A Robust Square-Root Cubature Kalman Filter With Gaussian-Student’s t Mixture Distribution and Variational Bayesian Method

This article mainly discusses the nonlinear state estimation problem with time-varying outlier-contaminated measurement. Firstly, to deal with the phenomenon of non-stationary heavy-tailed noises caused by randomly appearing measurement outliers, we model the measurement noise as a Gaussian-Student’s t mixture distribution (GSTM) and construct it as a hierarchical Gaussian expression. Then we choose the square-root cubature Kalman filter (SCKF) to ensure numerical stability during the calculation process. By fusing the GSTM distribution, the square-root cubature Kalman filter, and the existing variational Bayesian (VB) method, we derive a robust square-root cubature Kalman filter (VB-GSTMRSCKF). Finally, a target tracking model is utilized to evaluate the VB-GSTMRSCKF in terms of estimation accuracy. Experimental results illustrate that our proposed filter has better estimation accuracy and robustness than existing outlier-robust filters.