Decentralized quickest change detection

A decentralized formulation of the quickest change detection problem is studied, where the distributions of the observations at all of the sensors in the system change at the time of disruption, and the sensors communicate with a common fusion center. A Bayesian setting is considered in which a priori knowledge of the change time distribution is available. The observations are assumed to be independent from sensor to sensor, conditioned on the change hypothesis. An optimal solution to the problem is derived under a quasi-classical information structure, where each sensor retains only its messages from the past (restricted local memory), and receives feedback from the fusion center about the past messages of the other sensors (full feedback). A technique for implementation of the optimal solution is given, and the solution is extended to the situation where a priori change time distribution information is not available. The structure of the optimal solution is then used to arrive at a simple suboptimal policy that does not require any past message information. Numerical examples are given, which illustrate that the optimal solution offers little improvement over the suboptimal one, i.e., that feedback from the fusion center cannot be exploited to improve performance.