Robust distributed sequential hypothesis testing for detecting a random signal in non-Gaussian noise

Abstract

Abstract-This paper addresses the problem of sequential binary hypothesis testing in a multi-agent network to detect a random signal in non-Gaussian noise. To this end, the consensus+innovations sequential probability ratio test (CISPRT) is generalized for arbitrary binary hypothesis tests and a robust version is developed. Simulations are performed to validate the performance of the proposed algorithms in terms of the average run length (ARL) and the error probabilities.

Robust distributed sequential detection via robust estimation

“…The test statistic S i (t) is recursively updated over time until it crosses either one of the thresholds [5] …”

“…Since the update equation is recursive, replacing the sample mean in the innovations part with a robust alternative, such as the median, the M, or the Myriad estimator, will robustify the consensus part as well and, thus, yield a test statistic that can handle outliers. An advantage of introducing robustness by changing the combination rule instead of the log-likelihood ratio as proposed in [3], [5] is the fact that the thresholds and decision rules of the original CISPRT remain valid. In the following we will detail our approach for three different robust estimators.…”

“…In the following we evaluate the standard CISPRT, our three proposed robust algorithms, namely, the Median-CISPRT, the M-CISPRT, and the Myriad-CISPRT, as well as the R-CISPRT from [5] in a shift-in-mean as well as a changein-variance test. We compare the algorithms in terms of the empirical probabilities of false alarm P FA and misdetection P MD , respectively, as well as the average run length of the sequential test.…”

“…In order to be able to handle non-Gaussian noise, we propose a robust version of the Consensus+Innovations Sequential Probability Ratio Test (CISPRT) introduced in [3], [4]. In contrast to the approach in [5], which uses the concept of leastfavorable distributions to robustify the CISPRT, we robustify the innovations term of the update equation using a robust estimator.…”

“…First, we develop three robust versions of the CISPRT algorithm, namely, the Median-CISPRT, the M-CISPRT, and the Myriad-CISPRT, by replacing the sample mean in the innovation term of the update equation with the respective robust estimator. Second, we evaluate the performance of the three robust algorithms and compare them to the R-CISPRT from [5] in terms of the average run length and the empirical probability of false alarm and misdetection.…”