Fusion of labeled RFS densities with minimum information loss

Abstract: 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. In order to ensure the fused density to be consistent with the local ones when LRFS densities are marginal $\delta$-generalized labeled multi-Bernoulli (M$\delta$-GLMB) or labeled multi-Bernoulli (LMB) densities, the MIL rule is further elaborated by imposing the constraint that the fused density be in the same family of local ones. In order to deal with different fields-of-view (FoVs) of the local densities, the global label space is divided into disjoint subspaces which represent the exclusive FoVs and the common FoV of the agents, and each local density is decomposed into the sub-densities defined in the corresponding subspaces. Then fusion is performed subspace-by-subspace to combine local subdensities into global ones, and the global density is obtained by multiplying the global sub-densities. Further, in order to tackle the label mismatching issue arising in practical applications, a rank assignment optimization (RAO) of a suitably defined cost is carried out so as to match labels from different agents. Moreover, issues concerning implementation of the MIL rule and its application to distributed multitarget tracking (DMT) are discussed. Finally, the performance of the proposed fusion approach is assessed via simulation experiments considering DMT with either the same or different FoVs of the agents.