Optimal state estimation in the presence of deterministic perturbations of uncertain structure occuring at unknown times

The problem of optimally generating state estimates in the presence of uncertain deterministic perturbations is analyzed. Particular attention is paid to the question of rapidly coping with such changes. It is demonstrated that Bayes structures for priors with a finite number of points of positive support are optimal even if the underlying uncertainty cannot be described by a finite number of models. Such structures provide a simple way to properly choose reduced order models without compromising estimation accuracy. The resulting estimators are adaptive and precisely allocate identification and estimation effort in order to minimize state estimation error. A decision theoretic paradigm resulting in a non pessimistic minimax estimate is used to obtain the above results. Analytic asymptotic performance results and a design example are included.