A Stochastic Sensor Selection Scheme for Sequential Hypothesis Testing With Multiple Sensors

We study the problem of binary sequential hypothesis testing using multiple sensors with associated observation costs. An off-line randomized sensor selection strategy, in which a sensor is chosen at every time step with a given probability, is considered. The objective of this work is to find a sequential detection rule and a sensor selection probability vector such that the expected total observation cost is minimized subject to constraints on reliability and sensor usage. First, the sequential probability ratio test is shown to be the optimal sequential detection rule in this framework as well. Efficient algorithms for obtaining the optimal sensor selection probability vector are then derived. In particular, a special class of problems in which the algorithm has complexity that is linear in the number of sensors is identified. An upper bound for the average sensor usage to estimate the error incurred due to Wald's approximations is also presented. This bound can be used to set a safety margin for guaranteed satisfaction of the constraints on the sensor usage.