Methods for Improving the Linearization Problem of Extended Kalman Filter

Abstract

In this paper, in order to reduce the linearization error of Kalman filters family, three new methods are proposed and their effectiveness and feasibility are evaluated by means of Simultaneous Localization and Mapping (SLAM) problem. In derivative based methods of Kalman filters family, linearization error is brought into estimation unavoidably because of using Taylor expansion to linearize nonlinear motion model and observation model. These three methods lessen the linearization error by replacing the Jacobian matrix of observation function with new formulas. Simulation results done with `Car Park Dataset' indicate that all proposed methods have less linearization error than other mentioned methods and the method named Improved Weighted Mean Extended Kalman Filter (IWMEKF) performs much better than other mentioned Kalman filters in this paper on linearization error. In addition, simulation results confirm that our proposed approaches are computationally efficient. From estimation accuracy and computational complexity point of view, IWMEKF is the best solution for solving nonlinear SLAM problem among all Kalman filters mentioned in this paper.