A Novel Robust Rauch-Tung-Striebel Smoother Based on Slash and Generalized Hyperbolic Skew Student’s T-Distributions

In this paper, a novel robust Rauch-Tung-Striebel smoother is proposed based on the Slash and generalized hyperbolic skew Student’s t-distributions. A novel hierarchical Gaussian state-space model is constructed by formulating the Slash distribution as a Gaussian scale mixture form and formulating the generalized hyperbolic skew Student’s t-distribution as a Gaussian variance-mean mixture form, based on which the state trajectory, mixing parameters and unknown noise parameters are jointly inferred using the variational Bayesian approach. The posterior probability density functions of mixing parameters of the Slash and generalized hyperbolic skew Student’s t-distributions are, respectively, approximated as truncated Gamma and generalized inverse Gaussian. Simulation results illustrate that the proposed robust Rauch-Tung-Striebel smoother has better estimation accuracy than existing state-of-the-art smoothers.