includes an airborne radar transmitted signal model, a space propagation model, a target scattering model, and an electronic warfare jamming signal model, and obtain the analytical expression for the theoretical received signal. Preferably, the airborne radar transmission signal model adopts a linear frequency modulated pulse signal, the expression of which is:

[0013] in, For the amplitude of the transmitted signal, The pulse width. For carrier frequency, For frequency modulation slope, This is the initial phase; Based on the nonlinear characteristics of the actual transmitter hardware, the nonlinear characteristics are parameterized and introduced into the airborne radar transmission signal model. The expression of the transmission model, which includes the set of parameters to be corrected, is as follows:

[0014] Among them, the parameter set to be corrected Includes envelope fluctuation parameters and phase noise function .

[0015] Preferably, the electronic warfare jamming signal model includes a range-gate drag jamming model based on a digital radio frequency memory, and the expression for its jamming signal is:

[0016] in, For the amplitude of the interference signal, For the target true echo delay, For drag delay, Fixed processing delay for DRFM system, For Doppler frequency shift; The parameterized expression of the electronic warfare jamming signal model is as follows:

[0017] in, The parameter set to be corrected. Includes interference machine amplitude gain error Temperature drift delay Doppler modulation error and the phase noise inside the jammer .

[0018] Preferably, the spatial propagation model includes multipath effects, and the analytical expression of the theoretical received signal includes multipath propagation components.

[0019] Step S2: Under the same or similar combat scenarios, collect measured countermeasure data of airborne radar and electronic warfare systems, perform data preprocessing, and obtain measured received signals; It should be noted that the "same or similar combat scenarios" mentioned in this invention refer to the fact that the scenario in which the measured data was collected and the tactical scenario targeted by the subsequent simulation model are basically consistent in the following dimensions: (a) the spatial geometric configuration between the radar and the target / jammer (including range, azimuth, elevation angle and their rate of change); (b) radar operating parameters such as operating frequency band, signal bandwidth, and pulse repetition period; (c) jamming pattern and jamming strategy parameters (such as drag speed, false target density, etc.); and (d) electromagnetic environment background (including environmental clutter intensity, multipath conditions, etc.). Under the premise that the above conditions are consistent or similar, the real equipment nonlinear characteristics and environmental coupling information contained in the measured data can be effectively transmitted to the parameter correction process of the mechanism model. If the combat scenario changes significantly (for example, the radar operating mode changes from search to tracking, or the jamming pattern changes from range gate drag to velocity gate drag), it is necessary to re-collect the measured data under the corresponding scenario and perform parameter correction.

[0020] Specifically, in actual flight tests or semi-physical simulation experiments in a microwave anechoic chamber, orthogonal (IQ) baseband data sequences from a real radar receiver are collected. To ensure data availability and comparability, rigorous time alignment and amplitude calibration are required. The collected data includes real clutter components, target echo components, measured interference components, and system thermal noise.

[0021] Step S3: Define the error objective function and calculate the characteristic residual between the output of the theoretical received signal analytical expression under the current parameter set and the measured received signal; Preferably, the definition of the error objective function specifically includes: Set the measured received signal as Set the output of the theoretical parameterized model to ,in The set of parameters to be corrected; In the time domain residual function Its expression is:

[0022] Construct a second residual function in the frequency domain. Its expression is:

[0023] in, and These are the Fourier transforms of the measured signal and the model signal, respectively; Based on residual function Second residual function The joint objective function is expressed as follows:

[0024] in, and These are the weighting coefficients. The regularization coefficient is . These are prior parameters or state parameters from the previous time step. This invention, by introducing frequency domain residuals, can effectively correct frequency domain characteristic parameters in the mechanistic model, such as filter bandwidth characteristics, spurious level, and DRFM quantization noise floor. Simultaneously, the addition of a regularization term prevents the model parameters from overfitting the measured noise during the correction process, ensuring that the corrected parameters conform to physical prior knowledge.

