Aircraft trajectory forecasting method based on depth Kupman operator

Abstract

The invention discloses an aircraft trajectory forecasting method based on a deep Kupman operator, which combines deep learning with a Kupman operator theory, constructs a three-layer network to automatically extract Kupman features, introduces four physical constraints to improve the generalization ability of a model, realizes a three-section type forecasting strategy and two-channel online learning, and improves the prediction accuracy of the aircraft trajectory. The problems that a traditional method is low in prediction precision, poor in physical consistency, weak in adaptability and the like in a high-maneuverability flight scene are solved, high-precision aircraft trajectory prediction is achieved, reliable target information is provided for a seeker system, and the interception success rate is remarkably increased.

Description

Technical Field

[0001] The present invention belongs to the technical field of aircraft, and in particular relates to an aircraft trajectory prediction method based on a deep Koopman operator. Background Art

[0002] In modern intelligent aviation management systems, aircraft trajectory prediction is a key step in route planning and optimization, and is directly related to airspace utilization efficiency and flight safety. Traditional aircraft trajectory prediction methods mainly fall into the following categories:

[0003] 1. Physics-based methods: These methods rely on precise physical dynamics models, using Newton's equations of motion and aerodynamic principles to establish the aircraft's motion equations to predict future trajectories. However, these methods require extensive prior knowledge and accurate flight parameters. Model errors are significant in highly maneuverable flight conditions, making trajectory prediction for unknown aircraft particularly challenging.

[0004] 2. Traditional data-driven methods: Statistical prediction methods represented by Kalman filtering. This method performs well for linear or weakly nonlinear systems, but its prediction accuracy drops significantly when faced with highly nonlinear and highly maneuverable flight scenarios.

[0005] 3. Conventional machine learning methods: Although algorithms represented by support vector machines can learn patterns from historical data, they are unable to effectively capture the temporal dynamic characteristics and nonlinear features of aircraft trajectories, and the error accumulation is large in long-term predictions.

[0006] 4. Traditional deep learning methods: Although deep learning methods represented by long short-term memory networks (LSTMs) can process time series data, they have limited understanding of physical constraints and are prone to producing prediction results that do not conform to the laws of flight dynamics.

[0007] The main limitations of the above methods are: first, it is difficult to simultaneously take into account the interpretability of the physical model and the data-driven adaptability; second, the computational complexity is high when dealing with high-dimensional nonlinear dynamic systems; third, the prediction results are poorly consistent with the actual physical laws of flight; especially in high-speed and highly maneuverable flight scenarios, these problems are more prominent.

[0008] The Koopman operator theory provides a linear representation method for complex nonlinear dynamical systems, mapping nonlinear systems into a high-dimensional linear space for analysis. However, the traditional Koopman method faces problems in practical applications, such as difficulty in selecting observation functions and high computational complexity. Summary of the Invention

[0009] In order to overcome the shortcomings of the existing technology, the present invention provides an aircraft trajectory prediction method based on the deep Koopman operator. By combining deep learning with the Koopman operator theory, a three-layer network is constructed to automatically extract the Koopman features. Four physical constraints are introduced to improve the generalization ability of the model, and a three-stage prediction strategy and dual-channel online learning are implemented. The problems of low prediction accuracy, poor physical consistency, and weak adaptability of traditional methods in high-maneuverability flight scenarios are solved, and high-precision aircraft trajectory prediction is achieved. Reliable target information is provided for the seeker system, significantly improving the interception success rate.

[0010] The technical solutions adopted by the present invention to solve the technical problems are as follows:

[0011] Step 1: trajectory data acquisition and preprocessing;

[0012] Step 2: Deep Koopman model construction;

[0013] Step 3: Physically constrained deep Koopman model;

[0014] Step 4: Adaptive multi-step forecasting strategy;

[0015] Step 5: Online learning and model updating.

[0016] Preferably, the step 1 is specifically:

[0017] Step 1-1: Data acquisition: Use multi-sensor fusion technology to obtain the position, speed, and acceleration status information of the target aircraft to form the original trajectory sequence ,in express Moment dimensional state vector, ;

[0018] Step 1-2: Noise filtering: Use the unscented Kalman filter (UKF) method to filter the original data. During the filtering process, the state covariance matrix Q is set to a diagonal matrix with diagonal elements of [0.01, 0.01, 0.01, 0.05, 0.05, 0.05, 0.1, 0.1, 0.1], and the observation noise covariance matrix R is set to a diagonal matrix with diagonal elements of [0.1, 0.1, 0.1] to obtain the filtered data set. ;

[0019] Step 1-3: Data completion: For data missing due to sensor occlusion or failure, the cubic spline interpolation algorithm is used to complete the data. The spline smoothing parameter is set to 0.8 to generate a complete trajectory sequence. ;

[0020] Step 1-4: Feature extraction: extracting position coordinates from the complete trajectory ,speed and acceleration , construct a feature vector set ;

[0021] Steps 1-5: Data standardization: Standardize the feature data to eliminate the impact of different feature dimension differences and obtain a standardized data set ,in The length is The input sequence, The length is The predicted target sequence; Indicates the total number of samples in the dataset.

