Energy-Adaptive SGHSMC: A Particle-Efficient Nonlinear Filter for High-Maneuver Target Tracking

Tracking targets with nonlinear motion patterns remains a significant challenge in state estimation. We propose an energy-adaptive stochastic gradient Hamiltonian sequential Monte Carlo (SGHSMC) filter that combines adaptive energy dynamics with efficient particle sampling. The proposed method features a novel energy function that automatically adapts to target dynamics while minimizing the need for resampling operations. By integrating Hamiltonian Monte Carlo sampling with stochastic gradient techniques, our approach achieves a 40% reduction in computational overhead compared to traditional particle filters while maintaining particle diversity. We validate the method through both simulation and experimental studies. The simulation employs a univariate nonstationary growth model, demonstrating improvements of 39% in tracking accuracy over the extended Kalman filter (EKF) and 29% over standard sequential Monte Carlo methods. The experimental validation uses a bearing-only tracking scenario with a quadrupedal robot executing complex maneuvers, tracked by high-precision angular measurement systems. In practical tracking scenarios, the SGHSMC filter achieves a 77% better accuracy than EKF while maintaining the computational efficiency suitable for real-time applications. The algorithm demonstrates effectiveness in scenarios involving rapid state changes and irregular motion patterns, offering a robust solution for challenging target tracking problems.