Method and device for predicting flexible time-domain long-time trajectory of hypersonic gliding aircraft

Abstract

The invention belongs to the technical field of aerospace, and discloses a flexible time domain long-time trajectory prediction method and device for a hypersonic gliding aircraft. The method for predicting the flexible time domain long-time trajectory of the hypersonic-velocity gliding aircraft comprises the following steps: acquiring a known trajectory of the hypersonic-velocity gliding aircraft, performing spatial normalization preprocessing, performing trajectory prediction by using a trained pseudo-spectrum-TCN prediction model, performing reverse normalization on a trajectory prediction feature vector sequence, and obtaining a predicted trajectory of the hypersonic-velocity gliding aircraft. Obtaining a feature vector sequence of an original state magnitude; and according to the set predicted trajectory length, fitting the feature vector sequence of the original state magnitude by using a Gauss-Legendre polynomial to obtain a trajectory after space normalization, and performing reduction in the space direction to obtain a final trajectory prediction result. According to the method, the contradiction between the calculation efficiency and the flexible interval long-time prediction precision is effectively solved, and the dual requirements for the random starting moment and the variable prediction duration can be met.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace technology, and in particular relates to a method and device for predicting the flexible time-domain long-term trajectory of a hypersonic gliding aircraft. Background Art

[0002] The complex trajectory characteristics of hypersonic gliding vehicles (HGVs) lead to challenges in existing prediction methods, such as difficulty in capturing long-term dependencies, high sensitivity to prediction errors, and high computational complexity, making it difficult to smoothly carry out terminal guidance handover and interception prediction during the interception process.

[0003] At present, the mainstream prediction methods mainly include two types of methods: physical model-based and data-driven. Among them, most of the existing data-driven methods are based on the training model network of the original trajectory data length. In order to maintain the time series modeling capability, a complex multi-layer network structure and a large number of neuron nodes are usually required, which not only increases the computational burden, but also leads to serious error accumulation and convergence difficulties in long-term prediction, which seriously affects the real-time performance in engineering applications and the deployment problem of resource-constrained platforms. Due to this limitation, the existing technical solutions need to make the following compromises: First, for the prediction of a fixed arc segment, although a more streamlined network structure can be used, it requires the online predicted arc segment to strictly match the arc segment applied during training, which is difficult to guarantee in actual applications; second, for the prediction of equal-length sliding windows but short predicted arc segments, this method requires the network to learn the arc segments of each window, so it is necessary to build a complex network model and face the dilemma of selecting the sliding window interval size.

[0004] In practical engineering applications, in order to improve the success rate of interception missions, it is necessary to be able to quickly and easily predict the long-term trajectory of HGVs at any time. However, the above-mentioned existing technical solutions are difficult to balance the real-time calculation performance and the long-term prediction accuracy of flexible intervals. Summary of the Invention

[0005] The present invention aims to provide a method and apparatus for flexible, time-domain long-term trajectory prediction for hypersonic glide vehicles to address one or more of the aforementioned technical problems. The technical solution disclosed in this invention, specifically a flexible, time-domain long-term trajectory prediction scheme for hypersonic glide vehicles based on a pseudospectral-temporal convolutional network (TCN), utilizes only a lightweight network to achieve high-precision long-term prediction for any arc segment. This effectively resolves the conflict between computational efficiency and long-term prediction accuracy within flexible intervals in existing solutions, meeting the dual requirements of random start times and variable prediction durations.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions: In a first aspect, the present invention provides a method for predicting a long-term trajectory of a hypersonic glide vehicle in a flexible time domain, comprising the following steps: Acquire a known trajectory of a hypersonic glide vehicle and perform spatial normalization preprocessing to obtain a spatially normalized known trajectory; Based on the spatially normalized known trajectory, the trained pseudo-spectral-TCN prediction model is used to predict the trajectory in the future time period and obtain the trajectory prediction feature vector sequence; The trajectory prediction feature vector sequence is denormalized to obtain the feature vector sequence of the original state magnitude. According to the set predicted trajectory length, the Gauss-Legendre polynomial is used to fit the feature vector sequence of the original state magnitude to obtain the spatially normalized trajectory. The fitted trajectory is then restored in the spatial direction to obtain the final trajectory prediction result.

[0007] A further improvement of the technical solution of the present invention is that the pseudo-spectrum-TCN prediction model includes: a pseudo-spectral feature point extraction unit, configured to input a trajectory, extract a feature vector based on a pseudo-spectral method, and output a pseudo-spectral feature point; A feature normalization processing unit, configured to input pseudo-spectral feature points, perform normalization processing, and output normalized pseudo-spectral feature points; The temporal convolutional network (TCN) unit is used to input standardized pseudo-spectral feature points and perform trajectory prediction, and output a trajectory prediction feature vector sequence.

