Robust Cubature Kalman Filter With Gaussian-Multivariate Laplacian Mixture Distribution and Partial Variational Bayesian Method
Hongpo Fu, Wei Huang, Zhenwei Li, Yongmei Cheng, Tianyi Zhang
Abstract
This paper explores the problem of nonlinear state estimation in the presence of outlier-contaminated measurements. First, to deal with the non-stationary non-Gaussian noises caused by randomly occurring measurement outliers, we propose a new Gaussian-multivariate Laplacian mixture (GMLM) distribution and construct it as a hierarchical Gaussian expression. Next, utilizing the GMLM distribution and existing variational Bayesian (VB) method, a robust cubature Kalman filter is derived (VB-GMLMRCKF). Then, considering the high computational complexity of the existing VB inference process, a new partial VB (PVB) method is developed, which can separately estimate state vector and mismatched measurement noise covariance matrix. Building upon the VB-GMLMRCKF and PVB approach, a novel robust cubature Kalman filter is derived (PVB-GMLMRCKF). Finally, a target tracking model is utilized to evaluate the PVB-GMLMRCKF in terms of estimation accuracy, estimation consistency and computational efficiency.