Some minimax detection and estimation problems in a Hilbert space setting

The minimax approach to the design of systems which are robust with respect to modeling uncertainties is studied employing a game theoretic formulation in which the performance functional and the sets of modeling uncertainties and admissible design policies are arbitrary. It is shown that if the performance functional and the uncertainty set are convex then a certain type of regularity condition on the functional is sufficient in order to ensure that the optimal strategy for a least favorable element of the uncertainty set is minimax robust. The efficacy of this approach is tested in a Hilbert space formulation of the problems of matched filtering, Wiener filtering, quadratic detection and output energy filtering, in which uncertainties in their respective signal and noise models are assumed to exist.