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The wide variety of applications for wireless sensor networks combined with the energy constrained nature of sensor nodes has motivated research on algorithms for in-network estimation of measured physical quantities to reduce the amount of data that needs to be transmitted to the sink. The main contribution of this work is a distributed estimation solution that leverages the broadcast nature of the wireless channel in sensor networks. We present a data dissemination protocol, called Kalsip, which is designed to support the implementation of our distributed estimation algorithm based on Kalman filters. We show, through analysis and simulation, that our protocol provides accurate estimation of physical properties while minimizing the number of transmissions needed and requiring nodes to only overhear estimates broadcast by their neighbors.