A Sequential Problem in Decentralized Detection with Communication

A sequential problem in decentralized detection is considered. Two observers can make repeated noisy observations of a binary hypothesis on the state of the environment. At any time, observer 1 can stop and send a final binary message to observer 2 or it may continue to take more measurements. Every time observer 1 postpones its final message to observer 2, it incurs a penalty. Observer 2's operation under two different scenarios is explored. In the first scenario, observer 2 waits to receive the final message from observer 1 and then starts taking measurements of its own. It is then faced with a stopping problem on whether to stop and declare a decision on the hypothesis or to continue taking measurements. In the second scenario, observer 2 starts taking measurements from the beginning. It is then faced with a different stopping problem. At any time, observer 2 can decide whether to stop and declare a decision on the hypothesis or to continue to take more measurements and wait for observer 1 to send its final message. Parametric characterization of optimal policies for the two observers are obtained under both scenarios. A sequential methodology for finding the optimal policies is presented. The parametric characterizations are then extended to problem with increased communication alphabet for the final message from observer 1 to observer 2; and to the case of multiple peripheral sensors that each send a single final message to a coordinating sensor who makes the final decision on the hypothesis.