Heavy-tailed filtering with reduced sensitivity to inaccurate noise covariance

This paper addresses the state estimation problem for linear systems with inaccurate process and measurement noise covariance matrices in presence of outlier interference. To capture heavy-tailed characteristics, a new state-space model is introduced using the Gaussian-Exponential-Gamma (GEG) distribution, which separately allows the hierarchical modeling of noise covariance matrix and a heavy-tailed adjustment factor. Since the joint probability density function of the state vector and noise parameters is non-Gaussian, a fixed-point variational Bayesian method is applied to obtain a set of approximate posterior distributions, resulting in a heavy-tailed filter with reduced sensitivity to inaccurate noise covariance. The effectiveness and feasibility of the proposed method is demonstrated by simulation results on target tracking.