A New Approach to State Estimation for Uncertain Linear Systems in a Moving Horizon Estimation Setting

This paper addresses the state estimation problem for linear systems with additive uncertainties in both the state and output equations using a moving horizon approach.Based on the full information estimation setting and the game-theoretic approach to the H_∞ filtering,a new optimization-based estimation scheme for uncertain linear systems is proposed,namely the H_∞-full information estimator,H_∞-FIE in short.In this formulation,the set of processed data grows with time as more measurements are received preventing recursive formulations as in Kalman filtering.To overcome the latter problem,a moving horizon approximation to the H_∞-FIE is also presented,the H_∞-MHE in short.This moving horizon approximation is achieved since the arrival cost is suitably defined for the proposed scheme.Sufficient conditions for the stability of the H_∞-MHE are derived.Simulation results show the benefits of the proposed scheme when compared with two H_∞ filters and the well-known Kalman filter.