Distributed linear parameter estimation in sensor networks: Convergence properties

The paper considers the problem of distributed linear vector parameter estimation in sensor networks, when sensors can exchange quantized state information and the inter-sensor communication links fail randomly. We show that our algorithm LU leads to almost sure (a.s.) consensus of the local sensor estimates to the true parameter value, under the assumptions that, a minimal global observability criterion is satisfied and the network is connected in the mean, i.e., lambda₂(Lmacr) Gt 0, where Lmacr is the expected Laplacian matrix. We show that the local sensor estimates are asymptotically normal and characterize the convergence rate of the algorithm in the framework of moderate deviations.