Sequential Problems in Decentralized Detection With Communication

Sequential problems in decentralized detection are considered. Peripheral sensors make repeated noisy observations of a binary hypothesis. At each time, a peripheral sensor has to decide whether to stop and send a final binary message to a coordinating sensor/fusion center or to continue taking costly measurements. The coordinating sensor's operation is explored under two different scenarios. In the first scenario, the coordinating sensor waits to receive the final message from each of the peripheral sensors and then starts taking costly measurements of its own. The coordinating sensor 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, the coordinating sensor starts taking measurements from the beginning, without waiting for the final messages from the peripheral sensors. At any time, the coordinating sensor has to decide whether to stop and declare a decision on the hypothesis or to continue to take more measurements and wait for the peripheral sensors to send their final message. Parametric characterization of optimal policies for the peripheral and the coordinating sensors are obtained under both scenarios. A sequential methodology for finding the optimal policies is presented.