Detecting an Abrupt Change of Finite Duration

This paper addresses the detection of a suddenly arriving signal of finite duration. In contrast to the traditional abrupt change detection framework where the post-change period is assumed to be infinitely long, the detection of a suddenly arriving short signal should be done before it disappears. Hence, the maximum delay for detection should be upper bounded and the traditional quickest change detection criterion is compromised. The new proposed optimality criterion promotes the maximization of the signal detection probability provided that the detection delay and the false alarm rate are upper bounded. A suboptimal detection algorithm based on a window limited cumulative sum test with a variable threshold is offered. The proposed method is analyzed theoretically and by simulation in case of Gaussian observations. A finite variable threshold is necessary to optimize the proposed algorithm which outperforms the conventional CUSUM test. It is shown that the resulting algorithm coincides with the finite moving average one.