Sparse approximation based Gaussian mixture model approach for uncertainty propagation for nonlinear systems

A new method is proposed to determine the number of components that are sufficient to estimate the probability density function of a non-linear dynamic system using Gaussian sum filter. This method is based upon the combination of L₁ and L₂ norm. While L₁ norm tries to shift the solution towards one of the vertices of the simplex, thus, minimizing the number of non-zero quantities, the L₂ norm tries to reduce the error to as low as possible. Unlike previous methods, the method proposed in this paper is simple and computationally less expensive.