Generalized Labeled Multi-Bernoulli Approximation of Multi-Object Densities

In multiobject inference, the multiobject 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 multiobject density is generally intractable and tractable implementations usually require statistical independence assumptions between objects. In this paper we propose a tractable multiobject 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 multiobject 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 multiobject tracking algorithm for generic measurement models. Simulation results for a multiobject Track-Before-Detect example using radar measurements in low signal-to-noise ratio (SNR) scenarios verify the applicability of the proposed approach.