[0025] Step S4: Based on the feature residuals, a nonlinear optimization algorithm and a dynamic filtering algorithm are used to iteratively update and dynamically correct the parameter set to be corrected in the benchmark mathematical mechanism model, so as to obtain the corrected optimal parameter set; In radar and electronic warfare systems, different parameters to be corrected exhibit different time-varying characteristics. For example, the nonlinear characteristics of the transmitter power amplifier, the frequency response of the receiver front-end filter, and the nonlinear quantization characteristics of the ADC can be considered time-invariant or slowly time-varying parameters within the normal operating temperature range and a relatively short time scale. Their changes are mainly affected by factors such as equipment aging and the slow degradation of component performance, and offline parameter estimation can meet the accuracy requirements. However, during the flight of the carrier platform, transient phase errors of the T / R components caused by airframe vibration, multipath Doppler frequency shifts that change drastically with the line-of-sight angle, and frequency drift caused by rapid temperature changes in the local oscillator frequency of the jammer are time-varying or fast time-varying parameters, and online real-time tracking must be used for parameter estimation.

[0026] Therefore, this invention distinguishes the parameters to be corrected into time-invariant parameters and time-varying parameters, and adopts appropriate correction algorithms for each: For the time-invariant parameters in the set of parameters to be corrected, the Levenberg-Marquardt algorithm is used for iterative correction, and the correction expression is as follows:

[0027] in, The residual function is the set of parameters to be corrected. Jacobian matrix, It is the identity matrix. The damping factor, This is the residual vector under the current parameters.

[0028] The Levenberg-Marquardt algorithm combines the Gauss-Newton method and gradient descent: when the damping factor is small, the algorithm approximates the Gauss-Newton method, exhibiting second-order convergence speed; when the damping factor is large, the algorithm approximates gradient descent, ensuring stable convergence far from the minimum point. Since the mechanistic model in this invention has a clear analytical form, the Jacobian matrix of the parameter set to be corrected for the residual function can be directly obtained by taking the partial derivative of the mathematical formula, thus significantly improving the convergence speed and computational efficiency of parameter iteration correction.

[0029] For the time-varying parameters in the set of parameters to be corrected, an extended Kalman filter is used for real-time dynamic tracking and correction. The extended Kalman filter is a recursive Bayesian filtering algorithm for nonlinear systems. Its basic idea is to perform a Taylor expansion of the nonlinear state equation and observation equation at the current state estimate, retaining the first-order terms, thereby linearizing the nonlinear system before applying the standard Kalman filter framework. Specifically, the state equation and observation equation are as follows:

[0030]

[0031] in, For parameterized state transition functions, The feature vector extracted from actual measurements. For mechanism observation function, and These are process noise and observation noise, respectively.

[0032] In the prediction phase, the predicted state value and its covariance matrix are calculated using the state transition function. In the update phase, the predicted state value is corrected based on the observation information (i.e., the difference between the measured eigenvector and the predicted observation) and the Kalman gain to obtain the estimated state value. Through the above recursive process, the estimated values ​​of time-varying parameters can be updated in real time with the continuous input of measured data.

[0033] Step S5: Substitute the corrected optimal parameter set into the baseline mathematical mechanism model, and use a deep neural network to compensate for the unanalyzable nonlinear residual error to generate a high-fidelity airborne radar and electronic warfare model. It should be noted that no matter how sophisticated the mathematical formulas are or how accurately the parameters are corrected, there will always be "unmodeled dynamics" in the real physical world that are difficult to characterize analytically using mathematical models. These include irreversible abrupt changes in component parameters under extreme temperature conditions, slow nonlinear drift introduced by device aging, nonlinear crosstalk introduced by electromagnetic compatibility coupling, and the fine structure of DRFM quantization noise. These nonlinear distortions cannot be completely eliminated by adjusting the parameters of the mechanistic model.

[0034] Therefore, after completing the parameter correction in step S4, the present invention uses a deep neural network to compensate for the residual error in step S5, specifically including the following sub-steps: S501: Calculate the residual error signal after parameter correction. ,in The corrected optimal parameter set; S502: Construct and train the Transformer model, using the corrected output of the airborne radar and electronic warfare model. Using its intermediate layer features as input, predict the nonlinear residual sequence. (Explain the Transformer model in the instruction manual) S503: The predicted residual error sequence is superimposed onto the corrected mechanistic model output to obtain the final high-fidelity model output, the expression of which is: .

