  In multi-object inference, the multi-object probability density captures the
uncertainty in the number and the states of the objects as well as the
statistical dependence between the objects. Exact computation of the
multi-object density is generally intractable and tractable implementations
usually require statistical independence assumptions between objects. In this
paper we propose a tractable multi-object density approximation that can
capture statistical dependence between objects. In particular, we derive a
tractable Generalized Labeled Multi-Bernoulli (GLMB) density that matches the
cardinality distribution and the first moment of the labeled multi-object
distribution of interest. It is also shown that the proposed approximation
minimizes the Kullback-Leibler divergence over a special tractable class of
GLMB densities. Based on the proposed GLMB approximation we further demonstrate
a tractable multi-object tracking algorithm for generic measurement models.
Simulation results for a multi-object Track-Before-Detect example using radar
measurements in low signal-to-noise ratio (SNR) scenarios verify the
applicability of the proposed approach.
