  Belief propagation (BP) is a powerful tool to solve distributed inference
problems, though it is limited by short cycles in the corresponding factor
graph. Such cycles may lead to incorrect solutions or oscillatory behavior.
Only for certain types of problems are convergence properties understood. We
extend this knowledge by investigating the use of reweighted BP for distributed
likelihood fusion problems, which are characterized by equality constraints
along possibly short cycles. Through a linear formulation of BP, we are able to
analytically derive convergence conditions for certain types of graphs and
optimize the convergence speed. We compare with standard belief consensus and
observe significantly faster convergence.
