Distributed Local Linear Parameter Estimation Using Gaussian SPAWN

We consider the problem of estimating local sensor parameters, where the local parameters and sensor observations are related through linear stochastic models. We study the Gaussian Sum-Product Algorithm over a Wireless Network (gSPAWN) procedure. Compared with the popular diffusion strategies for performing network parameter estimation, whose communication cost at each sensor increases with increasing network density, gSPAWN 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 gSPAWN converges in mean and has mean-square stability under some technical sufficient conditions, and we describe an application of gSPAWN 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 per sensor, with comparable root-mean-square errors.