Distributed Linear Parameter Estimation in Sensor Networks based on Laplacian Dynamics Consensus Algorithm

Abstract

In this paper, we consider the problem of distributed linear parameter estimation in static and dynamic sensor networks. We propose iterative averaging algorithms based on Laplacian dynamics which converge to the centralized least squares solution asymptotically. In the first part of this paper, we consider the case of unclustered (flat architecture) sensor networks and analyze convergence of the iterative algorithm, for both static and dynamic topologies. Subsequently, we extend our analysis to static but clustered sensor networks with pulsed inter-cluster updates. In this scheme, we assume that all inter-cluster communications occur every H time steps, H > 1, and the corresponding updates are held till the next update instant. Depending on the sensor locations and the topology formation algorithm used, it may be the case that inter-cluster communications require higher transmitter power support than intra-cluster communications. From a power efficiency (or alternately, network lifetime) point of view, it may therefore be beneficial to limit the extent of inter-cluster communication, without significantly enhancing the convergence time of the distributed estimation algorithm. We anticipate that a pulsed inter-cluster update scheme will also be beneficial for applications such as military sensor networks, where low probability of detection and interception is essential. Our analysis provides sufficient conditions under which the distributed algorithm operating on a pulsed inter-cluster update scheme converges. Simulation results are provided which illustrate the dependence of the convergence rate of the algorithm on H