In-Network Local Distributed Estimation for Power-Constrained Wireless Sensor Networks

In this paper, we consider the problem of power-efficient distributed estimation of a localized event in the large-scale Wireless Sensor Networks (WSNs). In order to increase the power efficiency in these networks, we develop a joint optimization problem that involves both selecting a subset of active sensors and the routing structure so that the quality of estimation at a given querying node is the best possible subject to a total imposed communication cost. We first formulate our problem as an optimization problem and show that it is NP-Hard. Then, we propose a local distributed optimization algorithm that is based on an Estimate-and-Forward (EF) strategy, which allows to perform sequentially this joint optimization in an efficient way. We also provide a lower bound for our optimization problem and show that our local distributed optimization algorithm provides a performance that is close to this bound. Although there is no guarantee that the gap between this lower bound and the optimal solution of the main problem is always small, our numerical experiments support that this gap is actually very small in many cases. An important result from our work is that because of the interplay between the communication cost over the links and the gains in estimation accuracy obtained by choosing certain sensors, the traditional Shortest Path Tree (SPT) routing structure, widely used in practice, is no longer optimal, that is, our routing structures provide a better trade-off between the overall power efficiency and the final estimation accuracy obtained at the querying node. Our experimental results show that our algorithms yield a significant energy saving.