This paper considers the state-space smoothing problem in a distributed fashion. In the scenario of sensor networks, we assume that the nodes can be ordered in space and have access to noisy measurements relative to different but correlated states. The goal of each node is to obtain the minimum variance estimate of its own state conditional on all the data collected by the network using only local exchanges of information. We present a cooperative smoothing algorithm for Gauss Markov linear models and provide an exact convergence analysis for the algorithm, also clarifying its advantages over the Jacobi algorithm. Extensions of the numerical scheme able to perform field estimation using a grid of sensors are also derived. (C) 2013 Elsevier Ltd. All rights reserved.