[0022] Preferably, the step 2 is specifically as follows:

[0023] Step 2-1: Encoder Network Design: Build the Encoder Network ,in represents the network parameters, is the original state space dimension, is the Koopman feature space dimension; the encoder network adopts the multi-layer perceptron MLP structure;

[0024] Step 2-2: Decoder Network Design: Build the decoder network ,in represents the network parameters, which are used to map the state of the Koopman feature space back to the original state space;

[0025] Step 2-3: Koopman operator approximation: construct the Koopman matrix ,in is a learnable parameter used to linearly push forward the system state in the Koopman feature space;

[0026] Step 2-4: Network training: defining the total loss function , contains the following parts:

[0027] Reconstruction loss: ;

[0028] Prediction loss: ;

[0029] Linearizability loss: ;

[0030] Regularization loss: ;

[0031] Total loss function: ;

[0032] Minimize using Adam optimizer , update the parameters through back propagation 、 and , get the trained encoder network , decoder network and the Koopman matrix .

[0033] Preferably, the step 3 is specifically:

[0034] Step 3-1: Flight dynamics constraint definition: Based on the principles of aircraft flight dynamics, define a set of physical constraints ,include:

[0035] Velocity continuity constraint: ,in Second, 、 Represent the state vectors at time t+1 and time t respectively, They represent the speed at time t+1 and time t respectively, represents the acceleration at time t;

[0036] Acceleration range constraints: ,in , Indicates the maximum acceleration limit of the aircraft;

[0037] Turn rate constraint: , 25 deg / s is the maximum turning rate of the aircraft, represents the turning rate;

[0038] Energy conservation approximate constraints: ,in Indicates external work; Indicates the mass of the aircraft, represents the height at time t+1, represents the height at time t;

[0039] Step 3-2: Physical Constraint Loss Function: Define the physical constraint loss function :

[0040]

[0041] Among them, the coefficients 0.35, 0.25, 0.25, and 0.15 are the weights of each physical constraint, which are determined according to the importance of the constraint;

[0042] Step 3-3: Physical constraint optimization: Combine the total loss function and the physical constraint loss function to obtain a new total loss function:

[0043]

[0044] Among them, 0.2 is the weight coefficient of physical constraint loss;

[0045] The deep Koopman model is fine-tuned using the new total loss function. The number of training rounds is set to 50, and the learning rate is set to 1 / 10 of the original, i.e. 0.0001. The deep Koopman model after physical constraint optimization is obtained. ;

[0046] Step 3-4: Feature analysis and dimensionality reduction: Analyze the importance of each dimension in the Koopman feature space through principal component analysis (PCA) and sparse autoencoders, and select key features to simplify the model structure;

[0047] Principal component analysis: Perform PCA decomposition on the Koopman feature space and calculate the contribution rate of each principal component;

[0048] Sparsity analysis: Calculate the L1 norm of each feature dimension to evaluate its sparsity;

[0049] Feature selection: retain the features corresponding to the principal components that explain 95% of the variance to form a simplified model.

[0050] Preferably, the step 4 is specifically as follows:

[0051] Step 4-1: Recursive prediction baseline: based on the trained Koopman matrix Make a recursive prediction:

[0052] ...

[0053] in, Indicates the prediction step length; 、 、 Represent the predicted state vectors of step t+1, step t+2, and step t+h respectively;

[0054] Step 4-2: Error Analysis: Establish a model for the relationship between prediction step length and error to quantify the impact of prediction time on accuracy:

[0055]

[0056] in, represents the average error of h-step predictions, represents the predicted state vector of the i+h step, represents the state vector of step i+h;

[0057] Step 4-3: Adaptive prediction interval: Based on the error accumulation model, dynamically adjust the prediction interval and introduce multiple prediction starting points:

[0058] Short-term forecast: using the current moment As a starting point, the forecast interval;

[0059] Medium-term forecast: Moment of use As a starting point, the forecast interval;

[0060] Long-term forecasting: Moment of use As a starting point, the forecast interval;

[0061] Step 4-4: Integrated prediction fusion: Use the Bayesian model averaging method to fuse multiple prediction results:

[0062]

[0063] in, Indicates the Model for the moment The prediction results, Represents the corresponding weight, satisfying and ; represents the final fused predicted state vector;

[0064] Weight The Lagrange multiplier method is used to solve the following optimization problem by minimizing the prediction error on the validation set:

[0065]

[0066] subject to and

[0067] in, represents the optimal weight, represents the number of validation set samples, represents the prediction result of the state vector of the lth model, represents the true state vector, represents the weight vector;

[0068] The quadratic programming algorithm is used in the solution process;

[0069] Steps 4-5: Variational Inference: Use the Monte Carlo sampling variational algorithm to quantify the uncertainty of the prediction and generate confidence intervals for each prediction point:

[0070]

[0071] in, represents the prediction standard deviation.

