A Novel Case of Practical Exponential Observer Using Extended Kalman Filter

This technical note presents a case of practical exponential observer using extended Kalman filter (EKF) independent of certain restrictions, such as online check and estimation error of initial state. Recursive state estimation is usually a challenge for discrete-time nonlinear system in terms of computation cost. EKF is attractive with its simplicity since it is considered as an exponential observer given the above restrictions. However, those restrictions are so mathematically complicated that EKF cannot be practical in estimation. A novel case for an exponential observer using EKF is proposed, which is independent of such restrictions. However, these restrictions are proved to be unnecessary in the case. The proposed case is illustrated by a navigation system scenario. The validity of the case is demonstrated by a numerical simulation experiment. The system is deterministic.