Distributed Sequential Joint Detection and Estimation for non-Gaussian Noise

The problem of jointly testing a hypothesis and estimating a random parameter in non-Gaussian noise is investigated in a sequential and distributed setup. The non-Gaussian noise is modeled by a mixture of a completely known Gaussian distribution and an unknown contaminating distribution. Starting from the consensus+innovations approach, we present two robust communication schemes that are insensitive to the contaminating distribution. After deriving upper bounds for the variances of the estimators, a sequential scheme is designed at every sensor such that i) detection and estimation errors are limited for all possible contaminating distributions ii) the resulting scheme uses a minimum number of samples on average. A numerical example validates the proposed method.