Sparse Gauss-Hermite Quadrature Filter for Orbit Estimation
Bin Jia, Ming Xin, Yang Cheng · 2010
In this paper, a new nonlinear filter based on Sparse Gauss-Hermite Quadrature (SGHQ) is proposed for orbit estimation. Although Gauss-Hermite Quadrature (GHQ) has been widely used in numerical integration, its usage in nonlinear filtering is relatively new with a few successful applications to one-dimensional problems. It is difficult to use for higher dimensional nonlinear filtering problems because the conventional GHQ based filter that uses product operations is difficult to implement as the number of points increases exponentially with dimension. In this work, we use the sparse grid method based on the Smolyak’s Product Rule to design a new sparse GHQ filter to alleviate the curse-of-dimensionality problem. The number of SGHQ points needed for higher dimensional problems is dramatically less than that of the original method. The performance of this new filter is demonstrated through the orbit estimation problem, which demonstrates better results than the Extended Kalman Filter (EKF).