Robust state estimation in uncertain systems: Combined detection-estimation with incremental MSE criterion

Minimax state estimation for uncertain systems is discussed. The conservative performance of the standard minimax estimator in the absence of an intelligent adversary is reduced by a combined detectorestimator structure and an incremental mean-squared error (IMSE) performance criterion. The optimal structure is defined for a wide class of linear and nonlinear systems whose uncertain parameters are elements of some known compact space and is also obtained for convex parameter spaces. Since the complete specification of the optimal estimator detector is problem dependent, a computational procedure is outlined. In an example, the resulting combined detector-estimator is shown to increase the estimation accuracy in the incremental minimax sense by a factor of two over the standard minimax estimator.