A distributed classification/estimation algorithm for sensor networks

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