The Extended Kalman Filter as a Local Asymptotic Observer for Nonlinear Discrete-Time Systems

The convergence aspects of the extended Kalman filter, when used as a deterministic observer for a nonlinear discrete-time system, are analyzed. The case of systems with nonlinear output maps as well as with linear maps is treated and the conditions needed to ensure the uniform boundedness of certain Riccati equations are related to the observability properties of the underlying nonlinear system. Furthermore, we show the convergence of the filter without any a priori boundedness assumptions on the error covariances as long as the states stay within a convex compact domain.