A new sequential detector for short-duration signals

Abstract

For quickest detection of a permanent change in distribution of otherwise i.i.d. observations Page's test provides the optimal processor. Page's test has also been applied to the detection of transient (i.e. temporary) changes in distribution: it is easy to implement and has reliable performance, but as applied to the transient problem its optimality is questionable. In this paper we offer an alternative to the Page procedure which we call the iterated generalized sequential probability ratio test, or IGSPRT. While Page's test is itself an IGSPRT, its form and performance are constrained by its reliance on constant thresholds and biases. We demonstrate that with these time-varying, markedly increased detection probabilities are possible. The IGSPRT is easiest to understand and motivate in the Gaussian shift-in-mean problem, and we discuss this in detail, but since that problem is of limited practical interest, we also examine the effect of the IGSPRT in a more realistic situation.