[0072] Preferably, the step 5 is specifically as follows:

[0073] Step 5-1: Change point detection: Design a change point detection algorithm to identify changes in aircraft maneuvering patterns:

[0074]

[0075] in, represents the prediction error, is the standard deviation of the prediction error, is the indicator function, represents the change point detection result at time t, Indicates the predicted state value at time t; when three consecutive time steps are detected to meet the conditions, it is confirmed as a change point;

[0076] Step 5-2: Incremental learning strategy: Based on the detected change points, adjust the incremental learning strategy;

[0077] If a change point is detected, model update strategy 1 is used: all 3 layers of the encoder network are retrained and all parameters of the Koopman matrix are adjusted, with a learning rate of 1e-3;

[0078] If no change point is detected, the model update strategy 2 is used: only the parameters of the last layer of the encoder network and the diagonal elements of the Koopman matrix are adjusted, and the learning rate is set to 5e-5;

[0079] Step 5-3: Sliding window training: Use the sliding window method to train the model by combining new and old data;

[0080]

[0081] in, It represents the representative samples selected from the historical data. The specific selection method is as follows: 20% of the samples are randomly selected from the historical database, and then the 5 samples closest to each cluster center are selected through k-means clustering, for a total of 50 representative samples; Indicates the new trajectory data obtained in real time, represents the complete dataset used for sliding window training;

[0082] Step 5-4: Knowledge transfer: Use model distillation technology to transfer the prediction ability of the old model to the new model; the old model refers to the currently running trained deep Koopman model, and the new model refers to the new trajectory data obtained in real time. Reparameterized deep Koopman model;

[0083]

[0084] in, and Represent the encoders of the new model and the old model respectively, and Represent the decoders of the new model and the old model respectively, is a randomly sampled Koopman space point; represents the knowledge transfer loss function;

[0085] The knowledge of the old model is transferred to the new model:

[0086]

[0087] in, and Represent the prediction functions of the new model and the old model respectively;

[0088] Step 5-5: Model integration and update: Integrate the new model with the old model to form an updated model:

[0089]

[0090] in, is the update rate, with an initial value of 0.3, which is dynamically adjusted based on the performance of the new model on the validation set: if the root mean square error of the new model on the validation set is reduced by more than 15% compared to the old model, Increase by 0.2; if the new model's root mean square error on the validation set is less than 5% higher than that of the old model, then Decrease by 0.1; if the new model has a larger root mean square error on the validation set than the old model, then Set to 0.05.

[0091] Preferably, the structure of the encoder network is:

[0092] Input layer: nodes, corresponding to the original state vector;

[0093] Hidden layer 1: 128 nodes, activation function is ;

[0094] Hidden layer 2: 64 nodes, activation function is ;

[0095] Output layer: nodes, the activation function is .

[0096] Preferably, the structure of the decoder network is:

[0097] Input layer: nodes, corresponding to the Koopman eigenvector;

[0098] Hidden layer 1: 64 nodes, activation function is ;

[0099] Hidden layer 2: 128 nodes, activation function is ;

[0100] Output layer: nodes, linear activation function.

[0101] Preferably, in steps 2-4, when training the total loss function, the initial learning rate is set to 0.001, decays to 0.8 times the original rate every 50 epochs, and the batch size is set to 64.

[0102] The beneficial effects of the present invention are as follows:

[0103] The present invention combines deep learning with the Koopman operator theory to construct a three-layer network to automatically extract the Koopman features, introduces four physical constraints to improve the generalization ability of the model, and implements a three-stage prediction strategy and dual-channel online learning. It solves the problems of low prediction accuracy, poor physical consistency, and weak adaptability of traditional methods in high-maneuverability flight scenarios, realizes high-precision aircraft trajectory prediction, provides reliable target information for the seeker system, and significantly improves the interception success rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0104] Figure 1 2 is a comparison chart of aircraft trajectory prediction effects according to an embodiment of the present invention. DETAILED DESCRIPTION

[0105] The present invention will be further described below with reference to the accompanying drawings and examples.

[0106] The present invention proposes an aircraft trajectory prediction method based on deep learning Koopman operator. This method uses a deep neural network to automatically learn the Koopman eigenmapping function, converts the nonlinear flight dynamics system into a high-dimensional linear representation, and combines it with the physical constraint optimization prediction model to achieve high-precision and long-time-scale aircraft trajectory prediction.

[0107] Step 1: trajectory data acquisition and preprocessing;

[0108] This step collects the historical trajectory data of the target aircraft through various sensors such as infrared and radar, and preprocesses the data.

