Probabilistic trajectory prediction for reentry glider vehicles using koopman operators under uncertainty

Trajectory prediction for reentry glide vehicles (RGVs) under uncertainty is crucial for enhancing defensive capabilities. This paper proposes a probabilistic trajectory prediction framework based on Koopman theory, integrating higher order multi-resolution dynamic mode decomposition (HMDMD) with system dynamics to extract Koopman operators governing vehicle states and maneuver characteristics. The integration of HMDMD with Gaussian mixture model (GMM)-based uncertainty modeling enables robust prediction of maneuver parameters under complex uncertainties. A Halton sampling scheme, integrated with importance sampling, is employed to approximate the initial uncertainty distribution efficiently. Rather than explicitly evolving probability densities, the proposed method leverages the duality between the Frobenius-Perron and Koopman operators, utilizing the Koopman pull-back mechanism to propagate the expectation of observables. Simulation results show that the proposed method achieves high-accuracy RGV trajectory prediction, with prediction errors ranging from 10 km to 20 km over a 200-second prediction horizon. Sensitivity analyses confirm the algorithm’s robustness and provide practical guidelines for optimal parameter selection. This approach combines efficient expectation propagation, non-Gaussian uncertainty modeling, and robust sensitivity analysis, offering a significant advancement in RGV trajectory prediction.