Joint sensor selection and routing for distributed estimation in wireless sensor networks

We consider a wireless sensor network (WSN) deployed over a large geographical area, where a querying node wishes to perform a estimation of a localized phenomenon. We formulate the problem as a joint optimization of sensor selection and routing structure where we minimize the estimation distortion subject to a total communication power constraint for the WSN. Two scenarios are analyzed: measurement forwarding and estimation-and-forward at the nodes. We show that the optimization problems corresponding to these scenarios are both NP-hard and we propose two approximation algorithms. First, we present a sensor selection algorithm for a predefined routing structure based on a primal relaxation and then, a greedy approximation algorithm that jointly optimizes the sensor selection and routing structure. Numerical results show good performance of these algorithms in both estimation scenarios.