Distributed Maximum Likelihood Estimation with Time-Varying Network Topology

We consider a sensor network in which each sensor may take at every time iteration a noisy linear measurement of some unknown parameter. In this context, we study a distributed consensus diffusion scheme that relies only on bidirectional communication among neighbor nodes (nodes that can communicate and exchange data), and allows every node to compute an estimate of the unknown parameter that asymptotically converges to the true parameter. At each time iteration, a measurement update and a spatial diffusion phase are performed across the network, and a local least-squares estimate is computed at each node. We show that the local estimates converge to the true parameter value, under suitable hypotheses. The proposed scheme works in networks with dynamically changing communication topology, and it is robust to unreliable communication links and widespread failures in measuring nodes.