Ensuring High Performance of Consensus-Based Estimation by Lifetime Maximization in WSNs

The estimation of a parameter corrupted by noise is a common tasks in wireless sensor networks, where the deployed nodes cooperate in order to improve their own inaccurate observations. This cooperation usually involves successive data exchanges and local information updates until a global consensus value is reached. The quality of the final estimator depends on the amount of collected observations, hence the number of active nodes. Moreover, the inherent iterative nature of the consensus process involves a certain energy consumption. Since the devices composing the network are usually battery powered, nodes becoming inactive due to battery depletion emerges as a serious problem. In this work, we aim to maximize the lifetime of the most energy demanding nodes, such that the quality of the global estimator is maintained above a certain threshold. To this end, we optimize the network topology considering both the duration of each consensus process, given by the algebraic connectivity of the network, and the power consumption per iteration of the most demanding nodes. Numerical results are provided to demonstrate the validity and efficiency of our methodology.