Data-Efficient Quickest Change Detection in Sensor Networks

Abstract

A sensor network is considered where at each sensor a sequence of random variables is observed. At each time step, a processed version of the observations is transmitted from the sensors to a common node called the fusion center. At some unknown point in time the distribution of observations at an unknown subset of the sensor nodes changes. The objective is to detect the change in distribution as quickly as possible, subject to constraints on the false alarm rate, the cost of observations taken at each sensor, and the cost of communication between the sensors and the fusion center. Minimax formulations are proposed for the above problem and distributed algorithms are proposed in which on-off observation control and censoring is used at each sensor to meet the constraints on data. It is shown that the proposed algorithms are asymptotically optimal for the proposed formulations, as the false alarm rate goes to zero. The asymptotic optimality of the proposed algorithms implies that an arbitrary but fixed fraction of data can be skipped without any loss in asymptotic performance as compared to the scheme where all the observations are used for decision making. It is also shown, via numerical studies, that the proposed algorithms perform significantly better than those based on fractional sampling, in which the classical algorithms from the literature are used and the constraint on the cost of observations is met by skipping a fixed fraction of observations either deterministically or randomly, independent of the observation process.