Randomized Sensor Selection in Sequential Hypothesis Testing

We consider the problem of sensor selection for time-optimal detection of a hypothesis. We consider a group of sensors transmitting their observations to a fusion center. The fusion center considers the output of only one randomly chosen sensor at the time, and performs a sequential hypothesis test. We study a sequential multiple hypothesis test with randomized sensor selection strategy. We incorporate the random processing times of the sensors to determine the asymptotic performance characteristics of this test. For three distinct performance metrics, we show that, for a generic set of sensors and binary hypothesis, the time-optimal policy requires the fusion center to consider at most two sensors. We also show that for the case of multiple hypothesis, the time-optimal policy needs at most as many sensors to be observed as the number of underlying hypotheses.