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Belief propagation (BP) is a powerful tool to solve distributed inferenceproblems, though it is limited by short cycles in the corresponding factorgraph. Such cycles may lead to incorrect solutions or oscillatory behavior.Only for certain types of problems are convergence properties understood. Weextend this knowledge by investigating the use of reweighted BP for distributedlikelihood fusion problems, which are characterized by equality constraintsalong possibly short cycles. Through a linear formulation of BP, we are able toanalytically derive convergence conditions for certain types of graphs andoptimize the convergence speed. We compare with standard belief consensus andobserve significantly faster convergence.

Optimizing Reweighted Belief Propagation for Distributed Likelihood Fusion Problems