Adaptive Sensor Selection for Monitoring Stochastic Processes

We investigate an adaptive sensor selection problem in which a stochastic process is monitored by multiple sensors. We design a sensor selection policy that assigns a set of sensors to collect measurements for which the sensor selection depends on previously collected measurements and auxiliary data, and is subject to a constraint on the number of sensors to be selected. We use the mutual information to assess the performance of the policy. The goal of this paper is to find an approximate solution to the sensor selection problem and to assess the performance of the solution. For this purpose, we define greedy adaptive policies using greedy heuristics and derive a performance bound on greedy policies with respect to the performance of adaptive policies satisfying so-called diminishing property and optimality conditions. The main result shows that the performance of a greedy adaptive policy is at least frac{1}{2} of that of the best policy satisfying these two conditions.