[0008] A further improvement of the technical solution of the present invention is that the training step of the pseudo-spectrum-TCN prediction model includes: Obtain a trajectory dataset and select a nominal trajectory as a reference. Rotate and translate other trajectories according to the nominal trajectory direction to obtain a spatially normalized trajectory dataset. Based on the pre-set known trajectory length, a reasonable sampling interval for the starting point of the predicted trajectory is determined in the trajectories of the spatially normalized trajectory dataset. In each batch of each training epoch, a starting point is randomly selected within the reasonable sampling interval, and then the known trajectory and predicted trajectory pairs are divided to construct a dynamic training sample sequence. Based on a dynamic training sample sequence, the known and predicted trajectories are input into the pseudo-spectral-TCN prediction model. Pseudo-spectral feature points are extracted by the pseudo-spectral feature point extraction unit, and the obtained pseudo-spectral feature points are processed by the feature normalization unit to obtain standardized pseudo-spectral feature points. Based on the standardized pseudo-spectral feature points, known and predicted sequences are constructed for learning the temporal convolutional network (TCN) unit, and the constructed known and predicted feature vector sequences are output. Based on the constructed known and predicted feature vector sequences, the temporal convolutional network (TCN) unit is supervised trained and its parameters are updated to achieve the preset convergence conditions and obtain a trained pseudo-spectral-TCN prediction model.

[0009] A further improvement of the technical solution of the present invention lies in that, in the step of obtaining pseudo-spectral feature points through the pseudo-spectral feature point extraction unit, after the known trajectory and the predicted trajectory are input into the pseudo-spectral feature point extraction unit, the time interval is first subjected to pseudo-spectral time domain transformation, and a set of sparse and representative key feature moments is determined by solving the roots of the Legendre polynomial; then, the least squares optimization method is used to obtain the state values ​​of the corresponding feature points, and generate pseudo-spectral feature points reflecting the geometric and physical characteristics of the original trajectory.

[0010] A further improvement of the technical solution of the present invention lies in that, in the step of performing supervised training and parameter updating on the temporal convolutional network (TCN) unit based on the constructed known and predicted feature vector sequences to achieve preset convergence conditions and obtain a trained pseudo-spectral-TCN prediction model, the optimization process uses the Adam algorithm in combination with the MSE loss function, and the training termination condition is set to automatically save the optimal model when the loss of the validation set decreases by less than 0.1% for 10 consecutive epochs.

[0011] A further improvement of the technical solution of the present invention is that in the step of obtaining the known trajectory of the hypersonic glide vehicle and performing spatial normalization preprocessing to obtain the spatially normalized known trajectory, When performing spatial normalization preprocessing, the nominal trajectory direction is rotated and translated in space according to the training of the pseudo-spectral-TCN prediction model.

[0012] In a second aspect, the present invention provides a flexible time-domain long-term trajectory prediction system for a hypersonic glide vehicle, comprising: A data preprocessing module is used to obtain the known trajectory of the hypersonic glide vehicle and perform spatial normalization preprocessing to obtain the spatially normalized known trajectory; The prediction module is used to predict the trajectory of the future time period based on the spatially normalized known trajectory and use the trained pseudo-spectral-TCN prediction model to obtain the trajectory prediction feature vector sequence; The data post-processing module is used to denormalize the trajectory prediction feature vector sequence to obtain the feature vector sequence of the original state magnitude. According to the set predicted trajectory length, the feature vector sequence of the original state magnitude is fitted using Gauss-Legendre polynomials to obtain a spatially normalized trajectory. The fitted trajectory is then restored in the spatial direction to obtain the final trajectory prediction result.

[0013] In a third aspect of the present invention, an electronic device is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the method for predicting long-term flexible time-domain trajectories of a hypersonic glide vehicle as described in any one of the first aspects of the present invention is implemented.

[0014] In a fourth aspect, the present invention provides a non-transitory computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the method for predicting the flexible time-domain long-term trajectory of a hypersonic glide vehicle as described in any one of the first aspects of the present invention is implemented.

[0015] In a fifth aspect, the present invention provides a computer program product, which includes a computer program or instructions. When the computer program or instructions are executed by a communication device, the method for predicting the flexible time-domain long-term trajectory of a hypersonic glide vehicle described in any one of the first aspects of the present invention is executed.

[0016] Compared with the prior art, the present invention has the following beneficial effects: The present invention specifically discloses a flexible time-domain long-term trajectory prediction method for hypersonic glide vehicles. This method solves the technical challenge of implementing variable time-domain input prediction and arbitrary-length prediction using a single network model, thereby enhancing the flexibility of the prediction system. Specifically, the present invention combines the feature extraction advantages of the pseudospectral method with the time series prediction capabilities of the TCN model. The pseudospectral method's segmented feature extraction simplifies algorithm design, while the TCN model can efficiently capture the temporal dependencies in trajectory data, improving prediction accuracy and efficiency. During the prediction process, the trajectory data is spatially normalized and denormalized. Spatial normalization makes different trajectory data comparable, facilitating model processing; denormalization restores the prediction results to the magnitude of the original data, ensuring the physical significance and practicality of the prediction results. The predicted trajectory feature vector sequence is fitted using Gauss-Legendre polynomials to obtain a spatially normalized trajectory set, which is then restored in the spatial direction. This fitting method can more accurately describe the trajectory shape and changing trends, improving the accuracy and smoothness of the predicted trajectory.

[0017] In the preferred technical solution of the present invention, the feature extraction advantages of the pseudo-spectral method are innovatively combined with the time series modeling capabilities of the temporal convolutional network (TCN) to construct a pseudo-spectral-TCN prediction model. This design significantly reduces the number of parameters in network model construction, improves the network's ability to capture long-term dependencies and calculation speed, and effectively suppresses the cumulative impact of prediction errors by reducing redundant calculations.

