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We consider the problem of distributed estimation of an unknown deterministicscalar parameter (the target signal) in a wireless sensor network (WSN), whereeach sensor receives a single snapshot of the field. We assume that theobservation at each node randomly falls into one of two modes: a valid or aninvalid observation mode. Specifically, mode one corresponds to the desiredsignal plus noise observation mode (\emph{valid}), and mode two corresponds tothe pure noise mode (\emph{invalid}) due to node defect or damage. With noprior information on such local sensing modes, we introduce a learning-baseddistributed procedure, called the mixed detection-estimation (MDE) algorithm,based on iterative closed-loop interactions between mode learning (detection)and target estimation. The online learning step re-assesses the validity of thelocal observations at each iteration, thus refining the ongoing estimationupdate process. The convergence of the MDE algorithm is establishedanalytically. Asymptotic analysis shows that, in the high signal-to-noise ratio(SNR) regime, the MDE estimation error converges to that of an ideal(centralized) estimator with perfect information about the node sensing modes.This is in contrast to the estimation performance of a naive average consensusbased distributed estimator (without mode learning), whose estimation errorblows up with an increasing SNR.

Learning-Based Distributed Detection-Estimation in Sensor Networks with Unknown Sensor Defects