Feynman-Kac path integral extended Kalman filter with receding-horizon optimization for UAV-ASV landing mission

This study introduces an engineering integration framework with constraint-aware and anomaly-aware estimation capability, Receding Horizon Optimization Feynman-Kac Extended Kalman Filter (RHO-FK-EKF), designed to address the challenges of nonlinear disturbances, sensor anomalies, and malicious interference in high-dynamic inertial navigation environments for unmanned aerial vehicle and autonomous surface vessel (UAV-ASV). By integrating the Extended Kalman Filter, Support Vector Machine anomaly detection, receding-horizon optimization, Lagrange multiplier constraint handling, Bayesian recursive estimation, and Feynman-Kac path integrals, the proposed method achieves high precision and robustness in state estimation. Theoretical analysis establishes local convergence conditions for constrained optimization on differential manifolds, indicating that, under the linear independence constraint qualification (LICQ), system states remain confined to physically admissible manifolds. A stochastic-process-based derivation of the Feynman-Kac measure transformation confirms adaptability to non-Gaussian noise. Experimental evaluations, conducted under simulated shipborne landing scenarios, verify multi-level performance in filtering accuracy, constraint stability, interference rejection, and real-time responsiveness. The validation reported in this study combines numerical simulation, hardware-in-the-loop runs on the actual onboard processors, and engineering-level field tests using a VTOL UAV and an autonomous surface vessel platform. Results show that the proposed method maintains a positioning error within approximately ± 0.2 m, achieving a 60% improvement in accuracy over conventional techniques. During intentional interference, the anomaly detection system isolates attacks within 0.8 s and restores normal operation in 2.4 s. Under sea state level 4, the framework achieves a successful landing rate of approximately 96% on the present test set, significantly enhancing robustness in maritime operations. This research not only establishes an algorithmic integration for autonomous navigation but also provides rigorous mathematical and empirical foundations for reliable shipborne landings in non-radio-silent, high-risk environments.