Direct fusion of Dirac mixture densities using an efficient approximation in joint state space

In this paper, we present a direct fusion algorithm for processing the combination of two Dirac mixture densities. The proposed approach allows the multiplication of two Dirac mixture densities without requiring identical support and thus enables the fusion of two independently generated sample sets. The resulting posterior Dirac mixture density is an approximation of the true continuous density that would result from the processing of the underlying true continuous density functions. This procedure is based on a suboptimal greedy approximation of the joint state space by means of a Dirac mixture that iteratively increases the resolution of the fusion result while considering only the relevant regions in the joint state space, where the fusion constraint holds.