Clustering in Distributed Incremental Estimation in Wireless Sensor Networks

Energy efficiency, low latency, high estimation accuracy, and fast convergence are important goals in distributed incremental estimation algorithms for sensor networks. One approach that adds flexibility in achieving these goals is clustering. In this paper, the framework of distributed incremental estimation is extended by allowing clustering amongst the nodes. Among the observations made is that a scaling law exists where the estimation accuracy increases proportionally with the number of clusters. The distributed parameter estimation problem is posed as a convex optimization problem involving a social cost function and data from the sensor nodes. An in-cluster algorithm is then derived using the incremental subgradient method. Sensors in each cluster successively update a cluster parameter estimate based on local data, which is then passed on to a fusion center for further processing. We prove convergence results for the distributed in-cluster algorithm, and provide simulations that demonstrate the benefits clustering for least squares and robust estimation in sensor networks.