Robust Kalman Filtering Based on Multivariate Geometric Skew Normal Distribution
Wenxing Yan, Jialiang Wu, Jingxiang Ma, Dongyuan Lin, Qiangqiang Zhang, Shiyuan Wang · 2024
This paper introduces a novel robust Kalman filter, referred to as the robust Kalman filter based on multivariate geometric skew normal (MGSN) distribution (RKF-MGSN). The RKF -MGSN effectively tackles the challenge of linear state estimation under heavy-tailed or skewed measurement noise. First, the MGSN distribution is transformed into a hierarchical representation to model the measurement noise. Then, Gaussian, inverse-Wishart (IW), and Beta distributions are determined as the prior distributions for the three parameters of the MGSN distribution. Moreover, the analytical update forms of the posterior distributions for the state vector and noise modeling parameters are derived through the utilization of variational Bayesian (VB) method. Finally, simulations on maneuvering target tracking confirm the performance superiorities of the RKF-MGSN.