Joint parameter and state estimation for stochastic uncertain system with multivariate skew t noises

Due to the pulse interference, measurement outliers and artificial modeling errors, the multivariate skew t noise widely exists in the real environment. However, to date, little attention has been paid to the state estimation for systems in which the process noise and the measurement noise are both modeled as the heavy-tailed and skew non-Gaussian noise. In this paper, the multivariate skew t distribution is utilized to model the heavy-tailed and skew non-Gaussian noise. Then a probabilistic graphical form of the multivariate skew t distribution is given and proved. Based on the probabilistic graphical form, a hierarchical Gaussian state space model for stochastic uncertain systems is proposed, which transforms the estimation problem for systems with the heavy-tailed and skew non-Gaussian noises into the one with a hierarchical Gaussian state space model. Next, given the designed Gaussian state space model, the robust Bayesian filter and smoother based on the variational Bayesian inference are proposed to approximately estimate the system state and the unknown noise parameters. Furthermore, the complexity analysis together with the controllability and observability for stochastic uncertain systems with multivariate skew t noises is given. Finally, the simulation results of the target tracking scenario verify the validity of the proposed algorithms.