传感器网络中运动异常的快速检测
Quickest Detection of Moving Anomalies in Sensor Networks
摘要：
研究了传感器网络中移动异常随时间变化的检测问题。每个网络传感器的特征在于非异常和异常分布，控制传感器数据的生成。最初，每个传感器的观测值根据相应的非异常分布生成。在某个未知但确定的时刻之后，出现移动异常，随着时间的推移影响不同的传感器组。结果，根据相应的异常分布生成受影响的传感器的观测值。我们的目标是设计一个停止程序，以检测出现的异常，尽快受到限制的频率假警报。在最快的变化检测框架中研究了该问题，假设异常的演变是未知的，但确定性的。为此，我们提出了一个修改Lorden的最坏的平均检测延迟度量占异常的轨迹，最大限度地提高了候选检测过程的检测延迟。我们建立了一个累积和型测试解决了所产生的顺序检测问题时，传感器是均匀的。对于异构传感器的情况下，所提出的检测方案可以修改，以提供一阶渐近最优算法。最后，我们提出了数值模拟，以验证我们的理论分析。
英文摘要：
The problem of sequentially detecting a moving anomaly which affects different parts of a sensor network with time is studied. Each network sensor is characterized by a non-anomalous and anomalous distribution, governing the generation of sensor data. Initially, the observations of each sensor are generated according to the corresponding non-anomalous distribution. After some unknown but deterministic time instant, a moving anomaly emerges, affecting different sets of sensors as time progresses. As a result, the observations of the affected sensors are generated according to the corresponding anomalous distribution. Our goal is to design a stopping procedure to detect the emergence of the 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 evolution of the anomaly is unknown but deterministic. To this end, we propose a modification of Lorden's worst average detection delay metric to account for the trajectory of the anomaly that maximizes the detection delay of a candidate detection procedure. We establish that a Cumulative Sum-type test solves the resulting sequential detection problem exactly when the sensors are homogeneous. For the case of heterogeneous sensors, the proposed detection scheme can be modified to provide a first-order asymptotically optimal algorithm. We conclude by presenting numerical simulations to validate our theoretical analysis.
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