Polynomial Chaos Expansion Based Rauch-Tung-Striebel Smoothers

This article introduces Gaussian approximation-based smoothing algorithms for nonlinear stochastic state space models using the polynomial chaos expansion (PCE). Initially, we present a smoothing algorithm, where the nonlinear functions of the state space model are approximated using a PCE that is formed using a set of collocation points generated from the filtering distribution. Subsequently, an iterative variant of the proposed smoothing algorithm is also presented. It iteratively forms a PCE approximation to the nonlinear functions by using collocation points generated from the current posterior approximation. The performance of the algorithms is evaluated on pendulum and aircraft tracking problems.