Recursive Prediction of Stochastic Nonlinear Systems Based on Optimal Dirac Mixture Approximations

This paper introduces a new approach to the recursive propagation of probability density functions through discrete-time stochastic nonlinear dynamic systems. An efficient recursive procedure is proposed that is based on the optimal approximation of the posterior densities after each prediction step by means of Dirac mixtures. The parameters of the individual components are selected by systematically minimizing a suitable distance measure in such a way that the future evolution of the approximate densities is as close to the exact densities as possible.