Distribution Estimation for Global Data Association via Approximate Bayesian Inference

Global data association is an essential prerequisite for robot operation in environments seen at different times or by different robots. Repetitive or symmetric data creates significant challenges for existing methods, which typically rely on maximum likelihood estimation or maximum consensus to produce a single set of associations. However, in ambiguous scenarios, the distribution of solutions to global data association problems is often highly multimodal, and such single-solution approaches frequently fail. In this work, we introduce a data association framework that leverages approximate Bayesian inference to capture multiple solution modes to the data association problem, thereby avoiding premature commitment to a single solution under ambiguity. Our approach represents hypothetical solutions as particles that evolve according to a deterministic or randomized update rule to cover the modes of the underlying solution distribution. Furthermore, we show that our method can incorporate optimization constraints imposed by the data association formulation and directly benefit from GPU-parallelized optimization. Extensive simulated and real-world experiments with highly ambiguous data show that our method correctly estimates the distribution over transformations when registering point clouds or object maps.