[0109] Step 1-1: Data acquisition: Use multi-sensor fusion technology to obtain the position, speed, and acceleration status information of the target aircraft to form the original trajectory sequence ,in express Moment dimensional state vector, ;

[0110] Step 1-2: Noise filtering: Use the unscented Kalman filter (UKF) method to filter the original data. During the filtering process, the state covariance matrix Q is set to a diagonal matrix with diagonal elements of [0.01, 0.01, 0.01, 0.05, 0.05, 0.05, 0.1, 0.1, 0.1], and the observation noise covariance matrix R is set to a diagonal matrix with diagonal elements of [0.1, 0.1, 0.1] to obtain the filtered data set. ;

[0111] Step 1-3: Data completion: For data missing due to sensor occlusion or failure, the cubic spline interpolation algorithm is used to complete the data. The spline smoothing parameter is set to 0.8 to generate a complete trajectory sequence. ;

[0112] Step 1-4: Feature extraction: extracting position coordinates from the complete trajectory ,speed and acceleration , construct a feature vector set ;

[0113] Steps 1-5: Data standardization: Standardize the feature data to eliminate the impact of different feature dimension differences and obtain a standardized data set ,in The length is The input sequence, The length is The predicted target sequence;

[0114] Step 2: Deep Koopman encoder network construction;

[0115] In this step, a deep neural network architecture is designed to automatically learn the mapping of nonlinear systems to the Koopman feature space.

[0116] Step 2-1: Encoder Network Design: Constructing the Koopman Encoder Network ,in represents the network parameters, is the original state space dimension, is the Koopman feature space dimension; the encoder network adopts the multi-layer perceptron MLP structure;

[0117] Input layer: nodes, corresponding to the original state vector; hidden layer 1: 128 nodes, the activation function is ; Hidden layer 2: 64 nodes, activation function is ; Out of layer: nodes, the activation function is ;

[0118] Step 2-2: Decoder Network Design: Build the decoder network ,in represents the network parameters, which are used to map the state of the Koopman feature space back to the original state space;

[0119] Input layer: nodes, corresponding to the Koopman eigenvector; hidden layer 1: 64 nodes, the activation function is ; Hidden layer 2: 128 nodes, activation function is Output layer: nodes, linear activation function;

[0120] Step 2-3: Koopman operator approximation: construct the Koopman matrix ,in is a learnable parameter used to linearly push forward the system state in the Koopman feature space;

[0121] Step 2-4: Network training: defining the total loss function , contains the following parts:

[0122] Reconstruction loss: ;

[0123] Prediction loss: ;

[0124] Linearizability loss: ;

[0125] Regularization loss: ;

[0126] Total loss function: ;

[0127] Minimize using Adam optimizer , the initial learning rate is set to 0.001, decays to 0.8 times the original rate every 50 epochs, the batch size is set to 64, and the parameters are updated by back propagation 、 and , get the trained encoder network , decoder network and the Koopman matrix ;

[0128] Step 3: Physically constrained deep Koopman model;

[0129] This step introduces physical knowledge into the deep Koopman model to enhance the model's physical interpretability and predictive accuracy.

[0130] Step 3-1: Flight dynamics constraint definition: Based on the principles of aircraft flight dynamics, define a set of physical constraints ,include:

[0131] Velocity continuity constraint: ,in Second;

[0132] Acceleration range constraints: ,in , Indicates the typical maximum acceleration limit of the aircraft;

[0133] Turn rate constraint: , 25 deg / s is the typical maximum turning rate of the aircraft;

[0134] Energy conservation approximate constraints: ,in By thrust and drag estimation;

[0135] Step 3-2: Physical Constraint Loss Function: Define the physical constraint loss function :

[0136]

[0137] Among them, the coefficients 0.35, 0.25, 0.25, and 0.15 are the weights of each physical constraint, which are determined according to the importance of the constraint;

[0138] Step 3-3: Physical constraint optimization: Combine the total loss function and the physical constraint loss function to obtain a new total loss function:

[0139]

[0140] Among them, 0.2 is the weight coefficient of physical constraint loss;

[0141] The deep Koopman model is fine-tuned using the new total loss function. The number of training rounds is set to 50, and the learning rate is set to 1 / 10 of the original, i.e. 0.0001. The deep Koopman model after physical constraint optimization is obtained. ;

[0142] Step 3-4: Feature analysis and dimensionality reduction: Analyze the importance of each dimension in the Koopman feature space through principal component analysis (PCA) and sparse autoencoders, and select key features to simplify the model structure;

[0143] Principal component analysis: Perform PCA decomposition on the Koopman feature space and calculate the contribution rate of each principal component;

[0144] Sparsity analysis: Calculate the L1 norm of each feature dimension to evaluate its sparsity;

[0145] Feature selection: retain the features corresponding to the principal components that explain 95% of the variance to form a simplified model;

[0146] Step 4: Adaptive multi-step forecasting strategy;

[0147] In this step, an adaptive multi-step prediction strategy is designed to solve the problem of error accumulation in long-term prediction.

[0148] Step 4-1: Recursive prediction baseline: based on the trained Koopman matrix Make a recursive prediction:

[0149] ...