[0018] The preferred technical solution of the present invention proposes a flexible interval intelligent trajectory prediction training scheme. By dynamically adjusting the network input time domain range and output prediction length during training, the model can autonomously adapt to real-time trajectory changes. By designing a flexible interval trajectory prediction training mechanism, the model can achieve trajectory prediction for any starting point and any duration, flexibly responding to the possible changing tasks of hypersonic targets, which is of great significance to the interception decision-making and guidance control of hypersonic targets. Further explaining, the present invention innovatively combines the feature extraction advantages of pseudo-spectral methods with the time series modeling capabilities of TCN networks. By intelligently screening key feature points instead of traditional full data processing, this method not only enhances the network's ability to capture long-term dependencies, but also reduces network design complexity by reducing redundant calculations and effectively suppresses the cumulative impact of prediction errors, thereby improving prediction accuracy. Compared with existing methods (explanatory, traditional data-driven methods directly process raw trajectory data, relying on complex deep network structures and a large number of neuron nodes to maintain time series modeling capabilities, which not only brings high computational costs but also leads to serious error accumulation and convergence difficulties in long-term predictions), the technical solution of the present invention can train lightweight models to achieve high-precision long-term trajectory predictions, which not only improves the prediction speed but is also more conducive to engineering deployment on resource-constrained platforms such as embedded systems, and has important engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below; obviously, the drawings described below are some embodiments of the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0020] Figure 1 1 is a flow chart of a method for predicting long-term trajectory of a hypersonic glide vehicle in a flexible time domain according to an embodiment of the present invention; Figure 2 1 is a flow chart of training and testing in a method for predicting long-term trajectory in a flexible time domain for a hypersonic glide vehicle according to an embodiment of the present invention; Figure 3 Schematic diagram of the network structure of the pseudo-spectral-TCN prediction model in an embodiment of the present invention; Figure 4 1 is a schematic diagram of the position prediction results of a 900s jump glide trajectory using different methods in an embodiment of the present invention; Figure 5 Schematic diagram of position prediction results of 900s jump glide + C-type maneuver trajectory using different methods in an embodiment of the present invention; Figure 61 is a schematic diagram of the speed prediction results of a 900s jump glide trajectory using different methods in an embodiment of the present invention; Figure 7 1 is a schematic diagram of the speed prediction results of different methods for a 900s jump glide + C-type maneuver trajectory in an embodiment of the present invention; Figure 8 1 is a schematic diagram of a curve showing the change of the maximum absolute error of the jump-gliding trajectory prediction using different methods over time in an embodiment of the present invention; Figure 9 This is a diagram showing the curve of the average maximum error of the jump-glide trajectory prediction versus the prediction starting point; Figure 10 It is a schematic diagram of a flexible time-domain long-term trajectory prediction system for a hypersonic glide vehicle in an embodiment of the present invention. DETAILED DESCRIPTION

[0021] In order to make the purpose, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention; it is obvious that the described embodiments and technical solutions are only part of the embodiments of the present invention, not all of the embodiments.

[0022] All other embodiments obtained by persons of ordinary skill in the art based on the technical solutions disclosed in the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to these processes, methods, products, or apparatuses.

[0023] See also Figure 1 The embodiment of the present invention provides a method for predicting a long-term trajectory of a hypersonic glide vehicle in a flexible time domain, comprising the following steps: Step 1: Acquire a known trajectory of the hypersonic glide vehicle and perform spatial normalization preprocessing to obtain a spatially normalized known trajectory. In a specific exemplary technical solution, in the step of acquiring the known trajectory of the hypersonic glide vehicle and performing spatial normalization preprocessing, during the spatial normalization preprocessing, the nominal trajectory direction during training of the pseudo-spectral-TCN prediction model is rotated and translated in space. Step 2: Based on the spatially normalized known trajectory obtained in step 1, the trained pseudo-spectral-TCN prediction model is used to predict the trajectory in the future time period to obtain a trajectory prediction feature vector sequence; Step 3: Denormalize the trajectory prediction feature vector sequence obtained in step 2 to obtain the feature vector sequence of the original state magnitude. According to the set predicted trajectory length, use the Gauss-Legendre polynomial to fit the feature vector sequence of the original state magnitude to obtain the spatially normalized trajectory. After restoration in the spatial direction, the final trajectory prediction result is obtained.

[0024] In the technical solution of the above embodiment of the present invention, the trained pseudo-spectrum-TCN prediction model includes: a pseudo-spectral feature point extraction unit, configured to input a trajectory, extract feature vectors based on a pseudo-spectral method, and output pseudo-spectral feature points; a feature normalization processing unit, configured to input the obtained pseudo-spectrum feature points, perform normalization processing on them, and output normalized pseudo-spectrum feature points; The temporal convolutional network unit is used to input standardized pseudo-spectral feature points and output a trajectory prediction feature vector sequence.

[0025] In the technical solution of the above embodiment of the present invention, the training steps of the trained pseudo-spectrum-TCN prediction model include: Step 1: Obtain a trajectory dataset and select a nominal trajectory as a reference. Rotate and translate the other trajectories according to its orientation to achieve spatial normalization of the trajectories. Explanation: This step eliminates the randomness of the trajectories in spatial orientation, thereby reducing the network's sensitivity to trajectory pose differences, improving model generalization and simplifying the learning task.