[0035] The Transformer model is a deep neural network architecture based on a self-attention mechanism, proposed by Vaswani et al. in 2017. The lightweight Transformer model constructed in this invention mainly includes: an input embedding layer (mapping the mechanistic model output and intermediate layer features into a high-dimensional vector representation), a position encoding layer (introducing temporal position information into the sequence data), a multi-layer self-attention encoder (capturing long-range dependencies in the residual error), and an output regression layer (mapping the encoded features into predicted residual error values). The Transformer model of this invention adopts a lightweight design and can be deployed in real-time simulation systems. During training, the residual error sequence corresponding to the measured data is used. As a supervisory label, the network weights are optimized using the backpropagation algorithm with the goal of minimizing the mean squared error (MSE).

[0036] In a second aspect, the present invention also provides a dynamic correction system for airborne radar and electronic warfare models driven by measured data, characterized in that it includes: The mechanism modeling module is used to establish parameterized benchmark mathematical mechanism models for airborne radar and electronic warfare. The data acquisition module is used to acquire and preprocess measured radar and electronic countermeasures data from field tests or actual flights. The error analysis module is used to calculate the multidimensional characteristic residuals between the theoretical model and the measured data under the current parameters; The parameter correction and optimization module is used to execute nonlinear optimization algorithms and dynamic filtering algorithms to drive the iterative update of the baseline model parameters; The deep compensation and fusion module is used to learn and compensate for distortions that are difficult to be represented analytically by mathematical models through neural network models, and output the final high-fidelity simulation data.

[0037] Preferably, the parameter correction and optimization module includes: The time-invariant parameter correction unit is used to perform offline iterative optimization of the time-invariant parameters in the parameter set to be corrected using the Levenberg-Marquardt algorithm; The time-varying parameter tracking unit is used to perform real-time online estimation and tracking of the time-varying parameters in the set of parameters to be corrected using extended Kalman filtering.

[0038] Preferably, the depth compensation and fusion module includes: The residual calculation unit is used to calculate the residual error sequence between the output of the computer theoretical model after parameter correction and the measured data. Transformer network units are used to perform nonlinear mapping fitting on the residual error sequence, taking the intermediate layer features and output features of the mechanistic model as input. The fusion output unit is used to add the prediction residuals of the Transformer network units to the output of the mechanistic model to generate the final high-fidelity model output.

[0039] The present invention also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the above method.

[0040] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the above-described method.

[0041] The beneficial effects of this invention are as follows: (1) Significantly improves model realism and solves the problem of formula modeling being divorced from reality. This invention solves the problem of error propagation and evaluation distortion caused by simply relying on theoretical formulas by introducing measured data for inverse parameter correction. The real hardware nonlinear characteristics, environmental coupling information and system time-varying characteristics contained in the measured data are effectively extracted and embedded into the mechanism model, realizing a high-precision approximation of the simulation model to the characteristics of real equipment. Verified by measured data, the normalized mean square error (NMSE) of the model output after correction by this invention can be reduced by more than 60% compared with the pure mechanism model.

[0042] (2) The hierarchical correction strategy balances accuracy and efficiency. Based on the differences in the time-varying characteristics of the parameters, this invention employs the LM algorithm for offline iterative optimization of time-invariant parameters (directly calculating the Jacobian matrix using the analytical form of the model, resulting in fast convergence), and uses the EKF algorithm for real-time online tracking of time-varying parameters (utilizing a recursive filtering framework, resulting in low computational cost and strong adaptability). Compared to methods that uniformly apply the same optimization strategy to all parameters, the hierarchical correction strategy of this invention significantly improves the accuracy and computational efficiency of parameter estimation, making it particularly suitable for applications with high real-time requirements, such as airborne platforms.

[0043] (3) The gray-box hybrid modeling combines interpretability and high accuracy. Compared with the black-box model of pure deep learning, this invention is based on radar equations and electromagnetic propagation formulas, which have complete physical interpretability and the model output can be traced back to specific physical parameters; at the same time, it uses data-driven parameter optimization and neural network compensation for residuals to achieve extremely high fidelity. This gray-box architecture that combines white-box and black-box models ensures that the model follows strict physical laws in normal areas (preventing the collapse of the pure data-driven model in unknown scenarios) and can reproduce the distortion characteristics of real hardware under extreme boundary conditions, with strong generalization ability.

[0044] (4) Improve the confidence of electronic warfare countermeasure assessment. In the performance evaluation of electronic warfare equipment and the verification of radar anti-jamming algorithms, the modified model includes real hardware delay jitter, phase change characteristics and nonlinear distortion characteristics of jammers, making the simulation evaluation results closer to the performance in real combat environment, and significantly improving the practical reference value of the evaluation conclusions.

