Robust stochastic integration filtering for nonlinear systems under multivariate t-distributed uncertainties

Bayesian filtering solutions that are developed under the assumption of heavy-tailed uncertainties are more robust to outliers than the standard Gaussian ones. In this work, we consider robust nonlinear Bayesian filtering in the presence of multivariate t-distributed process and measurement noises. We develop a robust stochastic integration filter (RSIF) based on stochastic spherical-radial integration rule that achieves asymptotically exact evaluations of multivariate t-weighted integrals of nonlinear functions that arise in nonlinear Bayesian filtering framework. The superiority of the proposed scheme is demonstrated by comparing its performance against the cubature Kalman filter (CKF), a robust CKF, and the standard SIF in a representative example concerning bearings-only target tracking.