A robust Gaussian approximate filter for nonlinear systems with heavy tailed measurement noises

The scale matrix and degrees of freedom (dof) parameter of a Student's t distribution are important for nonlinear robust inference, and it is difficult to determine exact values in practical application due to complex environments. To solve this problem, an improved robust Gaussian approximate (GA) filter is derived based on the variational Bayesian approach, where the state together with unknown scale matrix and dof parameter are inferred. The proposed filter is applied to a target tracking problem with measurement outliers, and its performance is compared with an existing robust GA filter with fixed scale matrix and dof parameter. The results show the efficiency and superiority of the proposed filter as compared with the existing filter.