Detecting a Suddenly Arriving Dynamic Profile of Finite Duration

This paper addresses the detection of a suddenly arriving dynamic profile of a finite duration often called a transient change. In contrast to the traditional abrupt change detection, where the post-change period is assumed to be infinitely long, the detection of a suddenly arriving transient change should be done before it disappears. The detection of transient changes after their disappearance is considered as missed. Hence, the traditional quickest change detection criterion, minimizing the average detection delays provided a prescribed false alarm rate, is compromised. The proposed optimality criterion minimizes the worst case probability of missed detection provided that the worst case probability of false alarm during a certain period is upper bounded. A suboptimal CUSUM-type transient change detection algorithm, based on a subclass of truncated Sequential Probability Ratio Tests, is proposed. The optimization of the proposed algorithm in this subclass leads to a specially designed Finite Moving Average Test. The proposed method is analyzed theoretically and by simulation. A special attention is paid to the case of Gaussian observations with a dynamic profile.