The problem of quickest moving anomaly detection in networks is studied. Initially, the observations are generated according to a prechange distribution. At some unknown but deterministic time, an anomaly emerges in the network. At each time instant, one node is affected by the anomaly and receives data from a post-change distribution. The anomaly moves across the network, and the node that it affects changes with time. However, the trajectory of the moving anomaly is assumed to be unknown. A discrete-time Markov chain is employed to model the unknown trajectory of the moving anomaly in the network. A windowed generalized likelihood ratio–based test is constructed and is shown to be asymptotically optimal. Other detection algorithms including the dynamic Shiryaev-Roberts test, a quickest change detection algorithm with recursive change point estimation, and a mixture cumulative sum (CUSUM) algorithm are also developed for this problem. Lower bounds on the mean time to false alarm are developed. Numerical results are further provided to compare their performances.

研究了网络中最快的运动异常检测问题。最初，根据预变化分布生成观察值。在某个未知但确定的时间，网络中会出现异常。在每个时刻，一个节点都会受到异常影响，并从更改后的分布中接收数据。异常会在网络中移动，并且它影响的节点会随着时间而变化。但是，假定移动异常的轨迹是未知的。离散时间马尔可夫链用于模拟网络中运动异常的未知轨迹。构造了一个基于窗口的基于广义似然比的检验，并证明它是渐近最优的。其他检测算法包括动态Shiryaev-Roberts检验，针对此问题，还开发了具有递归变化点估计的最快变化检测算法以及混合累积和（CUSUM）算法。得出了平均误报时间的下限。进一步提供了数值结果以比较它们的性能。