Joint Sensor Selection and Multihop Routing for Distributed Estimation in Ad-hoc Wireless Sensor Networks

This paper considers the problem of power-efficient distributed estimation of vector parameters related to localized phenomena so that both sensor selection and routing structure in a Wireless Sensor Network (WSN) are jointly optimized to obtain the best possible estimation performance at a given querying node, for a given total power budget. First, we formulate our problem as an optimization problem and show that it is an NP-Hard problem. Then, we design two algorithms: a Fixed-Tree Relaxation-Based Algorithm (FTRA) and a very efficient Iterative Distributed Algorithm (IDA) to optimize the sensor selection and routing structure. We also provide a lower bound for our optimization problem and show that our IDA provides a performance that is close to this bound, and it is substantially superior to the previous approaches presented in the literature. An important result from our work is the fact that because of the interplay between communication cost and estimation gain when fusing measurements from different sensors, the traditional Shortest Path Tree (SPT) routing structure, widely used in practice, is no longer optimal. To be specific, our routing structure provides a better trade-off between the overall power efficiency and estimation accuracy. Comparing to more conventional sensor selection and fixed routing algorithms, our proposed algorithms yield a significant amount of energy saving for the same estimation accuracy.