On Sequential Random Distortion Testing of Non-Stationary Processes

Abstract

In this work, we propose a non-parametric sequential hypothesis test based on random distortion testing (RDT). RDT addresses the problem of testing whether or not a random signal, $\Xi$ , observed in independent and identically distributed (i.i.d) additive noise deviates by more than a specified tolerance, $\tau$ , from a fixed model, $\xi _0$ . The test is non-parametric in the sense that the underlying signal distributions under each hypothesis are assumed to be unknown. The need to control the probabilities of false alarm (PFA) and missed detection (PMD), while reducing the number of samples required to make a decision, leads to a novel sequential algorithm, Seq RDT. We show that under mild assumptions on the signal, Seq RDT follows the properties desired by a sequential test. We introduce the concept of a buffer and derive bounds on PFA and PMD, from which we choose the buffer size. Simulations show that Seq RDT leads to faster decision-making on an average compared to its fixed-sample-size (FSS) counterpart, Block RDT. These simulations also show that the proposed algorithm is robust to model mismatches compared to the sequential probability ratio test (SPRT).