Robust Distributed Block and Sequential Continuous-Time Detection.

Abstract

Two detectors making independent observations which are the outputs of stochastic dynamical systems driven by colored Gaussian noise must decide which one of two hypotheses is true. Detection with a fixed observation interval (block detection) and sequential detection are considered. The decisions are coupled through a common cost function, which for tests with a fixed observation interval consists of the sum of the error probabilities, while for sequential tests it comprises the sum of the error probabilities and the expected stopping times. For the case of block detection the time-varying parameters of the dynamical system belong to uncertainty classes determined by 2- alternating capacities or to classes with minimal and maximal elements. For the case of sequential detection the time-invariant parameters of the dynamical system belong to classes with minimal and maximal elements. A minimax robust (worst-case) design is pursued according to which the two detectors employ tests with a fixed observation interval or sequential probability ratio tests whose likelihood ratios and thresholds depend on the least- favorable parameters over the uncertainty class. For the aforementioned cost function the optimal thresholds of the two detectors turn out to be coupled. It is shown that, despite the uncertainty, the two detectors are thus guaranteed a minimum level of acceptable performance.