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

TL;DR

This paper introduces a learning-based distributed algorithm for sensor networks to accurately estimate a target signal despite some sensors providing invalid data due to defects, by iteratively learning sensor modes and refining estimates.

Contribution

It proposes the MDE algorithm that jointly learns sensor validity modes and estimates the target, with proven convergence and superior high-SNR performance.

Findings

MDE algorithm converges analytically.

Estimation error approaches ideal centralized performance at high SNR.

Outperforms naive consensus methods in presence of sensor defects.

Abstract

We consider the problem of distributed estimation of an unknown deterministic scalar parameter (the target signal) in a wireless sensor network (WSN), where each sensor receives a single snapshot of the field. We assume that the observation at each node randomly falls into one of two modes: a valid or an invalid observation mode. Specifically, mode one corresponds to the desired signal plus noise observation mode (\emph{valid}), and mode two corresponds to the pure noise mode (\emph{invalid}) due to node defect or damage. With no prior information on such local sensing modes, we introduce a learning-based distributed 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 the local observations at each iteration, thus refining the ongoing estimation update process. The convergence of the MDE algorithm is established analytically. 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 consensus based distributed estimator (without mode learning), whose estimation error blows up with an increasing SNR.