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 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