Stability in detection of signals in noise

Abstract

The topic of the paper is stable, or robust, detection of deterministic signals in noise, or the estimation of their amplitudes. The space of observations is an L2-space and the detectors or estimators are linear. For the case of one nominally known signal in nominally Gaussian noise, it is allowed that the actual underlying probability measure lies anywhere within distance ¿ of the nominal measure in the Prokhorov metric. An optimization problem is formulated and solved; its solution is a most stable detector according to a reasonable criterion for optimality for the class of perturbations mentioned. For the case of several nominally known signals in nominally known noise, the problem is recast as estimation of signal amplitudes. An optimization problem, similar to that for the one-signal case, is formulated and solved. The solution is a most stable estimator, by a criterion justified now only in an L2-context, without reference to probability measures.