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Quickest Detection of Anomalies of Varying Location and Size in Sensor Networks

机译：最快地检测传感器网络中不同位置和大小的异常

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摘要

The problem of sequentially detecting the emergence of a moving anomaly in a sensor network is studied. In the setting considered, the data-generating distribution at each sensor can alternate between a nonanomalous distribution and an anomalous distribution. Initially, the observations of each sensor are generated according to its associated nonanomalous distribution. At some unknown but deterministic time instant, a moving anomaly emerges in the network. It is assumed that the number as well as the identity of the sensors affected by the anomaly may vary with time. While a sensor is affected, it generates observations according to its corresponding anomalous distribution. The goal of this work is to design detection procedures to detect the emergence of such a moving anomaly as quickly as possible, subject to constraints on the frequency of false alarms. The problem is studied in a quickest change detection framework where it is assumed that the spatial evolution of the anomaly over time is unknown but deterministic. We modify the worst-path detection delay metric introduced in prior work on moving anomaly detection to consider the case of a moving anomaly of varying size. We then establish that a weighted dynamic cumulative sum type test is first-order asymptotically optimal under a delay-false alarm formulation for the proposed worst-path delay as the mean time to false alarm goes to infinity. We conclude by presenting numerical simulations to validate our theoretical analysis.
机译：研究了在传感器网络中顺序检测移动异常出现的问题。在考虑的设置中，每个传感器的数据产生分布可以在非同经分布和异常分布之间交替。最初，根据其相关的非正常分布产生每个传感器的观察。在一些未知但确定性的时间瞬间，在网络中出现了移动的异常。假设数量以及受异常影响的传感器的身份可能随时间而变化。当传感器受到影响时，它根据其相应的异常分布产生观察。这项工作的目标是设计检测程序，以便尽快检测这种移动异常的出现，但受到误报频率的限制。在最快的变化检测框架中研究了问题，其中假设随着时间的推移的异常的空间演化是未知的，但是确定性。我们修改了在移动异常检测的先前工作中引入的最坏路径检测延迟度量，以考虑不同尺寸的移动异常的情况。然后，我们建立了加权动态累积和类型测试是在延迟误报式制造下的一阶渐近最佳的最佳状态，因为所提出的最差路径延迟，因为误报的平均时间变为无穷大。我们通过呈现数值模拟来验证我们的理论分析。

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