Nonlinear smoothing with multivariable skew-t noises

The estimation of nonlinear systems has always been an interesting research topic. Meanwhile, heavy-tailed and skew non-Gaussian noise exists widely in the actual environment. At present, most of the measurement noise of linear systems is estimated by univariate skew-t distribution (UST) or multivariable skew-t distribution (MST). There is little research on non-Gaussian noise in linear systems where both process noise and measurement noise are subject to heavy-tailed and skew, and even less on nonlinear systems. In this paper, the heavy-tailed and skew non-Gaussian noise is modeled using the multivariate skew-t distribution. In addition, a hierarchical Gaussian state space model for stochastic uncertain systems is presented, and the system estimation problem of heavy-tailed and skew non-Gaussian noise is transformed into the estimation problem of hierarchical Gaussian state space model. And a robust Bayesian smoother based on variable Bayesian inference is proposed to approximate the system state and the measured unknown noise parameters. On this basis, the proposed algorithm is simulated through the target tracking scenario, and the simulation results are compared with the existing extended Rauch-Tung-Striebel smoother (ERTSS) to verify the effectiveness of the proposed algorithm. Finally, the advantages and disadvantages of the proposed algorithm and the possible development direction in the future are summarized.