Sequential Random Distortion Testing of Non-Stationary Processes

Khanduri, P and Pastor, D and Sharma, V and Varshney, PK (2019) Sequential Random Distortion Testing of Non-Stationary Processes. In: IEEE Transactions on Signal Processing, 67 (21). pp. 5450-5462.

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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, Ξ, observed in independent and identically distributed (i.i.d) additive noise deviates by more than a specified tolerance, τ, from a fixed model, ξ 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, SeqRDT. We show that under mild assumptions on the signal, SeqRDT 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 SeqRDT leads to faster decision-making on an average compared to its fixed-sample-size (FSS) counterpart, BlockRDT. These simulations also show that the proposed algorithm is robust to model mismatches compared to the sequential probability ratio test (SPRT).

Item Type:	Journal Article
Publication:	IEEE Transactions on Signal Processing
Publisher:	Institute of Electrical and Electronics Engineers Inc.
Additional Information:	Copyright of this article belongs to Institute of Electrical and Electronics Engineers Inc.
Keywords:	Decision making; Probability; Testing, Non-parametric; Nonstationary process; Random distortions; Robust hypothesis testing; Sequential algorithm; Sequential probability ratio test; Sequential testing; Signal distribution, Additive noise
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	05 Feb 2020 06:39
Last Modified:	05 Feb 2020 06:39
URI:	http://eprints.iisc.ac.in/id/eprint/64436

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