Optimal filtering for discrete-time nonlinear systems

Abstract

This correspondence is concerned with estimating a state variable for a discrete-time nonlinear system in the presence of random disturbance and measurement noise. A Bayesian approach is adopted in which the state conditioned upon the available measurement data is computed recursively. The new feature of the present method is that the stochastic differential rules can be applied for deriving the optimal nonlinear filter for a discrete-time system described by difference equations. Based on this estimator, the Kalman-Bucy filter and the Kushner filter are derived by the appropriate procedures.