A Novel Inverse-Wishart-Student’s t Mixture Distribution-Based Variational Bayesian Kalman Filter

Abstract

Considering the conventional Kalman filter (KF) has insufficient accuracy in state estimation under nonsmooth thick-tailed noise, a novel inverse-Wishart-student’s t mixed distribution (IWSTM) is proposed to adaptively learn the state vectors and associated auxiliary parameters using variational Bayesian (VB) approach. Then, a novel VB adaptive Kalman filter (VBAKF-IWSTM) is proposed to enhance state estimation accuracy under the conditions of nonsmooth thick-tailed measurement noise. Compared with RSTKF and GSTMKF, the novel VBAKF-IWSTM has a better fitting effect of nonsmooth thick-tailed noise based on the two auxiliary parameters, which are learned adaptively by VB to realize the correction of location parameter and scale parameter of the student’s t-distribution. The performance of the novel IWSTM is also demonstrated to outperform the existing KF in the simulation experiments and real trajectory experiments of the mobile robot conducted in this article.