[0150] in, Indicates the prediction step size. The basic prediction step size is set to 30 steps (equivalent to 3 seconds, sampling rate is 10Hz);

[0151] Step 4-2: Error Analysis: Establish a model for the relationship between prediction step length and error to quantify the impact of prediction time on accuracy:

[0152]

[0153] Through experiments on the training set, we obtained the growth curve of error with step length. The actual measurement results show that the prediction error grows slowly within h = 10 steps, grows at a medium speed in the range of h = 10 to 20 steps, and grows rapidly after h > 20 steps.

[0154] Step 4-3: Adaptive prediction interval: Based on the error accumulation model, dynamically adjust the prediction interval and introduce multiple prediction starting points:

[0155] Short-term forecast: using the current moment As a starting point, the forecast interval;

[0156] Medium-term forecast: Moment of use As a starting point, the forecast interval;

[0157] Long-term forecasting: Moment of use As a starting point, the forecast interval;

[0158] Step 4-4: Integrated prediction fusion: Use the Bayesian model averaging method to fuse multiple prediction results:

[0159]

[0160] in, Indicates the Model for the moment The prediction results, Represents the corresponding weight, satisfying and ;

[0161] Weight The following optimization problem is solved using the Lagrange multiplier method by minimizing the prediction error on the validation set:

[0162]

[0163] subject to and

[0164] The quadratic programming algorithm is used in the solution process; the upper limit of the number of iterations is set to 100, and the convergence threshold is set to 1e-6.

[0165] Steps 4-5: Variational Inference: Use the Monte Carlo sampling variational algorithm to quantify the uncertainty of the prediction and generate confidence intervals for each prediction point:

[0166]

[0167] in, represents the standard deviation of the predictions, calculated using the encoder network forward propagation, activating the Dropout layer (with probability 0.1) and performing 100 forward passes to calculate the standard deviation of the output. 1.96 is the z-score corresponding to the 95% confidence interval.

[0168] Step 5: Online learning and model updating;

[0169] This step implements online learning and continuous optimization of the model to adapt to changes in the maneuvering characteristics of the target aircraft.

[0170] Step 5-1: Change point detection: Design a change point detection algorithm to identify significant changes in the aircraft's maneuvering pattern:

[0171]

[0172] in, represents the prediction error, is the standard deviation of the forecast error, calculated over the last 30 time steps; It is an indicator function. When three consecutive time steps meet the conditions, it is confirmed as a change point.

[0173] Step 5-2: Incremental learning strategy: Based on the detected change points, adjust the incremental learning strategy;

[0174] If a change point is detected, model update strategy 1 is used: all 3 layers of the encoder network are retrained and all parameters of the Koopman matrix are adjusted, with a learning rate of 1e-3;

[0175] If no change point is detected, the model update strategy 2 is used: only the parameters of the last layer of the encoder network and the diagonal elements of the Koopman matrix are adjusted, and the learning rate is set to 5e-5;

[0176] Step 5-3: Sliding window training: Use the sliding window method to train the model by combining new and old data;

[0177]

[0178] in, It represents the representative samples selected from the historical data. The specific selection method is as follows: 20% of the samples are randomly selected from the historical database, and then the 5 samples closest to each cluster center are selected through k-means clustering, for a total of 50 representative samples;

[0179] Step 5-4: Knowledge transfer: Use model distillation technology to transfer the predictive ability of the old model to the new model;

[0180]

[0181] in, and Represent the encoders of the new model and the old model respectively, and Represent the decoders of the new model and the old model respectively, is a randomly sampled Koopman space point; the training uses the temperature parameter T = 2.0, the learning rate is 0.0005, and the training is 30 rounds; represents the knowledge transfer loss function, which is used to ensure that the new model can inherit the effective prediction ability of the old model;

[0182] The knowledge of the old model is transferred to the new model:

[0183]

[0184] in, and Represent the prediction functions of the new model and the old model respectively;

[0185] Step 5-5: Model integration and update: Integrate the new model with the old model to form an updated model:

[0186]

[0187] in, is the update rate, with an initial value of 0.3, which is dynamically adjusted according to the performance of the new model on the validation set; the root mean square error (RMSE) is used as the core indicator for performance evaluation, and the calculation formula is:

[0188]

[0189] The validation set contains 300 trajectory segments of different maneuver modes, each segment is 30 time steps long. The determination of depends on the change in the root mean square error of the new model on the validation set compared to the old model. If the root mean square error of the new model on the validation set is reduced by more than 15% compared to the old model, then Increase by 0.2; if the new model's root mean square error on the validation set is less than 5% higher than that of the old model, then Decrease by 0.1; if the new model has a larger root mean square error on the validation set than the old model, then Set to 0.05.

[0190] Step 6: System integration and application deployment;

[0191] This step integrates the trained model into the seeker system to achieve real-time trajectory prediction.

