Quickest detection of a change process across a sensor array

Recent attention in quickest change detection in a multi-sensor scenario has been on the case where the densities of the observations at all the sensors change instantaneously at the time of disruption. In this work, we consider a scenario where change propagates across the sensors and its propagation can be modeled as a Markov process. A centralized, Bayesian version of this problem, with a common fusion center that has perfect information about the observations and a priori knowledge of the statistics of the change process, is considered. We formulate the problem of minimizing the expected detection delay subject to false alarm constraints in a dynamic programming framework. Insights into the structure of the optimal stopping rule are presented. When the change process has a jointly geometric prior, the optimal test is seen to be the smallest time of cross-over in the space of sufficient statistics of a linear functional with a non-linear concave function. In the special case where disruption is uniformly likely across the time horizon, we show that the optimal test reduces to a simple threshold test.