Fusion of Labeled RFS Densities with Minimum Information Loss

This paper addresses fusion of labeled random finite set (LRFS) densities according to the criterion of minimum information loss (MIL). The MIL criterion amounts to minimizing the (weighted) sum of Kullback-Leibler divergences (KLDs) with the fused density appearing as righthand argument of the KLDs. The optimal fused density following the MIL rule is the linear opinion pool of local ones. However such results cannot be directly applied to the marginalized δ-generalized labeled multi-Bernoulli (Mδ-GLMB) and labeled multi-Bernoulli (LMB) densities since the resulting fused densities are not belonging to the same family of local ones, thus cannot be adopted in the context of Bayesian filtering which requires the conjugacy of prior. In order to overcome such difficulties, when LRFS densities are Mδ-GLMB or LMB, the MIL rule is further elaborated by imposing the constraint that the fused density be in the same family of local ones. The resulting fusion rules are derived in closed form and the error of replacing the optimal fused density with the best Mδ-GLMB/LMB one is theoretically analyzed. The derivation of MIL fusion of Mδ-GLMB/LMB densities is based on the assumption that their label spaces have been matched, which, however, cannot be satisfied in the majority of practical applications. It is shown theoretically that label matching can be solved as a separate problem with respect to LRFS density fusion by resorting to the MIL criterion. Finally, the performance of the proposed fusion approach is assessed via simulation experiments concerning distributed multitarget tracking (DMT) on a sensor network.