Data-efficient quickest change detection in distributed and multi-channel systems

Abstract

A distributed or multi-channel system consisting of multiple sensors is considered. At each sensor a sequence of observations is taken, and at each time step, a summary of available information is sent to a central decision maker, called the fusion center. At some point of time, the distribution of observations at an unknown subset of the sensor nodes changes. The objective is to detect this change as quickly as possible, subject to constraints on the false alarm rate, the cost of observations taken at the sensors and the cost of communication between the sensors and the fusion center. Minimax formulations are proposed for this problem. An algorithm called DE-CensorSum is proposed, and is shown to be asymptotically optimal for the proposed formulations, for each possible post-change scenario, as the false alarm rate goes to zero. It is also shown, via numerical studies, that the DE-Censor-Sum algorithm performs significantly better than the approach of fractional sampling, where the cost constraints are met based on the outcome of a sequence of biased coin tosses, independent of the observation process.

Data-Efficient Minimax Quickest Change Detection in a Decentralized System

“…In this case, one can use better fusion techniques at the fusion center to get improved performance. This is indeed true; see Banerjee and Veeravalli (2012b) and Banerjee and Veeravalli (2013b) for some preliminary results.…”

Quickest Change Detection in Adaptive Censoring Sensor Networks

“…The asymptotic optimality result of the paper does not hold if the total cost is considered (see Remark 3). A similar criterion called pre-change transmission cost is considered in [19].…”

“…To deal with communication constraints, in the existing literature [10], [12], [14], [19], CuSum-like algorithms (CuSum in [10], [12], a variant called DE-CuSum in [14], [19]) are run locally at the sensor nodes and the detection statistic of the algorithm is sent to the fusion center only when it is above a certain threshold. In this paper, a fundamentally different approach is adopted: the observations instead of the detection statistic are censored and transmitted to the fusion center.…”

“…Another advantage is that our algorithm is an equalizer rule, which helps reduce off-line computation complexity (see Remark 2). Compared with decentralized settings in [10], [12], [14], [19], where the communication is unidirectional and remote sensors implement the censoring strategy in an autonomous manner, our algorithm is centralized in the sense that the censoring strategies used at remote sensors are fed back by the fusion center. Evidently, the feedback transmission introduced complicates the system, although it occurs only occasionally and its message is rather simple.…”