On Byzantine Distributed Sequential Change Detection with Multiple Hypotheses

Abstract

Sequential change point detection with multiple decentralized sensors is studied. Each sensor makes a local decision based on its own observations and reports it through a bandlimited link to a fusion center, which then decides whether the change has occurred. Since sensors in many applications such as cyber-physical systems are prone to a number of attacks such as Byzantine attacks, combating such a security breach becomes one of the most crucial issues. Previous works on sequential change detection under Byzantine attacks only focus on binary-hypothesis case, which significantly limits the applicability. In this paper, we consider the extension to the multi-hypothesis setting. We show that naively extending the existing method from the binary case to the multi-hypothesis one can result in a catastrophic event preventing the fusion center from making a conclusive decision. Thus we propose the other two new methods by allowing each sensor to cast multiple local alarms, and both can avoid this catastrophic event and improve the asymptotic detection delay. In analyzing detection delays of our multi-hypothesis schemes, we also show that for each hypothesis, asymptotically, it suffices to focus on the competing hypothesis that is closest in Kullback-Leibler distance. Through large sensor analysis, we also show that as the number of honest sensors grows, one of the proposed scheme, called the simultaneous rule, approaches the optimal performance within a factor of 2.