[0045] (5) The technical solution has strong scalability. The general technical framework of "mechanism model framework + measured data parameter correction + neural network residual compensation" of the present invention is not only applicable to airborne radar and electronic warfare systems, but can also be extended to the modeling and simulation of shipborne radar systems, vehicle-mounted radar systems, ground-based early warning systems and various communication electronic warfare systems, and has good prospects for promotion and application.

[0046] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing embodiments of the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings. Attached Figure Description

[0047] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0048] Figure 1 This is a schematic diagram of the method of the present invention. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0050] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0051] Example 1: See Figure 1 This embodiment provides a method for dynamic correction of radar and electronic warfare models driven by measured data. The core idea of ​​this method is: "Preserving the physical mechanism framework, correcting parameters based on measured data, and using neural networks to compensate for residuals." Through the above method, a static model based on fixed formulas is transformed into a "living model" that can continuously evolve with measured data, thereby greatly improving the model's realism and accuracy.

[0052] Specifically, the method includes the following steps: S1: Establish a benchmark mathematical mechanism model for airborne radar and electronic warfare. The benchmark mathematical mechanism model includes an airborne radar transmitted signal model, a space propagation model, a target scattering model, and an electronic warfare jamming signal model, and obtain the analytical expression for the theoretical received signal. In this step, the basic mathematical mechanism model of radar and electronic warfare is first constructed. Taking a typical countermeasure scenario of airborne pulse-Doppler (PD) radar encountering RGPO jamming based on DRFM as an example, S1 includes the following sub-steps: S11: The airborne radar transmission signal model adopts a linear frequency modulated pulse signal, and its expression is: in, For the amplitude of the transmitted signal, The pulse width. For carrier frequency, For frequency modulation slope, This is the initial phase; In some specific embodiments, the reference time is set as Construct a model of the airborne radar transmission signal that incorporates hardware nonlinearity:

[0053] in, For nominal amplitude, Let be the envelope nonlinear fluctuation function to be corrected; For carrier frequency, This is the frequency modulation slope; The transmitter phase noise model can be modeled as colored noise or polynomial phase error. The phase distortion coefficient to be corrected.

[0054] However, due to the nonlinear characteristics of the power amplifier (PA) in a real transmitter, the output pulse envelope is not an ideal rectangle, but exhibits varying degrees of distortion at the rising and falling edges, and fluctuations at the pulse tip. Simultaneously, the transmitter's local oscillator is not an ideal single-frequency signal, but contains colored phase noise. Therefore, this embodiment parameterizes the aforementioned hardware non-ideal characteristics. Based on the nonlinear characteristics of the actual transmitter hardware, the parameterized nonlinear features are introduced into the airborne radar transmission signal model. The expression for the transmission model, which includes the set of parameters to be corrected, is as follows:

[0055] Among them, the parameter set to be corrected Includes envelope fluctuation parameters and phase noise function .

[0056] S12: When a radar signal propagates through space and encounters a target, it generates an echo. During propagation, there is not only a line-of-sight path but also a multipath effect caused by ground / sea surface reflection. The space propagation model in this embodiment includes multipath components:

[0057] This includes not only line-of-sight direct waves, but also... Multiple diameters. , , These represent the scattering coefficients, delays, and Doppler shifts for each path. Due to the complexity of the airborne environment, the actual delay... and Doppler This includes minute vibrations caused by the aircraft's vibration; these vibration terms are derived from the parameter set. control.

[0058] S13: Construct the target scattering model; the radar cross section (RCS) of the target can be modeled using Swerling type I / II / III / IV fluctuation models, or a more refined deterministic model based on the target's electromagnetic scattering characteristics. In this embodiment, the parameters to be corrected in the target scattering model mainly include the mean value of the target RCS and the fluctuation model parameters.

[0059] S14: This embodiment uses RGPO jamming as an example. After the jammer intercepts the radar's transmitted signal, it performs DRFM storage, modulation, and delayed forwarding to form range gate drag jamming. The parameterized jamming signal model is as follows: in, For the amplitude of the interference signal, For the target true echo delay, For drag delay, Fixed processing delay for DRFM system, For Doppler frequency shift; The parameterized expression of the electronic warfare jamming signal model is as follows:

[0060] in, The parameter set to be corrected. Includes interference machine amplitude gain error Temperature drift delay Doppler modulation error and the phase noise inside the jammer .

