A sequential problem in decentralized detection with communication

We consider a sequential problem in decentralized detection. 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 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. We consider observer 2´s operation under two different scenarios. 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. We obtain parametric characterization of optimal policies for the two observers under both scenarios. We then extend these characterizations to a problem with multiple peripheral sensors that each send a single final message to a coordinating sensor who makes the final decision on the hypothesis.