Abstract

We study the sequential quickest change point detection for systems with multiple possible postchange models. A change point is the time instant at which the distribution of a random process changes. In many practical applications, the prechange model can be easily obtained, yet the postchange distribution is unknown due to the unexpected nature of the change. In this article, we consider the case that the postchange model is from a finite set of possible models. The objective is to minimize the average detection delay (ADD), subject to upper bounds on the probability of false alarm (PFA). Two different quickest change detection algorithms are proposed under Bayesian and non-Bayesian settings. Under the Bayesian setting, the prior probabilities of the change point and prior probabilities of possible postchange models are assumed to be known, yet this information is not available under the non-Bayesian setting. Theoretical analysis is performed to quantify the analytical performance of the proposed algorithms in terms of exact or asymptotic bounds on PFA and ADD. It is shown through theoretical analysis that when PFA is small, both algorithms are asymptotically optimal in terms of ADD minimization for a given PFA upper bound. Numerical results demonstrate that the proposed algorithms outperform existing algorithms in the literature.

摘要

我们研究了具有多个可能的postchange模型的系统的顺序最快变化点检测。变化点是随机过程的分布发生变化的时刻。在许多实际应用中，可以很容易地获得变更前的模型，但是由于变更的意外性质，变更后的分布是未知的。在本文中，我们考虑后变更模型来自一组有限的可能模型的情况。目的是最大程度地降低平均检测延迟（ADD），但要以假警报（PFA）的上限为准。在贝叶斯和非贝叶斯设置下，提出了两种不同的最快变化检测算法。在贝叶斯设置下，假定更改点的先验概率和可能的变更后模型的先验概率是已知的，但是在非贝叶斯设置下该信息不可用。进行理论分析以根据PFA和ADD上的精确或渐近界限来量化所提出算法的分析性能。通过理论分析表明，当PFA较小时，对于给定的PFA上限，两种算法在ADD最小化方面都是渐近最优的。数值结果表明，所提出的算法优于文献中已有的算法。对于给定的PFA上限，两种算法在ADD最小化方面都是渐近最优的。数值结果表明，所提出的算法优于文献中已有的算法。对于给定的PFA上限，两种算法在ADD最小化方面都是渐近最优的。数值结果表明，所提出的算法优于文献中已有的算法。