  As a fundamental piece of multi-object Bayesian inference, multi-object
density has the ability to describe the uncertainty of the number and values of
objects, as well as the statistical correlation between objects, thus perfectly
matches the behavior of multi-object system. However, it also makes the set
integral suffer from the curse of dimensionality and the inherently
combinatorial nature of the problem. In this paper, we study the approximations
for the universal labeled multi-object (LMO) density and derive several
principled approximations including labeled multi-Bernoulli, labeled Poisson
and labeled independent identically clustering process based approximations.
Also, a detailed analysis on the characteristics (e.g., approximation error and
computational complexity) of the proposed approximations is provided. Then some
practical suggestions are made for the applications of these approximations
based on the preceding analysis and discussion. Finally, an numerical example
is given to support our study.
