A physics-informed and data-driven framework for robust trajectory estimation of constrained hypersonic gliding vehicles

Hypersonic gliding vehicles (HGVs), as noncooperative targets, pose significant challenges for accurate trajectory estimation due to their high maneuverability and non-ballistic flight characteristics, especially in complex multi-constrained environments such as no-fly zones. To address these challenges, this paper proposes a physics-informed and data-driven framework for robust trajectory estimation of HGVs. Specifically, we first derive the complete motion equations for the constrained HGV flight and formulate the trajectory estimation problem as identifying control inputs within a nonlinear system. To capture a diverse range of HGV maneuver patterns under complex constraints, we propose a scalable trajectory generation method based on multi-objective optimization and construct a corresponding dataset. Subsequently, to enhance robustness to measurement noise and recognition errors, we design a customized Transformer network architecture equipped with Rotary Position Embedding to effectively extract latent feature parameters from limited observational data. Furthermore, we propose two distinct feature parameter recognition methods, classification-based and regression-based, tailored for scenarios prioritizing estimation precision and computational efficiency, respectively. The final estimates of the HGV state are obtained by integrating the recognized feature parameters into the physics-based motion model, followed by filtering. Extensive simulation experiments under unseen scenarios demonstrate that our method achieves high recognition accuracy, minimal estimation errors, and rapid dynamic response. Together with the robustness tests in non-ideal environments, these results collectively highlight its efficacy and generalization capability for constrained trajectory estimation challenges.