[0192] Step 6-1: Model compression: Use structured pruning and quantization techniques to compress the model size and reduce computational complexity:

[0193] Weight pruning: Use L1 regularization to sparse the weights and remove weight parameters whose absolute value is less than the threshold 0.01;

[0194] Quantization: Use linear quantization algorithm to quantize 32-bit floating point weights into 8-bit integers, and the quantization ratio is (max-min) / 255;

[0195] Structure optimization: Reduce the hidden layers of the encoder and decoder from [128, 64] and [64, 128] to [64, 32] and [32, 64] respectively;

[0196] Step 6-2: Hardware Adaptation: Optimize the model for the seeker DSP chip (TI TMS320C6678) to achieve real-time calculation:

[0197] Instruction set optimization: Use DSP SIMD instructions to accelerate matrix operations;

[0198] Memory layout: optimize data storage structure and reduce cache misses;

[0199] Parallel computing: Utilizes multi-core architecture to achieve 2-thread parallel processing, and the computing delay is controlled within 10ms;

[0200] Step 6-3: System Integration: Integrate the trajectory prediction module with the guidance law module and control system to form a complete interception system:

[0201] Prediction interface design: The input is the aircraft status data of the last 20 time steps, and the output is the predicted trajectory of the next 30 time steps;

[0202] Data transmission protocol: UDP protocol, transmission frequency 100Hz, delay tolerance 20ms;

[0203] Guidance law integration: The predicted trajectory is directly input into the proportional guidance law algorithm with a guidance gain factor of 3.5.

[0204] Step 6-4: Performance Monitoring: Design a real-time monitoring system based on thresholds to monitor key indicators:

[0205] Error monitoring: Calculate the short-term (1s) prediction error every second, with a threshold of 10m;

[0206] Latency monitoring: measures prediction calculation time and issues a warning if it exceeds 15ms;

[0207] Data logging: Performance metrics are recorded every minute, including average error, maximum error, and computational delay.

[0208] Step 6-5: Fault-tolerance mechanism: Implement a multi-level fault protection mechanism to ensure system reliability:

[0209] Data anomaly processing: When detecting data anomalies, use the valid data at the previous moment to replace them;

[0210] Insufficient resources handling: Switch to a lightweight model (prediction step size is halved) when computing resources are insufficient;

[0211] Backup system: maintain an unscented Kalman filter as a backup, which automatically switches when the main system fails;

[0212] like Figure 1 To verify the effectiveness of the proposed method, a real-world aircraft trajectory dataset was collected and compared with existing mainstream trajectory prediction methods. The experimental results are shown in Table 1:

[0213] Table 1

[0214] Prediction Methods Short-term (1s) prediction error (m) Medium-term (3s) forecast error (m) Long-term (5s) prediction error (m) Computation time (ms) Physical consistency score (0-1) Kalman filter 8.5 26.3 58.7 2.1 0.72 LSTM 5.2 18.9 45.3 12.5 0.65 Classic Koopman method 6.1 15.2 32.6 8.3 0.83 GRU-Physical Hybrid Model 4.8 14.7 28.9 10.2 0.85 Method of the present invention 3.6 10.5 19.3 9.5 0.94

[0215] As can be seen from the table, our method significantly outperforms existing methods in short-, medium-, and long-term prediction accuracy. In particular, for long-term predictions (5 seconds), the error is 33.2% lower than that of the second-place method (GRU-Physical Hybrid Model). Furthermore, our method maintains a high physical consistency score, indicating that the predictions conform to the laws of flight dynamics. While computational time is slightly longer than that of the Kalman filter method, it still meets real-time processing requirements and boasts superior computational efficiency to other deep learning methods.

[0216] Innovations of the present invention:

[0217] 1. Deep Koopman Coding Network: This invention automatically learns the Koopman feature representation of complex nonlinear systems through a three-layer neural network architecture ([d→128→64→32]), replacing the manually designed observation function in the traditional Koopman method. The feature representation capability is improved by 89%, enabling the Koopman method to be successfully applied to high-dimensional complex flight trajectory prediction problems.

[0218] 2. Flight dynamics constraint integration: This invention integrates flight dynamics knowledge into the deep learning framework in the form of clear mathematical constraints, including velocity continuity constraints, 9g acceleration limit constraints, 25 degree / second turn rate constraints, and energy conservation constraints. This enables the model to maintain both data-driven adaptability and the generalization ability based on physical models, reducing errors by 37.5%.

[0219] 3. Adaptive multi-segment prediction strategy: This paper designs a segmented prediction and fusion strategy, dividing the 30-step prediction into three intervals: short-term [t+1, t+10], medium-term [t+11, t+20], and long-term [t+21, t+30]. The results are fused through the Bayesian model averaging method, and the long-term prediction error is reduced by 33.2%.

[0220] 4. Dual-channel update mechanism: This invention implements a dual-channel online learning mechanism based on change point detection. The change point detection threshold is 2.5σ. When there is a change, all three layers of network parameters are retrained (learning rate 1e-3). When there is no change, only the last layer parameters are adjusted (learning rate 5e-5), which improves the model adaptability by 42%.

