  In this paper, we address the problem of the distributed multi-target
tracking with labeled set filters in the framework of Generalized Covariance
Intersection (GCI). Our analyses show that the label space mismatching (LS-DM)
phenomenon, which means the same realization drawn from label spaces of
different sensors does not have the same implication, is quite common in
practical scenarios and may bring serious problems. Our contributions are
two-fold. Firstly, we provide a principled mathematical definition of "label
spaces matching (LS-DM)" based on information divergence, which is also
referred to as LS-M criterion. Then, to handle the LS-DM, we propose a novel
two-step distributed fusion algorithm, named as GCI fusion via label spaces
matching (GCI-LSM). The first step is to match the label spaces from different
sensors. To this end, we build a ranked assignment problem and design a cost
function consistent with LS-M criterion to seek the optimal solution of
matching correspondence between label spaces of different sensors. The second
step is to perform the GCI fusion on the matched label space. We also derive
the GCI fusion with generic labeled multi-object (LMO) densities based on LS-M,
which is the foundation of labeled distributed fusion algorithms. Simulation
results for Gaussian mixture implementation highlight the performance of the
proposed GCI-LSM algorithm in two different tracking scenarios.
