I. Introduction
This paper provides an efficient method for approximating a given continuous probability density function (pdf) by a deterministic Dirac mixture density. The resulting Dirac mixture density is then used to simplify the typical operations in system identification, state estimation, filtering, data fusion, and control such as transforming random variables with nonlinear mappings or performing numerical integration for calculating nonlinear moments. State-of-the-art Dirac mixture approximations are currently used in diverse nonlinear filters such as Gaussian filters, e.g., the S2KF [1] and PGF42 [2], or in particle-based model-predictive control.