This paper deals with the problem of estimating the state of a discrete-time linear stochastic dynamical system on the basis of data collected from multiple sensors subject to a limitation on the communication rate from the sensors. More specifically, the attention is devoted to a centralized sensor network consisting of: (1) multiple remote nodes which collect measurements of the given system, compute state estimates at the full measurement rate and transmit data (either raw measurements or estimates) at a reduced communication rate; (2) a fusion node that, based on received data, provides an estimate of the system state at the full rate. Local data-driven transmission strategies are considered and issues related to the stability and performance of such strategies are investigated. Simulation results confirm the effectiveness of the proposed strategies. (C) 2012 Elsevier Ltd. All rights reserved.