Wireless Sensor Networks (WSNs) enable a wealth of new applications where remote estimation is essential. Individual sensors simultaneously sense a dynamic process and transmit measured information over a shared channel to a central base station. The base station computes an estimate of the process state by means of a Kalman filter. In this paper we assume that, at each time step, only a subset of all sensors are selected to send their observations to the fusion center due to channel capacity constraints or limited energy budget. We propose a multi-step sensor selection strategy to schedule sensors to transmit for the next T steps of time with the goal of minimizing an objective function related to the Kalman filter error covariance matrix. This formulation, in a relaxed convex form, defines an unified framework to solve a large class of optimization problems over energy constrained WSNs. We offer some numerical examples to further illustrate the efficiency of the algorithm. (C) 2011 Elsevier Ltd. All rights reserved.