Sequential detection of an unknown transient change profile by the finite moving average test - Nikiforov, Igor (Sequential analysis, 2025)
The paper addresses the sequential transient change detection (TCD) by using the finite moving average (FMA) test. Unlike the conventional quickest change detection, which assumes that the post-change period is infinitely long, sometimes it is necessary to detect a change with a priori upper-bounded (usually short) detection delay. All detections that exceed the required time to alert are assumed missed. We relax the assumption that the profile of a transient change is known. New versions of the FMA test are designed by using the generalized likelihood ratio (GLR) test in the Gaussian mean case. A Gaussian linear model with transient changes and nuisance parameters is also considered. These new quadratic FMA tests are compared to each other and with the FMA test based on a priori known transient change profile by their operating characteristics.