[0026] Step 2: Based on the input known trajectory length, determine a reasonable sampling interval for the predicted trajectory starting point within the spatially normalized trajectory. Within each batch of each training epoch, a starting point is randomly selected within this interval, which is then used to divide the known trajectory into pairs of predicted trajectories, constructing a dynamic training sample sequence. This strategy forms the core mechanism of the flexible interval trajectory prediction training method proposed in this paper, improving the model's adaptability to different prediction locations and lengths, and enhancing the flexibility of temporal modeling.

[0027] Step 3: Input the known trajectory and predicted trajectory into the pseudo-spectral feature point extraction unit in the pseudo-spectral-TCN prediction model, perform pseudo-spectral time domain transformation on their time intervals, and determine a set of sparse and representative key feature moments by solving the roots of the Legendre polynomial. In particular, considering the problem that the state values ​​of the feature points corresponding to some feature moments are missing due to the discretization of the actual observation data, the least squares optimization method is used to obtain the state values ​​of the corresponding feature points and generate pseudo-spectral feature points that reflect the geometric and physical characteristics of the original trajectory. Explanatoryally, this process reduces the computational complexity of model training and improves the model's ability to model long-term dependencies by replacing the full trajectory input in traditional training with a sparse but high-information pseudo-spectral feature sequence. At the same time, it effectively alleviates the problems of error accumulation and gradient degradation in long sequence modeling.

[0028] Step 4: The resulting pseudo-spectral feature vector sequence is normalized and reorganized through the feature normalization unit and the reconstructed data unit in the pseudo-spectral-TCN network to generate a known feature vector sequence (input) and a predicted feature vector sequence (label) for TCN learning. Specifically, the reconstructed data unit is used to input the standardized pseudo-spectral feature points and construct the known and predicted sequences for TCN learning, outputting the constructed known and predicted feature vector sequences. Step 5: Input the known feature vector sequence and the predicted feature sequence into the TCN unit of the pseudo-spectral TCN prediction model. Training is performed using the Adam optimization algorithm and the MSE loss function. The optimal prediction model for the known and predicted feature sequences is saved when the validation set loss decreases by less than 0.1% for 10 consecutive epochs. To further explain, the TCN unit inputs the constructed known and predicted feature vector sequences, learns the mapping between them, and outputs the prediction model for the known and predicted feature vector sequences.

[0029] Existing HGV trajectory prediction methods have significant limitations (explained by the fact that, in terms of prediction timeliness, existing prediction models are only applicable to prediction tasks within a fixed time window; in terms of prediction flexibility, prediction methods that support random starting points are limited by the constraints of equal-length prediction and short-term prediction). This technological status quo results in existing methods being unable to meet the dual requirements of random starting times and variable prediction durations. In view of the above technical issues, an embodiment of the present invention specifically discloses a flexible time-domain long-term trajectory prediction method for hypersonic glide vehicles. It proposes a flexible interval intelligent trajectory prediction training scheme. By dynamically adjusting the network input time-domain range and output prediction length during training, the model can autonomously adapt to real-time trajectory changes, solving the technical difficulty of using a single network model to achieve variable time-domain input prediction and arbitrary length prediction, thereby improving the flexibility of the prediction system.

[0030] See also Figures 1 to 3In a specific embodiment of the present invention, a flexible time-domain long-term trajectory prediction method for a hypersonic glide vehicle based on pseudo-spectral-TCN is proposed, which is divided into two parts: offline model training and online prediction.

[0031] In the embodiment of the present invention, the specific process of offline model training is as follows: The HGV trajectory expression constructed in the embodiment of the present invention is: (1) Where, is the distance between the aircraft and the center of the earth, t For time; Represents the flight speed; represents the track angle; 、 are geocentric longitude and latitude respectively; represents the heading angle; is the mass of the aircraft; 、 are aerodynamic drag and lift respectively; is the Earth's gravitational constant; is the angular velocity of the Earth's rotation; represents the roll angle; (2) (3) Where, is the atmospheric density; is the characteristic area of ​​the aircraft; 、 is the flight Mach number , angle of attack , representing the drag coefficient and lift coefficient respectively.

[0032] In an embodiment of the present invention, a typical C-type maneuver is achieved through trajectory planning with preset waypoints in the lateral plane. At the same time, based on dynamic control under an unbalanced force state, an acceleration perturbation model is established by introducing control variables, so that the aircraft produces motion characteristics that deviate from the balanced gliding trajectory.

[0033] Based on this, the kinematic equation of the jump glide trajectory is derived from formula (1): (4) The JG and JGLCM trajectory datasets were generated based on the above modeling equations. During the trajectory generation process, the overall parameters of the aircraft were kept constant, the jump mode was configured according to the maximum lift-to-drag ratio, and the initial position (longitude, latitude) and heading angle were uniformly and randomly selected on the Earth's surface. The range was [4000km, 5000km], and the jump starting altitude range was [30km, 50km]. Finally, the generated trajectory was converted to the Earth-centered Earth-fixed coordinate system to obtain the first Trajectory description of the position vector and velocity components of the trajectory , where 、 、 Indicates the position coordinates of the aircraft in the x, y, and z directions; 、 、 Indicates the velocity coordinates of the aircraft in the x, y, and z directions.

