Robust Bayesian Recursive Ensemble Kalman Filter Under the Nonstationary Heavy-Tailed Noise

For the issue of target tracking in nonlinear and nonstationary heavy-tailed noise systems, this article proposed a novel robust Bayesian recursive ensemble Kalman filter (RBREnKF), breaking through the limitations of EnKF under highly nonlinear and non-Gaussian noise conditions. Initially, to counteract the problem of divergence observed in the EnKF under highly nonlinear conditions, a Bayesian recursive update (BRU) method is introduced to further improve the performance of the filter, resulting in more precise nonlinear approximation. Subsequently, a more robust Gaussian-generalized hyperbolic (GGH) distribution is adopted to model the nonstationary heavy-tailed measurement noise, and the Student’s t distribution is used to model the non-Gaussian process noise at the same time. The variational Bayesian (VB) method is then applied to solve the joint posterior probability density of the target state, yielding the new RBREnKF. Finally, the simulation results conducted in scenarios of both point target and extended target tracking and along with the sensitivity analysis of the filter’s parameters, demonstrate the superiority of the proposed algorithm over existing methods, exhibiting more accurate estimation of the target state and significantly improved performance.