Optimum performance levels for minimax filters, predictors and smoothers

For both discrete and continuous-time linear time-varying systems, we obtain the achievable performance levels for minimax filters, predictors and smoothers, in terms of the finite escape times of some related (discrete and continuous-time) Riccati equations. Our game-theoretic approach also yields an alternative derivation for the corresponding minimax estimators which were first obtained in [1]. They are all Bayes estimators with respect to particular Gaussian distributions, and admit recursive structures.