Robust Distributed Discrete-Time Block and Sequential Detection in Uncertain Environments.

Abstract

Two detectors making independent observations must decide which one of two hypotheses is true. Both fixed-sample-size (block) detection and sequential detection are considered. The decisions are coupled through a common cost function which for tests with fixed sample size consists of the sum of the error probabilities while for sequential tests it comprises the sum of the error probabilities and the expected sample sizes. The probability measures which govern the statistics of the i.i.d. observations belong to uncertainty classes determined by 2-alternating capacities. A minimax robust (worst-case) design is pursued according to which the two detectors employ fixed-sample-size tests or sequential probability ratio tests whose likelihood ratios and thresholds depend on the least-favorable probability measures 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.