A Spherical Simplex Unscented Rauch-Tung-Striebel Smoother for a Vehicle Localization Problem

The unscented Kalman filter (UKF) has become relatively a new technique used in a number of nonlinear estimation problems to overcome the limitation of Taylor series linearization. It uses a deterministic sampling approach known as sigma points to propagate nonlinear systems and has been discussed in many literature. However, a nonlinear smoothing problem has received less attention than the filtering problem. Therefore, in this article an unscented smoother based on Rauch-Tung-Striebel form is examined for discrete-time dynamic systems. It has advantages available in unscented transformation over approximation by Taylor expansion as well as its benefit in derivative free. In addition, new sampling technique known as a spherical simplex has been introduced and evaluated. To show the effectiveness of the proposed method, the unscented smoother is implemented and evaluated through a vehicle localization problem.