  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.
