  Multi-object density is a fundamental descriptor of a point process and has
ability to describe the randomness of number and values of objects, as well as
the statistical correlation between objects. Due to its comprehensive nature,
it usually has a complicate mathematical structure making the set integral
suffering from the curse of dimension and the combinatorial nature of the
problem. Hence, the approximation of multi-object density is a key research
theme in point process theory or finite set statistics (FISST). Conventional
approaches usually discard part or all of statistical correlation mechanically
in return for computational efficiency, without considering the real situation
of correlation between objects. In this paper, we propose an enhanced
approximation of labeled multi-object (LMO) density which evaluates the
correlation between objects adaptively and factorizes the LMO density into
densities of several independent subsets according to the correlation analysis.
Besides, to get a tractable factorization of LMO density, we derive the set
marginal density of any subset of the universal labeled RFS, the generalized
labeled multi-Bernoulli (GLMB) RFS family and its subclasses. The proposed
method takes into account the simplification of the complicate structure of LMO
density and the reservation of necessary correlation at the same time.

Systems and Control