[0034] In the specific exemplary technical solution, a dataset of 5000 samples of jump glide mode (JG) and 5000 samples of jump glide mode with lateral C-type maneuver (JGLCM) is used to form the dataset. The total number of samples in the dataset is , divided into training set, validation set and test set in the ratio of 8:1:1. The time length of each trajectory is , the state quantity is a 6-dimensional vector, which represents the three-dimensional position and velocity components of the HGV trajectory in the Earth-centered Earth-fixed coordinate system. Each trajectory is recorded as , where is the total number of samples, The set of natural numbers.

[0035] In the embodiment of the present invention, after the JG and JGLCM trajectory datasets are generated according to the modeling equation, model training is performed based on them, including: in order to reduce the complexity of network recognition, rotation and translation are required to eliminate the randomness of the original trajectory in the direction; in the specific exemplary technical solution, the number of training set samples is , where we select the reference trajectory , calculate the center coordinates of the trajectory to be rotated and , and get the covariance matrix: (5) And perform the following singular value decomposition: (6) in, and is an orthogonal matrix, is a diagonal matrix; According to the following formula, the The rotation matrix of the trajectory and translation vectors : (7) (8) Finally, the spatial normalized trajectory is obtained: (9) and Same, it's about time The function consists of a 6-dimensional state vector at each moment. For the convenience of subsequent processing, the converted state vector is The state vector at time ( ), where 、 、 express The position coordinates of the aircraft in the x, y, and z directions after time-space normalization; 、 、 express The velocity coordinates of the aircraft in the x, y, and z directions after time and space normalization.

[0036] In order to adapt the model to the changes in the prediction interval, the random sampling method is used to randomly select trajectory segments to train the model parameters. To ensure the existence of label data, it is necessary to determine the length of the input data. , in this case , so the random starting point Then we get the known trajectory tensor and the predicted trajectory tensor for: (10) (11) Where, For ( ) The trajectory state tensor of the aircraft at the moment.

[0037] The training method chooses small batch training, so , is the mini-batch sample size, then the batch in each epoch satisfy , where For the Batch No. The track in The spatially normalized state at time t.

[0038] In the embodiment of the present invention, the steps of extracting feature vectors based on pseudo-spectral method include: time domain transformation, characteristic moment solution, least squares optimization, and obtaining pseudo-spectral feature vector sequence. The specific implementation process is as follows: Figure 3 In order to simplify the algorithm process, before extracting the feature points, the predicted trajectory is calculated according to the known trajectory length. , divided into paragraph, therefore, (12) Where, is the original tag data length, and then the following formula is used to convert and The time domain of each segment Shoot : (13) Assume that each trajectory is represented by The feature vector represents (in this case ), its characteristic time point Select the pseudospectral method Order Legendre-Gauss point, that is, solving the roots of the following Legendre polynomial: (14) get characteristic time points , and add For the feature points; Then according to the formula: (15) Will The feature points are mapped to the original time interval, and their corresponding state values are discrete feature points that can be used to characterize the geometric and physical properties of the original trajectory.

[0039] Considering the problem that the state values ​​of feature points corresponding to some feature moments are missing due to the discretization of actual observation data, the embodiment of the present invention adopts a 15th-order polynomial to fit the extracted feature points by the least squares fitting method. By optimizing the feature points and minimizing the error between the fitting curve and the original trajectory, a pseudo-spectral feature sequence is obtained for each segment that can more accurately characterize the geometry and physical characteristics of the trajectory. . The technical solution of the embodiment of the present invention significantly reduces the computational complexity through feature extraction, and enhances the ability to capture long-term features while improving the model convergence speed. Its core advantages are: effectively suppressing the error accumulation effect through key information reinforcement; achieving a significant improvement in computational efficiency while maintaining prediction accuracy; and eliminating the need for subsequent design of complex network structures to improve prediction accuracy. Therefore, the trained model can achieve fast calculations when used for online predictions, and is conducive to engineering deployment on resource-constrained platforms such as embedded systems.

[0040] In this embodiment of the present invention, the feature normalization step includes: the high speed and strong maneuverability of HGV targets result in significant dimensional differences in multi-dimensional feature data. Due to the magnitude difference, the original data will cause large numerical features to dominate the training, affecting model convergence and prediction accuracy. Therefore, the following formula is used to normalize the input features: (16) in: (17) (18) (19) (20) Where, and Respectively Moment The track in Position and velocity state quantities on coordinate components; and Respectively represent all trajectories in the training set The maximum values ​​of position and velocity on the coordinate components; and Respectively represent all trajectories in the training set Position and velocity minimums on coordinate components; and are the maximum and minimum state vectors in feature normalization, Before feature normalization The state vector of the trajectory at time t, After feature normalization The state vector of the trajectory at time instant.

[0041] In the embodiment of the present invention, the step of extracting TCN model training data includes: extracting original trajectory segments according to the pseudo-spectral feature extraction method and The corresponding pseudo-spectral characteristic vector sequence and And use feature normalization to get the corresponding feature sequence: (twenty one) (twenty two) in, , In order to give full play to the advantages of parallel computing, such as Figure 3 As shown, construct the input known feature vector sequence for TCN learning: (twenty three) The predicted feature vector sequence is .

