Bayesian quickest change point detection and localization in sensor networks

The problem of quickly detecting and locating a statistical change point using multiple sensors is considered. Specifically, a statistical change point occurs at a random time and at a random location in the coverage region (or the region of interest) of a multi-sensor network. Each sensor node in the network has a limited detection range hence the observations of each sensor would be affected by the change point only if the change point occurs in its vicinity. The region of interest is partitioned by the detection ranges of all the sensors in the network. One is required to detect the presence of the change and to locate the partition of the change based on the sequential observations from all sensor nodes. Three performance metrics, namely the average detection delay, the false alarm probability and the false location probability, are of interest. The goal is to find a stopping time τ, at which the decision maker stops taking more observations and claims the change has occurred, and a terminal decision rule δ, by which the decision maker locates the partition that the change occurs at, to minimize a weighted sum of these three performance metrics. We obtain the optimal solution by first converting the proposed problem to a Markovian stopping time problem and then solving the problem using the tools from the optimal stopping theory.