A new nonlinear state estimator using the fusion of multiple extended Kalman filters

For linear systems, the optimal filtering is provided by the celebrated Kalman filter. For nonlinear systems, only suboptimal filters can be obtained in general. The Extended Kalman filter (EKF) is such a suboptimal filter. It helped the promotion of the Kalman filter. With the development of more advanced nonlinear filters, however, the EKF is receiving less and less attention because it performs the worst most often. The EKF is based on the first-order Taylor series expansion. Ideally, the ground truth of the state should be picked as the expansion points, which are unfortunately unavailable in estimation problem. Instead, the most recent estimates are used. As a result of this misspecification, the EKF may have degraded performance or even failure. To overcome this, a multiple model extension to the EKF is proposed in this paper. Its key idea is to use multiple probabilistically weighted points to represent the whole state space. Then the linearization about each weighted point will lead to a possible model. Correspondingly, the original nonlinear filtering problem is changed into a variable structure multi-model estimation problem. How to design finite number of probabilistically weighted points to approximate the posterior densities is suggested. Numerical examples show that the proposed extension to the EKF is quite promising when compared to several existing competitive nonlinear filters.