Sigma point transformation for gaussian mixture distributions

This paper describes the development of an approximate method for propagating un- certainty through stochastic dynamical systems using a quadrature rule integration based method. The development of quadrature rules for Gaussian mixture distributions is dis- cussed. A numerical solution to this problem is considered that uses a Gram-Schmidt process. Simulation results are presented where the quadrature points are calculated in two different ways, one using an unscented transformation and the other using the method discussed in this work. The proposed method outperforms the unscented transformation and provides signs of optimism for improving nonlinear filtering.