Quickest Change Detection of a Markov Process Across a Sensor Array
Quickest Change Detection of a Markov Process Across a Sensor Array
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DOI：
10.1109/tit.2010.2040869
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发表时间：
2010-04-01
影响因子：
2.5
通讯作者：
Veeravalli, Venugopal V.
中科院分区：
文献类型：
--
作者：
Raghavan, Vasanthan;Veeravalli, Venugopal V.
在多传感器设置下的最快变化检测中，最近的关注集中在由于干扰而导致所有传感器的观测密度在同一时刻发生变化的情况上。在这项工作中，考虑了一个更一般的场景，其中变化在传感器之间传播，其传播可以建模为马尔可夫过程。考虑了这个问题的一个集中的贝叶斯版本，融合中心具有关于观察的完美信息和变化过程统计的先验知识。在动态规划框架中提出了在虚警约束下最小化平均检测延迟的问题。对最优停车规则的结构进行了深入研究。在罕见中断的极限情况下，证明了最优检验的结构将没有发生变化的假设的后验概率降低到阈值。在变化后密度与变化前密度之间的K-L散度的一定条件下，建立了阈值检验是渐近最优的（在虚警概率消失状态下）。数值研究表明，这种低复杂性阈值测试比单纯的测试（如单传感器测试或错误地假设变化瞬间传播的测试）在性能上有实质性的提高。
Recent attention in quickest change detection in the multisensor setting has been on the case where the densities of the observations change at the same instant at all the sensors due to the disruption. In this work, a more general scenario is considered where the change propagates across the sensors, and its propagation can be modeled as a Markov process. A centralized, Bayesian version of this problem is considered, with a fusion center that has perfect information about the observations and a priori knowledge of the statistics of the change process. The problem of minimizing the average detection delay subject to false alarm constraints is formulated in a dynamic programming framework. Insights into the structure of the optimal stopping rule are presented. In the limiting case of rare disruptions, it is shown that the structure of the optimal test reduces to thresholding the a posteriori probability of the hypothesis that no change has happened. Under a certain condition on the Kullback-Leibler (K-L) divergence between the post- and the pre-change densities, it is established that the threshold test is asymptotically optimal (in the vanishing false alarm probability regime). It is shown via numerical studies that this low-complexity threshold test results in a substantial improvement in performance over naive tests such as a single-sensor test or a test that incorrectly assumes that the change propagates instantaneously.