AbstractIn this paper we examine the stability of estimators on the infinite time horizon in the case where mismatch exists between the true system and the system model assumed by the filters. A counterexample is given to show that standard stability requirements on the true system and the filters are not sufficient to guarantee that covariance of the error between the actual state and the estimate remains finite in the limit. Sufficient conditions for uniformly bounded error covariance are presented and in a special case, necessary and sufficient conditions are given. These will ensure that a filter is implementable and will remain stable over the infinite time horizon. We also show that an asymptotically stable system will not necessarily have finite state covariance in the limit ast→ ∞, and give the necessary and sufficient conditions to assure boundedness of the covaria
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