Convergence analysis of the extended Kalman filter as an observer for nonlinear discrete-time systems

In the current paper, a modified version of the extended Kalman filter (EKF), when used as an observer for nonlinear discrete-time systems, is presented. The approach proposed consists in introducing time varying matrices to enhance convergence and stability of the obtained estimator. Based on a new formulation of the first order linearization technique, sufficient conditions to ensure local asymptotic convergence are established. Efficiency of this approach, compared to the classical version of the EKF, is shown through a nonlinear identification problem.