On Robust Continuous-Time Discrimination.

Abstract

Continuous-time discrimination problems characterized by observations which are the output of stochastic dynamical systems driven by colored Gaussian noise are considered. The parameters of the dynamical systems belong to one of the following distinct uncertainty classes: (i) classes determined by 2-alternating capacities and (ii) classes with minimal or maximal elements. Discrimination tests with a fixed observation interval and sequential tests are derived whose likelihood ratios depend on the least-favorable pairs of parameters in the aforementioned uncertainty classes and are shown to have an acceptable level of performance despite the uncertainty. For tests with a fixed observation interval the performance measures considered are the actual error probabilities and the Chernoff upper bounds on them; the latter are shown to preserve their desirable asymptotic properties in the presence of the uncertainties. For sequential tests the performance measures are the error probabilities and the average required length of the observation interval under each hypothesis.