[0061] In some specific embodiments, the expression for the constructed actual electronic station interference signal model is as follows:

[0062] in, The gain function of the jammer varies with operating frequency and temperature. It is the spatial propagation delay of radar to jammer. This indicates the drag pattern in electronic warfare tactical settings. The core parameters to be corrected are the inherent hardware latency of DRFM and its dynamic changes due to temperature drift. The non-ideal impulse response function of the jammer's RF front-end filter is given by its actual bandwidth and group delay. control, This represents the convolution operation. The phase truncation error is caused by the local oscillator phase noise and quantization of the interference machine.

[0063] Combining the above sub-models, the analytical expression for the theoretical received signal is denoted as: ,in To synthesize the set of parameters to be corrected.

[0064] S2: In the same or similar combat scenarios, collect measured countermeasure data of airborne radar and electronic warfare systems, perform data preprocessing, and obtain measured received signals; In a live-fire flight test of a certain type of airborne radar, a typical air combat scenario incorporating RGPO jamming was set up, and IQ baseband data was collected from the radar receiver. The specific data collection process included: (1) Test scenario setup: The carrier aircraft cruises at a speed of Ma=0.8 at an altitude of 3000m, and the target / jamming aircraft is located about 30km ahead of the carrier aircraft with a relative radial speed of about 150m / s. The jamming aircraft adopts the RGPO jamming pattern and the towing speed is set to 50m / s.

[0065] (2) Data acquisition: Using the high-speed data recording equipment inside the radar system, the IQ baseband data sequence after down-conversion by the receiver is acquired at a sampling rate of not less than twice the signal bandwidth. The data acquisition time is no less than 1 second, and the acquired data includes real noise. Target echo Actual interference and system thermal noise It must cover at least one complete gate drag cycle.

[0066] (3) Data preprocessing: Time alignment is performed on the collected raw data to eliminate the fixed delay between the start time of data recording and the start time of radar transmission pulse; amplitude calibration is performed, and the receiver link gain is calibrated according to the injected calibration signal to obtain the normalized amplitude reference: ,

[0067] in, For the in-phase components of the original data, These are the orthogonal components of the original data. The imaginary unit, This represents the number of sampling points.

[0068] S3: Define the error objective function and calculate the characteristic residual between the output of the theoretical received signal analytical expression under the current parameter set and the measured received signal; Because the phase of high-frequency radar signals is extremely sensitive, point-to-point subtraction in the time domain is highly susceptible to trapping in local minima. Therefore, this invention proposes a multi-domain joint feature residual correction method, which specifically includes the following steps: S31: The defined error objective function specifically includes: Set the measured received signal as Set the output of the theoretical parameterized model to ,in The set of parameters to be corrected; In the time domain residual function Its expression is:

[0069] Construct a second residual function in the frequency domain. Its expression is:

[0070] in, and These are the Fourier transforms of the measured signal and the model signal, respectively; Based on residual function Second residual function The joint objective function is expressed as follows:

[0071] in, and These are the weighting coefficients. The regularization coefficient is . These are prior parameters or state parameters from the previous time step.

[0072] S32: Extract the measured received signal With model signal The complex envelope, separating amplitude and phase; S33: Calculate the power spectral density using short-time Fourier transform. and :

[0073] in, This represents the frequency domain power spectrum residual, which is used to correct the filter bandwidth, spurious level, and DRFM quantization noise floor parameter.

[0074] S34: Calculate the composite residual for:

[0075] Among the additions Regularization term This is to prevent the model parameters from overfitting the measured noise during the correction process, so that they conform to the prior physical common sense.

[0076] S4: Based on the feature residuals, a nonlinear optimization algorithm and a dynamic filtering algorithm are used to iteratively update and dynamically correct the parameter set to be corrected in the benchmark mathematical mechanism model, so as to obtain the corrected optimal parameter set; Based on the rate of change of the parameters, this invention adopts a "graded correction" strategy. This step includes the following sub-steps: S41: For slowly changing parameters such as filter frequency response, system fixed attenuation, and ADC nonlinear polynomial coefficients, the Levenberg-Marquardt algorithm is used to solve the nonlinear least squares problem.