[0221] In summary, the present invention combines deep learning with the Koopman operator theory to construct a three-layer network to automatically extract the Koopman features, introduces four physical constraints to improve the generalization ability of the model, and implements a three-stage prediction strategy and dual-channel online learning. It solves the problems of low prediction accuracy, poor physical consistency, and weak adaptability of traditional methods in high-maneuverability flight scenarios, realizes high-precision aircraft trajectory prediction, provides reliable target information for the seeker system, and significantly improves the interception success rate.

Claims

1. A method for predicting aircraft trajectories based on a deep Koopman operator, characterized in that: The steps include: Step 1: trajectory data acquisition and preprocessing; Step 2: Deep Koopman model construction; Step 3: Physically constrained deep Koopman model; Step 4: Adaptive multi-step forecasting strategy; Step 5: Online learning and model updating.

2. The aircraft trajectory prediction method based on the deep Koopman operator according to claim 1, characterized in that: The step 1 is specifically as follows: Step 1-1: Data acquisition: Use multi-sensor fusion technology to obtain the position, speed, and acceleration status information of the target aircraft to form the original trajectory sequence ,in express Moment dimensional state vector, ; Step 1-2: Noise filtering: Use the unscented Kalman filter (UKF) method to filter the original data. During the filtering process, the state covariance matrix Q is set to a diagonal matrix with diagonal elements of [0.01, 0.01, 0.01, 0.05, 0.05, 0.1, 0.1, 0.1], and the observation noise covariance matrix R is set to a diagonal matrix with diagonal elements of [0.1, 0.1, 0.1] to obtain the filtered data set. ; Step 1-3: Data completion: For data missing due to sensor occlusion or failure, the cubic spline interpolation algorithm is used to complete the data. The spline smoothing parameter is set to 0.8 to generate a complete trajectory sequence. ; Step 1-4: Feature extraction: extracting position coordinates from the complete trajectory ,speed and acceleration , construct a feature vector set ; Steps 1-5: Data standardization: Standardize the feature data to eliminate the impact of different feature dimension differences and obtain a standardized data set ,in The length is The input sequence, The length is The predicted target sequence; Indicates the total number of samples in the dataset.

3. The aircraft trajectory prediction method based on the deep Koopman operator according to claim 2, characterized in that: The step 2 is specifically as follows: Step 2-1: Encoder Network Design: Build the Encoder Network ,in represents the network parameters, is the original state space dimension, is the dimension of the Koopman eigenspace; The encoder network adopts a multi-layer perceptron MLP structure; Step 2-2: Decoder Network Design: Build the decoder network ,in represents the network parameters, which are used to map the state of the Koopman feature space back to the original state space; Step 2-3: Koopman operator approximation: construct the Koopman matrix ,in is a learnable parameter used to linearly push forward the system state in the Koopman feature space; Step 2-4: Network training: defining the total loss function , contains the following parts: Reconstruction loss: ; Prediction loss: ; Linearizability loss: ; Regularization loss: ; Total loss function: ; Minimize using Adam optimizer , update the parameters through back propagation 、 and , get the trained encoder network , decoder network and the Koopman matrix .

4. The aircraft trajectory prediction method based on the deep Koopman operator according to claim 3 is characterized in that: The step 3 is specifically as follows: Step 3-1: Flight dynamics constraint definition: Based on the principles of aircraft flight dynamics, define a set of physical constraints ,include: Velocity continuity constraint: ,in Second, 、 Represent the state vectors at time t+1 and time t respectively, They represent the speed at time t+1 and time t respectively, represents the acceleration at time t; Acceleration range constraints: ,in , Indicates the maximum acceleration limit of the aircraft; Turn rate constraint: , 25 deg / s is the maximum turning rate of the aircraft, represents the turning rate; Energy conservation approximate constraints: ,in Indicates external work; Indicates the mass of the aircraft, represents the height at time t+1, represents the height at time t; Step 3-2: Physical Constraint Loss Function: Define the physical constraint loss function : ； Among them, the coefficients 0.35, 0.25, 0.25, and 0.15 are the weights of each physical constraint, which are determined according to the importance of the constraint; Step 3-3: Physical constraint optimization: Combine the total loss function and the physical constraint loss function to obtain a new total loss function: ； Among them, 0.2 is the weight coefficient of physical constraint loss; The deep Koopman model is fine-tuned using the new total loss function. The number of training rounds is set to 50, and the learning rate is set to 1 / 10 of the original, i.e. 0.0001. The deep Koopman model after physical constraint optimization is obtained. ; Step 3-4: Feature analysis and dimensionality reduction: Analyze the importance of each dimension in the Koopman feature space through principal component analysis (PCA) and sparse autoencoders, and select key features to simplify the model structure; Principal component analysis: Perform PCA decomposition on the Koopman feature space and calculate the contribution rate of each principal component; Sparsity analysis: Calculate the L1 norm of each feature dimension to evaluate its sparsity; Feature selection: retain the features corresponding to the principal components that explain 95% of the variance to form a simplified model.

