Stability in linear detection

The stability of linear detectors for signals nominally known except for amplitude in correlated nominally Gaussian noise is considered. Stability is defined in terms of bounds on the distribution of the test statistic as the true probability measure on the observation space varies in a Prokhorov neighborhood of the nominal; the derived stability index is independent of the neighborhood size. An optimization problem is formulated and solved to give the most stable linear detector meeting a Constraint on the nominal level of detectability.