Stochastic integration Student's-t filter

The paper deals with the nonlinear state estimation of stochastic dynamic systems with a special focus on coping with outliers appearing in the system. A new stochastic integration Student's-t filter is developed based on the generic Student's-t filter and assuming the density of random variables present in the model and the conditional density of the state be Student's-t distributed. For evaluation of the integrals with Student's-t weights present in the filter relations, the stochastic integration rule is used. In contrast to other integration rules, it provides asymptotically exact values of the integrals. Performance of the proposed stochastic integration Student's-t filter is illustrated using a numerical simulation involving the coordinated-turn motion model.