An unscented Rauch-Tung-Striebel smoother for a bearing only tracking problem

The unscented Kalman filter (UKF) has become 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 we examine an unscented smoother based on Rauch-Tung-Striebel form for discrete-time dynamic systems. This smoother has advantages available in unscented transformation over approximation by Taylor expansion as well as its benefit in derivative free. To evaluate the performance of this smoother, we compare this algorithm with an extended Rauch-Tung-Striebel algorithm through the simulations of a bearing-only tracking problem.