Extension of the sparse grid quadrature filter

The sparse grid quadrature filter is a point-based Gaussian filter in which expectations of nonlinear functions of Gaussian random vectors are computed using the sparse grid quadrature. The sparse grid quadrature can be considered a generalization of the Unscented Transform in that the Unscented Transform is equivalent to the level-2 sparse grid quadrature. A novel extension of the sparse grid quadrature filter is presented that directly transforms the points in time update and measurement update to eliminate repeated covariance decomposition based point generation and to relax the Gaussian assumption inherent in the sparse grid quadrature filter as well as the sigma-point filters. A tracking example is presented to demonstrate the performance of the novel filter.