Physics-Constrained Relative-State Prediction of Encounter Point and Encounter Time for Penetration Decision Support

In the information-supported penetration scenario, the predicted encounter point and encounter time can provide the future spatial threat position and the time margin for avoidance maneuver, respectively, which are important prior information for dangerous-area judgment, avoidance triggering, and penetration decision making. However, the data-driven prediction method based on absolute coordinates is likely to depend on the fixed training airspace, resulting in insufficient cross-space generalization ability. Meanwhile, the unconstrained prediction space will lead to an excessively large sample size and an unbalanced sample distribution. Aiming at the above problems, this paper proposes a physics-constrained relative-state prediction framework for the rapid prediction of the encounter point and encounter time. Firstly, the relative-state input centered on the maneuvering vehicle is adopted to reduce the dependence of the model on the fixed global coordinate system. Secondly, a concentric double-layer spherical-shell detectable threat domain is constructed to limit the approximately unbounded prediction space to a finite region that satisfies the sensor detection condition and the maneuvering constraint of the maneuvering vehicle. Furthermore, a physical geometric stratified sampling strategy based on relative distance, azimuth angle, and pitch angle is designed, and a sample-weight correction mechanism is combined to improve the balance of sample coverage under different distance layers and incoming directions. Finally, a ResNet-MLP joint regression model is constructed and trained using offline numerical simulation samples, which is used as an online rapid predictor. The simulation results show that, on the stratified training subset, the mean absolute error of the proposed model for encounter time is 0.1775 s, and the three-dimensional Euclidean error of the encounter point is 129.89 m. The tests with spatial position variation and bounded measurement noise further verify the generalization ability and robustness of the model. The proposed method can provide rapid spatial threat information and time-margin information for dynamic penetration decision making and reduce the computational requirement of repeated online numerical propagation.