Asymptotic Optimality in Byzantine Distributed Quickest Change Detection

Abstract:The Byzantine distributed quickest change detection (BDQCD) is studied, where a fusion center monitors the occurrence of an abrupt event through a bunch of distributed sensors that may be compromised. We first consider the binary hypothesis case where there is only one post-change hypothesis and prove a novel converse to the first-order asymptotic detection delay in the large mean time to a false alarm regime. This converse is tight in that it coincides with the currently best achievability shown by Fellouris et al.; hence, the optimal asymptotic performance of binary BDQCD is characterized. An important implication of this result is that, even with compromised sensors, a 1-bit link between each sensor and the fusion center suffices to achieve asymptotic optimality. To accommodate multiple post-change hypotheses, we then formulate the multi-hypothesis BDQCD problem and again investigate the optimal first-order performance under different bandwidth constraints. A converse is first obtained by extending our converse from binary to multi-hypothesis BDQCD. Two families of stopping rules, namely the simultaneous d-th alarm and the multi-shot d-th alarm, are then proposed. Under sufficient link bandwidth, the simultaneous d-th alarm, with d being set to the number of honest sensors, can achieve the asymptotic performance that coincides with the derived converse bound; hence, the asymptotically optimal performance of multi-hypothesis BDQCD is again characterized. Moreover, although being shown to be asymptotically optimal only for some special cases, the multi-shot d-th alarm is much more bandwidth-efficient and energy-efficient than the simultaneous d-th alarm. Built upon the above success in characterizing the asymptotic optimality of the BDQCD, a corresponding leader-follower Stackelberg game is formulated and its solution is found.View less &nbsp;</p

Quickest Detection of False Data Injection Attack in Distributed Process Tracking

This paper addresses the problem of detecting false data injection (FDI) attacks in a distributed network without a fusion center, represented by a connected graph among multiple agent nodes. Each agent node is equipped with a sensor, and uses a Kalman consensus information filter (KCIF) to track a discrete time global process with linear dynamics and additive Gaussian noise. The state estimate of the global process at any sensor is computed from the local observation history and the information received by that agent node from its neighbors. At an unknown time, an attacker starts altering the local observation of one agent node. In the Bayesian setting where there is a known prior distribution of the attack beginning instant, we formulate a Bayesian quickest change detection (QCD) problem for FDI detection in order to minimize the mean detection delay subject to a false alarm probability constraint. While it is well-known that the optimal Bayesian QCD rule involves checking the Shriyaev's statistic against a threshold, we demonstrate how to compute the Shriyaev's statistic at each node in a recursive fashion given our non-i.i.d. observations. Next, we consider non-Bayesian QCD where the attack begins at an arbitrary and unknown time, and the detector seeks to minimize the worst case detection delay subject to a constraint on the mean time to false alarm and probability of misidentification. We use the multiple hypothesis sequential probability ratio test for attack detection and identification at each sensor. For unknown attack strategy, we use the window-limited generalized likelihood ratio (WL-GLR) algorithm to solve the QCD problem. Numerical results demonstrate the performances and trade-offs of the proposed algorithms