[0077] The Levenberg-Marquardt algorithm is used for iterative correction, and the corrected expression is as follows:

[0078] in, The residual function is the set of parameters to be corrected. Jacobian matrix, It is the identity matrix. The damping factor, This is the residual vector under the current parameters; Let the residual vector be Jacobian matrix The elements in are:

[0079] Because the mechanistic model has an analytical form, some Jacobian matrices can be obtained directly by taking partial derivatives of the formula, thereby improving the convergence speed. Its parameter update iteration formula is as follows:

[0080] Through repeated iterations, the originally rough theoretical formulas can be given precise values ​​that perfectly match the actual hardware.

[0081] S42: For the transient phase error of the T / R assembly and the multipath Doppler frequency shift that varies drastically with the line-of-sight angle caused by airframe vibration during airborne platform flight, offline fitting is ineffective. This invention treats these dynamic parameters as state variables. An extended Kalman filter is used for real-time dynamic tracking and correction, and real-time estimation is performed using continuously input measured data. The state transition equation is defined as follows:

[0082] in, Here is the state transition matrix. This represents process noise. The observation equation is defined as follows:

[0083] in, It is the parameterized nonlinear equation constructed in step S1.

[0084] S5: Substitute the modified optimal parameter set into the baseline mathematical mechanism model, and use a deep neural network to compensate for the non-analyzable nonlinear residual error to generate a high-fidelity airborne radar and electronic warfare model.

[0085] S5 is the output after the theoretical model has undergone parameter optimization correction in S4. Now calculate the residual error:

[0086] if The presence of only Gaussian white noise indicates that the physical model is perfect.

[0087] However, in electronic warfare, Complex nonlinear stray characteristics are often hidden within them.

[0088] This invention constructs a lightweight Transformer model. Using the parameter characteristics and intermediate states of the optimal mechanism model as input, the residual error is fitted and predicted:

[0089] Using the residual sequence of measured data to weight the neural network Backpropagation training was performed. The final high-fidelity radar and electronic warfare output model is as follows:

[0090] in, It is a formula mechanism (white box) based on actual measurement correction. It is a data-driven nonlinear compensation (black box). This gray box architecture, which combines white box and black box, ensures that the model follows strict radar equations and electromagnetic propagation laws in normal areas, while also reproducing the distortion characteristics of real hardware under extreme boundary conditions.

[0091] Example 2 This embodiment provides a radar and electronic warfare model dynamic correction system driven by measured data. This system is used to implement the method described in Embodiment 1 above. The system includes: Mechanism Modeling Module: This module is used to establish parameterized benchmark mathematical mechanism models for radar and electronic warfare. The module includes a built-in library of radar transmitted signal models (containing various waveforms such as LFM, phase coding, and frequency agility), a space propagation model library (containing free space propagation, multipath propagation, and atmospheric attenuation propagation), a target scattering model library (containing Swerling I-IV types and deterministic RCS models), and an electronic warfare jamming model library (containing jamming styles such as RGPO, VGPO, coherent decoys, and noise suppression). Users can select the desired model combinations through configuration files, and the module automatically generates parameterized theoretical analytical expressions for the received signals.

[0092] Data Acquisition Module: This module is used to acquire and preprocess measured radar and electronic countermeasures data from field tests or actual flights. The module includes: a data interface unit (supporting multiple data bus interfaces such as SCSI, PCIe, and Ethernet, and compatible with importing various IQ data file formats), a time alignment unit (using GPS timestamps or radar synchronization pulses to align the time reference of measured and simulated data), an amplitude calibration unit (completing receiver link gain calibration based on injected calibration signals or built-in self-test signals), and a clutter filtering unit (used to remove non-cooperative clutter components from the measured data, improving the signal-to-noise ratio).

[0093] Error Analysis Module: This module calculates the multidimensional feature residuals between the theoretical model and measured data under current parameters. The module includes: a time-domain feature extraction unit (calculating signal envelope, instantaneous phase, instantaneous frequency, etc.), a frequency-domain feature extraction unit (calculating power spectral density, center frequency, bandwidth, spurious level, etc. via FFT), a time-frequency domain feature extraction unit (calculating the time-frequency spectrum via STFT), and a residual weighting calculation unit (calculating the weighted joint objective function value based on preset weighting coefficients). The output of this module is the comprehensive residual vector and its Jacobian matrix with respect to each parameter.

