Robust distributed sequential detection via robust estimation

Abstract

Abstract-We study the problem of sequential binary hypothesis testing in a distributed multi-sensor network in nonGaussian noise. To this end, we develop three robust extensions of the Consensus+Innovations Sequential Probability Ratio Test (CISPRT), namely, the Median-CISPRT, the M-CISPRT, and the Myriad-CISPRT, and validate their performance in a shiftin-mean as well as a change-in-variance test. Simulations show the superiority of the proposed algorithms over the alternative R-CISPRT.

Robust Sequential Detection in Distributed Sensor Networks

“…With the Median-CISPRT, the M-CISPRT, and the Myriad-CISPRT we propose three robust distributed sequential detectors based on this concept and analyze their suitability for Gaussian shift-in-mean and shift-in-variance tests. These results generalize and extend our first approaches from [31] and [32] and provide a unified framework for robust sequential detection in distributed sensor networks. An extension of some of the presented concepts to multiple hypothesis tests can be found in [33].…”

“…Regarding our proposed algorithms, this has the following implication: Since the median is only a robust estimator for the mean of symmetric distributions, the Median-CISPRT is not suitable for general shift-in-variance problems. It might give correct detection results for certain parameter choices as can be seen in the promising simulation results from [32], but we cannot guarantee a reliable performance for arbitrary shift-in-variance tests. Therefore, we will consider the Median-CISPRT only for shift-in-mean tests.…”

“…First, they only hold for the specific case of symmetric Gaussian shift-in-mean hypothesis tests. In [31] and [32], we generalized these thresholds for use in arbitrary binary hypothesis tests. Second, the derivation of the thresholds relies on the symmetry of W , an assumption that is usually not valid in distributed sensor networks.…”

“…Second, the derivation of the thresholds relies on the symmetry of W , an assumption that is usually not valid in distributed sensor networks. In the sequel, we improve the generalized thresholds from [31] and [32] by requiring only the right-stochasticity of W in the derivation. First, however, expressions for the mean and the variance of the test statistic under H 0 and H 1 are derived, which will be needed in the subsequent steps.…”

“…Thus, the thresholds and decision rules of the original CISPRT, which are based on the mean and the variance of the log-likelihood ratio, remain valid. A first attempt at using this approach was presented in [32], where we successfully used the median, the M-estimator, and the sample myriad [39], [40] for sequential detection. In the sequel, we will briefly summarize these algorithms and investigate their suitability for different binary hypothesis tests.…”