[0042] In the embodiment of the present invention, the step of obtaining the parameter model file includes: using TCN to learn the mapping relationship between the known feature vector sequence and the predicted feature sequence in order to obtain the optimal model parameters, and outputting the prediction model of the known and predicted feature sequences. Figure 3 As shown in Figure 1, its core is a set of two-layer dilated causal convolutional structures, supplemented by residual connections to achieve effective information transmission and stable gradient updates. Specifically: (1) The first dilated causal convolution layer (Dilated Causal Conv): The input is a known feature vector sequence, and the dilated causal convolution operation is performed to output a three-dimensional tensor feature. This layer expands the receptive field by setting the dilation coefficient, capturing dynamic evolution information over a longer time span while ensuring temporal causality.

[0043] (2) Batch Normalization Layer (Batch Norm): Receives the three-dimensional tensor features output by the convolutional layer, receives the three-dimensional tensor output by the convolutional layer, performs normalization along the channel dimension, and introduces learnable scaling and offset parameters to improve training stability and convergence speed. The output is the normalized tensor of each channel feature.

[0044] (3) Activation function layer (ReLU): The input is the three-dimensional tensor output by the batch normalization layer. The ReLU function is applied element by element to set negative values ​​to zero, introduce nonlinear mapping, enhance feature expression capabilities, and output the processed tensor.

[0045] (4) Dropout layer: The input is the three-dimensional tensor output by the ReLU activation layer. During the training phase, some channel features in the tensor are randomly deactivated with a set dropout probability to obtain an output tensor with unchanged dimension but partially masked features. This is intended to prevent the model from overfitting and enhance its generalization ability.

[0046] (5) The second layer of dilated causal convolution layer and its subsequent batch normalization layer, activation function layer, and random dropout layer are basically the same as the first layer. The input is the output of the first layer of Dropout layer, and the output is feature data that is consistent with the dimension of the predicted feature vector sequence. This setting is mainly used to further explore the deep feature patterns in time series.

[0047] (6) 1D Convolutional Layer (1*1 Conv): The input is a sequence of known feature vectors. The module maps the channel dimension of the input tensor through a 1×1 convolution operation, converting the number of input channels to the same number of channels as the main branch output. The output is a channel-adjusted tensor with the same shape as the input, but with a transformed number of channels. The function of this module is to ensure that the channel dimensions of the two paths in the residual connection are consistent to meet the requirements of the subsequent element-by-element addition operation.

[0048] (7) Weighting module: This module receives two input tensors: the output tensor of the main branch after two layers of dilated causal convolution and related processing, and the input tensor of the residual path after 1×1 convolution mapping. The two have the same shape. The module performs an element-by-element addition operation on the two input tensors to obtain the final output features of this two-layer residual structure. The function of this module is to implement residual connection and enhance the training stability and feature expression ability of the model by fusing the information of the main branch and the residual branch.

[0049] The simulation deployment in this example uses a network architecture consisting of three TCN hidden layers, each containing 20 neurons, achieving efficient modeling. Compared to traditional data-driven approaches, this network is lightweight and scales well. In this specific exemplary technical solution, model training uses the optimized parameter configuration shown in Table 1.

[0050] Table 1. Hyperparameter settings

[0051] The optimization process uses the Adam algorithm combined with the MSE loss function. The training termination condition is set to automatically save the optimal model when the validation set loss decreases by less than 0.1% for 10 consecutive epochs. The trajectory feature prediction model file is generated and packaged in .pt format to ensure integrity and reliability during deployment.

[0052] In the embodiment of the present invention, the specific process of online prediction is as follows: Step 1: Process the acquired observation data, including: intercepting known trajectories Seconds data, calculate the rotation matrix of the known trajectory and translation vectors , and the trajectory after spatial normalization is obtained by formula (9) , is the number of trajectories that need to be predicted; Step 2: Extract the feature vector sequence of the known trajectory and perform numerical normalization, including: using the pseudo-spectral feature point extraction unit of the pseudo-spectral-TCN prediction model and the feature normalization processing unit for processing. The specific principle is: According to formulas (13), (14), and (15), calculate characteristic time points, and then obtain the feature vector set based on least squares optimization , and normalize it numerically according to (16) to obtain ,in , .

[0053] Step 3: Prediction of trajectory feature vector sequence, including: setting the trajectory length to be predicted , load the saved trajectory feature prediction model into the designed prediction network, input , calculate the number of feature vectors that need to be predicted according to the following formula: (27); enter , execute the TCN unit in the pseudo-spectral-TCN prediction model to obtain the predicted trajectory feature vector sequence, where It is worth noting that since the feature extraction is performed segment by segment using the pseudo-spectral method, in order to simplify the design of the algorithm, the predicted trajectory length is generally set to an integer multiple of the input trajectory length.

[0054] Step 4: Denormalization of features, including: Denormalizing the predicted feature vector sequence according to the following formula (28) to obtain the feature vector sequence of the original state magnitude ,in ; (28) Step 5: Get the predicted trajectory, including: the predicted trajectory length according to the settings , using Gauss-Legendre polynomials to predict the trajectory feature vector sequence Fitting is performed to obtain a set of spatially normalized trajectories ,in Finally, each trajectory is restored in the spatial direction according to the following formula: (29) The left side of the equation This is the desired final predicted trajectory result.