[0094] Parameter Correction and Optimization Module: This module executes nonlinear optimization algorithms and dynamic filtering algorithms to drive iterative updates of the baseline model parameters. This module includes: The time-invariant parameter correction unit employs the Levenberg-Marquardt algorithm for offline iterative optimization of the time-invariant parameters in the parameter set to be corrected. The core of this unit is the LM algorithm solver, which takes the residual vector and Jacobian matrix provided by the error analysis module as input and outputs the optimal time-invariant parameter estimates. This unit also includes a convergence monitoring subunit to determine whether the iteration satisfies the convergence condition.

[0095] The time-varying parameter tracking unit employs an extended Kalman filter to perform real-time online estimation and tracking of time-varying parameters in the parameter set to be corrected. The core of this unit is an EKF recursive solver, which takes as input the continuous measured feature stream provided by the data acquisition module and outputs the estimated time-varying parameters at each time step. This unit also includes a divergence monitoring subunit, used to determine whether the filter has diverged due to model mismatch and to perform filter reset when divergence occurs.

[0096] Deep Compensation and Fusion Module: This module is used to learn and compensate for distortions that are difficult to be represented analytically by mathematical models through neural network models, and output the final high-fidelity simulation data.

[0097] This module includes: The residual calculation unit is used to calculate the residual error sequence between the computer theoretical model output and the measured data after parameter correction, and to normalize the residual error sequence to facilitate neural network training.

[0098] The Transformer network unit is used to perform nonlinear mapping fitting on the residual error sequence, taking the intermediate layer features and output features of the mechanistic model as input. This unit includes a pre-trained Transformer model weight file and an inference engine, supporting forward propagation computation.

[0099] The fusion output unit is used to add the prediction residuals of the Transformer network unit to the output of the mechanistic model to generate the final gray-box hybrid model output, and supports the export of output data in multiple formats (including MATLAB, NumPy, HDF5 and other formats).

[0100] Example 3 This embodiment provides a computer device, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements all the steps of the method described in Embodiment 1. The processor may be one or more of a central processing unit (CPU), a graphics processing unit (GPU), a digital signal processor (DSP), or an application-specific integrated circuit (ASIC). The memory may be one or more of a read-only memory (ROM), random access memory (RAM), flash memory, a solid-state drive (SSD), or a hard disk drive (HDD).

[0101] This embodiment also provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, it implements all the steps of the method described in Embodiment 1. The computer-readable storage medium can be any one of a floppy disk, optical disk, DVD, CD-ROM, Blu-ray disc, flash drive, memory card, solid-state drive, hard disk drive, or cloud storage medium.

[0102] Regarding the apparatus in the above embodiments, the specific manner in which each module performs its operation has been described in detail in the embodiments related to the method, and will not be elaborated upon here.

[0103] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0104] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for dynamic correction of radar and electronic warfare models driven by measured data, characterized in that, include: A baseline mathematical mechanism model for airborne radar and electronic warfare is established, which includes an airborne radar transmitted signal model, a space propagation model, a target scattering model, and an electronic warfare jamming signal model, thereby obtaining an analytical expression for the theoretical received signal. In the same or similar combat scenarios, collect measured countermeasure data of airborne radar and electronic warfare systems, perform data preprocessing, and obtain measured received signals; Define an error objective function and calculate the characteristic residual between the output of the theoretical received signal analytical expression under the current parameter set and the measured received signal. Based on the aforementioned feature residuals, a nonlinear optimization algorithm and a dynamic filtering algorithm are used to iteratively update and dynamically correct the parameter set to be corrected in the benchmark mathematical mechanism model, thereby obtaining the corrected optimal parameter set. The modified optimal parameter set is substituted into the baseline mathematical mechanism model, and a high-fidelity airborne radar and electronic warfare model is generated by compensating for the unanalyzable nonlinear residual error through a deep neural network.

2. The method for dynamic correction of radar and electronic warfare models driven by measured data according to claim 1, characterized in that, The airborne radar transmission signal model uses a linear frequency modulated pulse signal, and its expression is as follows: in, For the amplitude of the transmitted signal, The pulse width. For carrier frequency, For frequency modulation slope, This is the initial phase; Based on the nonlinear characteristics of the actual transmitter hardware, the nonlinear characteristics are parameterized and introduced into the airborne radar transmission signal model. The expression of the transmission model, which includes the set of parameters to be corrected, is as follows: Among them, the parameter set to be corrected Includes envelope fluctuation parameters and phase noise function .

