Quickest Change Detection Under Transient Dynamics: Theory and Asymptotic Analysis
Quickest Change Detection Under Transient Dynamics: Theory and Asymptotic Analysis
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瞬态动力学下最快的变化检测：理论和渐近分析
DOI：
10.1109/tit.2018.2877972
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发表时间：
2017
影响因子：
2.5
通讯作者：
V. Veeravalli
中科院分区：
文献类型：
--
作者：
Shaofeng Zou;Georgios Fellouris;V. Veeravalli
研究了瞬态动力学下的最快变化检测问题，其中从初始分布到最终持续分布的变化不是瞬时发生的，而是在一系列瞬态阶段之后。不同阶段内的观测值由不同的分布生成。我们的目标是尽可能快地检测到的变化，同时控制的平均游程长度（ARL）的虚警，当瞬态阶段的持续时间是完全未知的。考虑两种算法：动态累积和（CuSum）算法，在早期的工作中提出，和一个新构造的加权动态CuSum算法。这两种算法承认递归，方便他们的实际实施，他们是自适应的未知的瞬态持续时间。具体而言，他们的渐近最优性建立相对于Lorden的和Pollak的标准作为ARL虚警和瞬态阶段的持续时间去无穷大，在任何相对速率。数值结果证明了所提出的算法的自适应性，并验证了理论结果。
The problem of quickest change detection under transient dynamics is studied, where the change from the initial distribution to the final persistent distribution does not happen instantaneously, but after a series of transient phases. The observations within the different phases are generated by different distributions. The objective is to detect the change as quickly as possible, while controlling the average run length (ARL) to false alarm, when the durations of the transient phases are completely unknown. Two algorithms are considered: the dynamic Cumulative Sum (CuSum) algorithm, proposed in earlier work, and a newly constructed weighted dynamic CuSum algorithm. Both algorithms admit recursions that facilitate their practical implementation, and they are adaptive to the unknown transient durations. Specifically, their asymptotic optimality is established with respect to both Lorden’s and Pollak’s criteria as the ARL to false alarm and the durations of the transient phases go to infinity at any relative rate. Numerical results are provided to demonstrate the adaptivity of the proposed algorithms and to validate the theoretical results.