Convergence of loopy belief propagation for data association

Data association is the problem of determining the correspondence between targets and measurements. In this paper, we present a graphical model approach to data association and apply an approximate inference method, loopy belief propagation, to obtain the marginal association weights (e.g., for JPDA). In general, loopy belief propagation is not guaranteed to converge, and when convergence is obtained the result is not guaranteed to be the correct answer. We investigate the convergence properties of a loopy belief propagation algorithm for data association, proving that it converges, and demonstrating its practical efficiency. A greatly simplified implementation is provided, which exploits the structure in the factors to reduce the cost per iteration from O(m²n²) to O(mn) operations where n is the number of targets and m is the number of measurements. Combined with the previously published results on the accuracy of the approximation, the convergence results reveal loopy belief propagation as a highly attractive method for approximate calculation of joint association weights.