H∞Nonlinear Filtering of Discrete-Time Processes

This correspondence investigates the problem of H∞ estimation of a discrete-time nonlinear process. An estimator, which may be nonlinear, is introduced so that an H∞ -norm-like of what we call a generalized estimation error is guaranteed to be bounded by a prescribed level. Conditions for the existence of such an estimator, and formulae for its derivation, are obtained utilizing a discrete-time analog of the Hamilton-Jacobi inequality. An approximate filter that is based on linearization is developed. This filter relates to the extended Kalman filter in the same way that the linear H∞ filter relates to the Kalman filter.