A distributed classification/estimation algorithm for sensor networks

TL;DR

This paper introduces a novel distributed algorithm for sensor networks that simultaneously classifies sensors as faulty or non-faulty and estimates a common parameter, with proven convergence and asymptotic optimality.

Contribution

It presents a new cooperative iterative algorithm that handles communication constraints and achieves convergence, with theoretical analysis and numerical validation.

Findings

Algorithm converges with proof.

Estimates become arbitrarily accurate as sensors increase.

Classification error approaches optimal centralized performance.

Abstract

In this paper, we address the problem of simultaneous classification and estimation of hidden parameters in a sensor network with communications constraints. In particular, we consider a network of noisy sensors which measure a common scalar unknown parameter. We assume that a fraction of the nodes represent faulty sensors, whose measurements are poorly reliable. The goal for each node is to simultaneously identify its class (faulty or non-faulty) and estimate the common parameter. We propose a novel cooperative iterative algorithm which copes with the communication constraints imposed by the network and shows remarkable performance. Our main result is a rigorous proof of the convergence of the algorithm and a characterization of the limit behavior. We also show that, in the limit when the number of sensors goes to infinity, the common unknown parameter is estimated with arbitrary small error, while the classification error converges to that of the optimal centralized maximum likelihood estimator. We also show numerical results that validate the theoretical analysis and support their possible generalization. We compare our strategy with the Expectation-Maximization algorithm and we discuss trade-offs in terms of robustness, speed of convergence and implementation simplicity.