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This paper proposes a discrete-time observer to estimate states of continuous-time nonlinear systems with presences of noises. Most conventional discrete-time state observers are designed using discrete-time models, which are derived by applying the forward-difference method to continuous-time models without considering their poor accuracy. This poor accuracy of the discretization may affect the accuracy of the observer-based on it and lead to a misevaluation. The proposed observer is based on an application of the extended Kalman filter (EKF) for a discrete-time model derived by a discretization method called continualized discretization. The proposed observer was applied to estimate the states of the Lorenz and van der Pol oscillators, which have complex dynamics such as limit cycle and chaos. The simulation results showed that the proposed observer gives better performances in estimating the real state and retaining the system dynamics of the original continuous-time model than the conventional method.

A Discrete-Time State Estimation for Nonlinear Systems With Noises