Deterministic Dirac mixture approximation of Gaussian mixtures

In this work, we propose a novel way to approximating mixtures of Gaussian distributions by a set of deter-ministically chosen Dirac delta components. This approximation is performed by adapting a method for approximating single Gaussian distributions to the considered case. The proposed method turns the approximation problem into an optimization problem by minimizing a distance measure between the Gaussian mixture and its Dirac mixture approximation. Compared to the simple Gaussian case, the minimization criterion is much more complex as multiple, non-standard Gaussian distributions have to be considered.