[0055] Among the specific exemplary technical solutions of the present invention, 1000 (i.e. ) Trajectories outside the training set and validation set are used as the test set for the online prediction step. The test set consists of 500 JG pattern samples and 500 JGLCM pattern samples. To demonstrate the superiority of the method of the present invention, the following system comparison experiments are designed: 1) A TCN benchmark model for equal interval feature extraction (TCN-EIFE) is constructed, and 10 feature points are extracted from a 100-second trajectory using uniform sampling; 2) The traditional TCN method for processing raw trajectory data is used as a reference benchmark. In order to objectively evaluate the prediction performance of the model, the mean absolute error is used. , root mean square error and the maximum mean error Three indicators quantify the trajectory prediction error, and the calculation formula of each indicator is as follows: ; ; ; in, For the Samples in The prediction vector at time t, The corresponding actual vector is, The total number of test samples, Length of the forecast period, and are the predicted start and end times, express norm.

[0056] The simulation results are as follows: Figure 4 、 Figure 5 、 Figure 6 、 Figure 7 The 900-second prediction results of the position and velocity of jumping and gliding trajectories using three methods are presented. It can be seen that the proposed method can more accurately capture the periodic oscillation characteristics of trajectories with jumping maneuvers. Figure 8 The maximum absolute error (RMSE) for predicting 900-second trajectories based on 100-second observations on the JG and JGLCM test sets varies over time. It can be seen that the error increases with the prediction duration. Table 2 compares the RMS error (RMSE) of 900-second trajectory predictions using different methods. It can be seen that this model achieves at least six times better position accuracy and six times better velocity accuracy than the other two methods. Figure 9 The model's maximum error average changes as the prediction starting point shifts backward. This indicates that prediction accuracy improves with a later starting point. It's particularly noteworthy that while this method significantly outperforms the maneuvering JGLCM trajectory for JG trajectories, the predictions still effectively reflect the overall maneuvering trends of the HGV, providing critical support for interception missions.

[0057] Table 2. RMSE of different methods for 900-second jump-glide trajectory prediction

[0058] The following are device embodiments of the present invention, which can be used to perform the method embodiments of the present invention. For details not disclosed in the device embodiments, please refer to the method embodiments of the present invention.

[0059] See also Figure 10 In an embodiment of the present invention, a flexible time-domain long-term trajectory prediction system for a hypersonic glide vehicle is provided, comprising: A data preprocessing module is used to obtain the known trajectory of the hypersonic glide vehicle and perform spatial normalization preprocessing to obtain the spatially normalized known trajectory; The prediction module is used to predict the trajectory of the future time period based on the spatially normalized known trajectory and use the trained pseudo-spectral-TCN prediction model to obtain the trajectory prediction feature vector sequence; The data post-processing module is used to denormalize the trajectory prediction feature vector sequence to obtain the feature vector sequence of the original state magnitude. According to the set predicted trajectory length, the feature vector sequence of the original state magnitude is fitted using Gauss-Legendre polynomials to obtain a spatially normalized trajectory. The fitted trajectory is then restored in the spatial direction to obtain the final trajectory prediction result.

[0060] In one embodiment of the present invention, a computer device is provided, comprising a processor and a memory. The memory is configured to store a computer program, the computer program including program instructions, and the processor is configured to execute the program instructions stored in the computer storage medium. The processor may be a central processing unit (CPU), or may also be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It serves as the computing and control core of a terminal and is adapted to implement one or more instructions, specifically, to load and execute one or more instructions from a computer storage medium to implement a corresponding method flow or function. The processor described in this embodiment of the present invention can be used to perform operations in a method for predicting flexible time-domain long-term trajectories of a hypersonic glide vehicle.

[0061] In one embodiment of the present invention, a storage medium is provided, specifically a computer-readable storage medium (Memory). The computer-readable storage medium is a memory device in a computer device, used to store programs and data. It is understood that the computer-readable storage medium herein may include both built-in storage media in the computer device and, of course, extended storage media supported by the computer device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for being loaded and executed by a processor. These instructions may be one or more computer programs (including program code). It should be noted that the computer-readable storage medium herein may be a high-speed random access memory (RAM) or a non-volatile memory, such as at least one disk drive. The processor may load and execute the one or more instructions stored in the computer-readable storage medium to implement the corresponding steps of the method for flexible time-domain long-term trajectory prediction of a hypersonic glide vehicle in the above-described embodiment.

[0062] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, optical storage, etc.) containing computer-usable program code.

[0063] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0064] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0065] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0066] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the scope of protection of the claims of the present invention.

Claims

1. A method for predicting long-term trajectory of a hypersonic glide vehicle in flexible time domain, characterized in that: The following steps are involved: Acquire a known trajectory of a hypersonic glide vehicle and perform spatial normalization preprocessing to obtain a spatially normalized known trajectory; Based on the spatially normalized known trajectory, the trained pseudo-spectral-TCN prediction model is used to predict the trajectory in the future time period and obtain the trajectory prediction feature vector sequence; The trajectory prediction feature vector sequence is denormalized to obtain the feature vector sequence of the original state magnitude. According to the set predicted trajectory length, the Gauss-Legendre polynomial is used to fit the feature vector sequence of the original state magnitude to obtain the spatially normalized trajectory. The fitted trajectory is then restored in the spatial direction to obtain the final trajectory prediction result.

