On sequential random distortion testing of non-stationary processes

International audienceRandom distortion testing (RDT) addresses the problem of testing whether or not a random signal, ¥, deviates by more than a specified tolerance, ¿, from a fixed value, "0 [1]. The test is nonparametric in the sense that the distribution of the signal under each hypothesis is assumed to be unknown. The signal is observed in independent and identically distributed (i.i.d) additive noise. The need to control the probabilities of false alarmand missed detection while reducing the number of samples required to make a decision leads to the SeqRDT approach. We show that under mild assumptions on the signal, the SeqRDT will follow the properties desired by a sequential test. Simulations showthat the SeqRDT approach leads to faster decision making compared to it's fixed sample counterpart Block-RDT [2] and is robust to model mismatches compared to the Sequential Probability Ratio Test (SPRT) [3] when the actual signal is a distorted version of the assumed signal especially at low Signal-to-Noise Ratios (SNRs)