Robust Student’s t-based Rauch-Tung-Striebel Smoother for Non-stationary Heavy-tailed Measurement Noises

To address the fixed-interval smoothing problem for a linear state-space model with non-stationary heavy-tailed measurement noises, a robust Student’s t-based Rauch-Tung-Striebel smoother is proposed in this paper. The measurement noise is modelled as a non-stationary Student’s t-distribution, which is written as a Gaussian hierarchical form by introducing Gaussian and Gamma random variables. The time-varying state trajectory, Student’s t-distribution parameters and auxiliary random variables are jointly estimated by using the variational Bayesian method. Simulation study shows that the proposed smoother outperforms the existing up-to-date smoothers in the face of non-stationary heavy-tailed measurement noises.