Nonparametric Sequential Signal Change Detection Under Dependent Noise

Abstract

A nonparametric version of the sequential signal detection problem is studied. Our signal model includes a class of time-limited signals for which we collect data in the sequential fashion at discrete points in the presence of correlated noise. For such a setup we introduce a novel signal detection algorithm relying on the postfiltering smooth correction of the classical Whittaker–Shannon interpolation series. Given a finite frame of noisy samples of the signal, we design a detection algorithm being able to detect a departure from a reference signal as quickly as possible. Our detector is represented as a normalized partial-sum continuous time stochastic process, for which we obtain a functional central limit theorem under weak assumptions on the correlation structure of the noise. Particularly, our results allow for noise processes such as ARMA and general linear processes as well as$ \alpha $-mixing processes. The established limit theorems allow us to design monitoring algorithms with the desirable level of the probability of false alarm and able to detect a change with probability approaching one.

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