Fusion in sensor networks: convergence study

In sensor networks, many sensors cooperate and collaborate to monitor overlapping subsets from a set of targets. We consider the important issue of fusing their soft decisions. These soft decisions depend on the sensor measurements and take the form of probability densities. Consequently, data fusion becomes a problem of probabilistic inference on a factor graph of arbitrary topology, which can be accomplished by belief propagation. This paper studies the convergence of belief propagation when the soft decisions are Gaussian densities, that is, studies the convergence of the variances and means computed by belief propagation. We show that if the spectral radius ρ of a certain matrix is less than one, the means resulting from belief propagation converge to the true means. This extends to general topology sensor networks the results for a fully-connected network of two sensors and m targets in (P. Rusmevichientong et al., IEEE Trans. Inform. Theory, vol.47, no.2, p.745-765, 2001).