Quickest Change Detection With Controlled Sensing

被引:6
作者
Veeravalli, Venugopal V. [1 ]
Fellouris, Georgios [2 ]
Moustakides, George V. [3 ]
机构
[1] Univ Illinois, ECE Dept, Urbana, IL 61801 USA
[2] Univ Illinois, Dept Stat, Urbana, IL 61801 USA
[3] Univ Patras, ECE Dept, Patras 26500, Greece
来源
IEEE JOURNAL ON SELECTED AREAS IN INFORMATION THEORY | 2024年 / 5卷
基金
美国国家科学基金会;
关键词
Sequential change detection; experimental design; observation control; CuSum test; SEQUENTIAL DESIGN; ANOMALY DETECTION;
D O I
10.1109/JSAIT.2024.3362324
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
In the problem of quickest change detection, a change occurs at some unknown time in the distribution of a sequence of random vectors that are monitored in real time, and the goal is to detect this change as quickly as possible subject to a certain false alarm constraint. In this work we consider this problem in the presence of parametric uncertainty in the post-change regime and controlled sensing. That is, the post-change distribution contains an unknown parameter, and the distribution of each observation, before and after the change, is affected by a control action. In this context, in addition to a stopping rule that determines the time at which it is declared that the change has occurred, one also needs to determine a sequential control policy, which chooses the control action at each time based on the already collected observations. We formulate this problem mathematically using Lorden's minimax criterion, and assuming that there are finitely many possible actions and post-change parameter values. We then propose a specific procedure for this problem that employs an adaptive CuSum statistic in which (i) the estimate of the parameter is based on a fixed number of the more recent observations, and (ii) each action is selected to maximize the Kullback-Leibler divergence of the next observation based on the current parameter estimate, apart from a small number of exploration times. We show that this procedure, which we call the Windowed Chernoff-CuSum (WCC), is first-order asymptotically optimal under Lorden's minimax criterion, for every possible value of the unknown post-change parameter, as the mean time to false alarm goes to infinity. We also provide simulation results to illustrate the performance of the WCC procedure.
引用
收藏
页码:1 / 11
页数:11
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