We consider the problem of estimating local sensor parameters, where the local parameters and sensor observations are related through linear stochastic models. Sensors exchange messages and cooperate with each other to estimate their own local parameters iteratively. We study the Gaussian Sum-Product Algorithm over a Wireless Network (gSPAWN) procedure, which is based on belief propagation, but uses fixed size broadcast messages at each sensor instead. Compared with the popular diffusion strategies for performing network parameter estimation, whose communication cost at each sensor increases with increasing network density, the gSPAWN algorithm allows sensors to broadcast a message whose size does not depend on the network size or density, making it more suitable for applications in wireless sensor networks. We show that the gSPAWN algorithm converges in mean and has mean-square stability under some technical sufficient conditions, and we describe an application of the gSPAWN algorithm to a network localization problem in non-line-of-sight environments. Numerical results suggest that gSPAWN converges much faster in general than the diffusion method, and has lower communication costs, with comparable root mean square errors.
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