5. The aircraft trajectory prediction method based on the deep Koopman operator according to claim 4, characterized in that: The step 4 is specifically as follows: Step 4-1: Recursive prediction baseline: based on the trained Koopman matrix Make a recursive prediction: ... ； in, Indicates the prediction step length; 、 、 Represent the predicted state vectors of step t+1, step t+2, and step t+h respectively; Step 4-2: Error Analysis: Establish a model for the relationship between prediction step length and error to quantify the impact of prediction time on accuracy: ； in, represents the average error of h-step predictions, represents the predicted state vector of the i+h step, represents the state vector of step i+h; Step 4-3: Adaptive prediction interval: Based on the error accumulation model, dynamically adjust the prediction interval and introduce multiple prediction starting points: Short-term forecast: using the current moment As a starting point, the forecast interval; Medium-term forecast: Moment of use As a starting point, the forecast interval; Long-term forecasting: Moment of use As a starting point, the forecast interval; Step 4-4: Integrated prediction fusion: Use the Bayesian model averaging method to fuse multiple prediction results: ； in, Indicates the Model for the moment The prediction results, Represents the corresponding weight, satisfying and ; represents the final fused predicted state vector; Weight The Lagrange multiplier method is used to solve the following optimization problem by minimizing the prediction error on the validation set: ； subject to and ; in, represents the optimal weight, represents the number of validation set samples, represents the prediction result of the state vector of the lth model, represents the true state vector, represents the weight vector; The quadratic programming algorithm is used in the solution process; Steps 4-5: Variational Inference: Use the Monte Carlo sampling variational algorithm to quantify the uncertainty of the prediction and generate confidence intervals for each prediction point: ； in, represents the prediction standard deviation.

6. The aircraft trajectory prediction method based on the deep Koopman operator according to claim 5, characterized in that: The step 5 is specifically as follows: Step 5-1: Change point detection: Design a change point detection algorithm to identify changes in aircraft maneuvering patterns: ； in, represents the prediction error, is the standard deviation of the prediction error, is the indicator function, represents the change point detection result at time t, Indicates the predicted state value at time t; when three consecutive time steps are detected to meet the conditions, it is confirmed as a change point; Step 5-2: Incremental learning strategy: Based on the detected change points, adjust the incremental learning strategy; If a change point is detected, model update strategy 1 is used: all 3 layers of the encoder network are retrained and all parameters of the Koopman matrix are adjusted, with a learning rate of 1e-3; If no change point is detected, the model update strategy 2 is used: only the parameters of the last layer of the encoder network and the diagonal elements of the Koopman matrix are adjusted, and the learning rate is set to 5e-5; Step 5-3: Sliding window training: Use the sliding window method to train the model by combining new and old data; ； in, It represents the representative samples selected from the historical data. The specific selection method is as follows: 20% of the samples are randomly selected from the historical database, and then the 5 samples closest to each cluster center are selected through k-means clustering, for a total of 50 representative samples; Indicates the new trajectory data obtained in real time, represents the complete dataset used for sliding window training; Step 5-4: Knowledge transfer: Use model distillation technology to transfer the prediction ability of the old model to the new model; the old model refers to the currently running trained deep Koopman model, and the new model refers to the new trajectory data obtained in real time. Reparameterized deep Koopman model; ； in, and Represent the encoders of the new model and the old model respectively, and Represent the decoders of the new model and the old model respectively, is a randomly sampled Koopman space point; represents the knowledge transfer loss function; The knowledge of the old model is transferred to the new model: ； in, and Represent the prediction functions of the new model and the old model respectively; Step 5-5: Model integration and update: Integrate the new model with the old model to form an updated model: ； in, is the update rate, with an initial value of 0.3, which is dynamically adjusted based on the performance of the new model on the validation set: if the root mean square error of the new model on the validation set is reduced by more than 15% compared to the old model, Increase by 0.2; if the new model's root mean square error on the validation set is less than 5% higher than that of the old model, then Decrease by 0.1; if the new model has a larger root mean square error on the validation set than the old model, then Set to 0.

05.

7. The aircraft trajectory prediction method based on the deep Koopman operator according to claim 6, characterized in that: The structure of the encoder network is: Input layer: nodes, corresponding to the original state vector; Hidden layer 1: 128 nodes, activation function is ; Hidden layer 2: 64 nodes, activation function is ; Output layer: nodes, the activation function is .

8. The aircraft trajectory prediction method based on the deep Koopman operator according to claim 7, characterized in that: The structure of the decoder network is: Input layer: nodes, corresponding to the Koopman eigenvector; Hidden layer 1: 64 nodes, activation function is ; Hidden layer 2: 128 nodes, activation function is ; Output layer: nodes, linear activation function.

9. The aircraft trajectory prediction method based on the deep Koopman operator according to claim 8, characterized in that: In steps 2-4, when training the total loss function, the initial learning rate is set to 0.001, decays to 0.8 times the original rate every 50 epochs, and the batch size is set to 64.

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