3. The method for dynamic correction of radar and electronic warfare models driven by measured data according to claim 1, characterized in that, The electronic warfare jamming signal model includes a range-gate drag jamming model based on a digital radio frequency memory, and the expression for its jamming signal is as follows: in, For the amplitude of the interference signal, For the target true echo delay, For drag delay, Fixed processing delay for DRFM system, For Doppler frequency shift; The parameterized expression of the electronic warfare jamming signal model is as follows: in, The parameter set to be corrected. Includes interference machine amplitude gain error Temperature drift delay Doppler modulation error and the phase noise inside the jammer .

4. The method for dynamic correction of radar and electronic warfare models driven by measured data according to claim 1, characterized in that, The defined error objective function specifically includes: Set the measured received signal as Set the output of the theoretical parameterized model to ,in The set of parameters to be corrected; In the time domain residual function Its expression is: Construct a second residual function in the frequency domain. Its expression is: in, and These are the Fourier transforms of the measured signal and the model signal, respectively; Based on residual function Second residual function The joint objective function is expressed as follows: in, and These are the weighting coefficients. The regularization coefficient is . These are prior parameters or state parameters from the previous time step.

5. The method for dynamic correction of radar and electronic warfare models driven by measured data according to claim 4, characterized in that, The time-invariant parameters in the set of parameters to be corrected are iteratively corrected using the Levenberg-Marquardt algorithm, and the corrected expression is as follows: in, The residual function is the set of parameters to be corrected. Jacobian matrix, It is the identity matrix. The damping factor, This is the residual vector under the current parameters.

6. The method for dynamic correction of radar and electronic warfare models driven by measured data according to claim 4, characterized in that, For the time-varying parameters in the set of parameters to be corrected, an extended Kalman filter is used for real-time dynamic tracking and correction. The state equation and observation equation are as follows: in, For parameterized state transition functions, The feature vector extracted from the actual measurement. For mechanism observation function, and These are process noise and observation noise, respectively.

7. The method for dynamic correction of radar and electronic warfare models driven by measured data according to claim 1, characterized in that, The method for compensating for residual errors using deep neural networks includes the following steps: S501: Calculate the residual error signal after parameter correction. ,in The corrected optimal parameter set; S502: Construct and train the Transformer model, using the corrected output of the airborne radar and electronic warfare model. Using its intermediate layer features as input, predict the nonlinear residual sequence. ; (The Transformer model is explained in the instruction manual.) S503: The predicted residual error sequence is superimposed onto the corrected mechanistic model output to obtain the final high-fidelity model output, the expression of which is: .

8. A dynamic correction system for airborne radar and electronic warfare models driven by measured data, characterized in that, include: The mechanism modeling module is used to establish parameterized benchmark mathematical mechanism models for airborne radar and electronic warfare. The data acquisition module is used to acquire and preprocess measured radar and electronic countermeasures data from field tests or actual flights. The error analysis module is used to calculate the multidimensional characteristic residuals between the theoretical model and the measured data under the current parameters; The parameter correction and optimization module is used to execute nonlinear optimization algorithms and dynamic filtering algorithms to drive the iterative update of the baseline model parameters; The deep compensation and fusion module is used to learn and compensate for distortions that are difficult to be represented analytically by mathematical models through neural network models, and output the final high-fidelity simulation data.

9. The measured data-driven dynamic correction system for airborne radar and electronic warfare models according to claim 8, characterized in that, The parameter correction and optimization module includes: The time-invariant parameter correction unit is used to perform offline iterative optimization of the time-invariant parameters in the parameter set to be corrected using the Levenberg-Marquardt algorithm; The time-varying parameter tracking unit is used to perform real-time online estimation and tracking of the time-varying parameters in the set of parameters to be corrected using extended Kalman filtering.

10. The measured data-driven dynamic correction system for airborne radar and electronic warfare models according to claim 8, characterized in that, The depth compensation and fusion module includes: The residual calculation unit is used to calculate the residual error sequence between the output of the computer theoretical model after parameter correction and the measured data. Transformer network units are used to perform nonlinear mapping fitting on the residual error sequence, taking the intermediate layer features and output features of the mechanistic model as input. The fusion output unit is used to add the prediction residuals of the Transformer network units to the output of the mechanistic model to generate the final high-fidelity model output.

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