Optimal Fault-Tolerant Data Fusion in Sensor Networks: Fundamental Limits and Efficient Algorithms

TL;DR

This paper investigates the fundamental limits and develops efficient algorithms for fault-tolerant data fusion in sensor networks, balancing estimation accuracy and consensus despite sensor faults.

Contribution

It introduces a formal tradeoff framework, characterizes the optimal sensor fusion problem, and proposes low-complexity algorithms with performance analysis.

Findings

Tradeoff between accuracy and consensus objectives identified

Optimal fusion problem characterized via a computable optimization

Brooks-Iyengar algorithms perform well compared to optimal estimators

Abstract

Distributed estimation in the context of sensor networks is considered, where distributed agents are given a set of sensor measurements, and are tasked with estimating a target variable. A subset of sensors are assumed to be faulty. The objective is to minimize i) the mean square estimation error at each node (accuracy objective), and ii) the mean square distance between the estimates at each pair of nodes (consensus objective). It is shown that there is an inherent tradeoff between the former and latter objectives. Assuming a general stochastic model, the sensor fusion algorithm optimizing this tradeoff is characterized through a computable optimization problem, and a Cramer-Rao type lower bound for the achievable accuracy-consensus loss is obtained. Finding the optimal sensor fusion algorithm is computationally complex. To address this, a general class of low-complexity Brooks-Iyengar Algorithms are introduced, and their performance, in terms of accuracy and consensus objectives, is compared to that of optimal linear estimators through case study simulations of various scenarios.