Sequential Random Distortion Testing of Non-Stationary Processes

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, <inline-formula><tex-math notation="LaTeX">$\Xi$</tex-math></inline-formula>, observed in independent and identically distributed (i.i.d) additive noise deviates by more than a specified tolerance, <inline-formula><tex-math notation="LaTeX">$\tau$</tex-math></inline-formula>, from a fixed model, <inline-formula><tex-math notation="LaTeX">$\xi _0$</tex-math></inline-formula>. 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, <italic>Seq</italic>RDT. We show that under mild assumptions on the signal, <italic>Seq</italic>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 <italic>Seq</italic>RDT leads to faster decision-making on an average compared to its fixed-sample-size (FSS) counterpart, <italic>Block</italic>RDT. These simulations also show that the proposed algorithm is robust to model mismatches compared to the sequential probability ratio test (SPRT).