2. The method for predicting long-term trajectory of a hypersonic glide vehicle in flexible time domain according to claim 1, characterized in that: The pseudo-spectrum-TCN prediction model includes: a pseudo-spectral feature point extraction unit, configured to input a trajectory, extract a feature vector based on a pseudo-spectral method, and output a pseudo-spectral feature point; A feature normalization processing unit, configured to input pseudo-spectral feature points, perform normalization processing, and output normalized pseudo-spectral feature points; The temporal convolutional network (TCN) unit is used to input standardized pseudo-spectral feature points and perform trajectory prediction, and output a trajectory prediction feature vector sequence.

3. The method for predicting long-term trajectory of a hypersonic glide vehicle in flexible time domain according to claim 2, characterized in that: The training steps of the pseudo-spectrum-TCN prediction model include: Obtain a trajectory dataset and select a nominal trajectory as a reference. Rotate and translate other trajectories according to the nominal trajectory direction to obtain a spatially normalized trajectory dataset. Based on the pre-set known trajectory length, a reasonable sampling interval for the starting point of the predicted trajectory is determined in the trajectories of the spatially normalized trajectory dataset. In each batch of each training epoch, a starting point is randomly selected within the reasonable sampling interval, and then the known trajectory and predicted trajectory pairs are divided to construct a dynamic training sample sequence. Based on a dynamic training sample sequence, the known and predicted trajectories are input into the pseudo-spectral-TCN prediction model. Pseudo-spectral feature points are extracted by the pseudo-spectral feature point extraction unit, and the obtained pseudo-spectral feature points are processed by the feature normalization unit to obtain standardized pseudo-spectral feature points. Based on the standardized pseudo-spectral feature points, known and predicted sequences are constructed for learning the temporal convolutional network (TCN) unit, and the constructed known and predicted feature vector sequences are output. Based on the constructed known and predicted feature vector sequences, the temporal convolutional network (TCN) unit is supervised trained and its parameters are updated to achieve the preset convergence conditions and obtain a trained pseudo-spectral-TCN prediction model.

4. The method for predicting long-term trajectory of a hypersonic glide vehicle in flexible time domain according to claim 3, characterized in that: In the step of obtaining pseudo-spectral feature points through the pseudo-spectral feature point extraction unit, after the known trajectory and the predicted trajectory are input into the pseudo-spectral feature point extraction unit, the time interval is first subjected to pseudo-spectral time domain transformation, and a set of sparse and representative key feature moments is determined by solving the roots of the Legendre polynomial; then, the least squares optimization method is used to obtain the state values ​​of the corresponding feature points, and pseudo-spectral feature points reflecting the geometric and physical characteristics of the original trajectory are generated.

5. The method for predicting long-term trajectory of a hypersonic glide vehicle in flexible time domain according to claim 3, characterized in that: In the step of performing supervised training and parameter updating on the temporal convolutional network (TCN) unit based on the constructed known and predicted feature vector sequences to achieve preset convergence conditions and obtain a trained pseudo-spectral-TCN prediction model, the optimization process uses the Adam algorithm in combination with the MSE loss function, and the training termination condition is set to automatically save the optimal model when the loss of the validation set decreases by less than 0.1% for 10 consecutive epochs.

6. The method for predicting long-term trajectory of a hypersonic glide vehicle in flexible time domain according to claim 3, characterized in that: In the step of obtaining the known trajectory of the hypersonic glide vehicle and performing spatial normalization preprocessing to obtain the spatially normalized known trajectory, When performing spatial normalization preprocessing, the nominal trajectory direction is rotated and translated in space according to the training of the pseudo-spectral-TCN prediction model.

7. A flexible time-domain long-term trajectory prediction system for hypersonic gliding vehicles, characterized by: include: A data preprocessing module is used to obtain the known trajectory of the hypersonic glide vehicle and perform spatial normalization preprocessing to obtain the spatially normalized known trajectory; The prediction module is used to predict the trajectory of the future time period based on the spatially normalized known trajectory and use the trained pseudo-spectral-TCN prediction model to obtain the trajectory prediction feature vector sequence; The data post-processing module is used to denormalize the trajectory prediction feature vector sequence to obtain the feature vector sequence of the original state magnitude. According to the set predicted trajectory length, the feature vector sequence of the original state magnitude is fitted using Gauss-Legendre polynomials to obtain a spatially normalized trajectory. The fitted trajectory is then restored in the spatial direction to obtain the final trajectory prediction result.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the method for predicting long-term trajectory of a hypersonic glide vehicle in flexible time domain is implemented according to any one of claims 1 to 6.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for predicting long-term trajectory of a hypersonic glide vehicle in flexible time domain is implemented according to any one of claims 1 to 6.

10. A computer program product, characterized in that The computer program product includes a computer program or instructions. When the computer program or instructions are executed by a communication device, the method for predicting the flexible time-domain long-term trajectory of a hypersonic glide vehicle according to any one of claims 1 to 6 is executed.

Images