Sparse Gauss-Hermite Quadrature filter for spacecraft attitude estimation

In this paper, a new nonlinear filter based on Sparse Gauss-Hermite Quadrature (SGHQ) is proposed for spacecraft attitude estimation. Gauss-Hermite Quadrature (GHQ) has been widely used in numerical integration and nonlinear filtering. However, for multi-dimensional problems, the conventional GHQ based filter using product operations is difficult to implement because the number of points increases exponentially with dimensions. To solve this problem, the Smolyak´s product rule has been used to extend GHQ rule to high dimensional problems. The contribution of this work is to design a new sparse-grid GHQ filter using Smolyak´s product rule to alleviate the curse-of-dimensionality problem of the conventional GHQ filter. The number of SGHQ points needed for high dimensional problems is considerably smaller than the original GHQ method. Hence, the efficiency of using GHQ can be significantly improved. The performance of this new filter is demonstrated by the application to the spacecraft attitude estimation problem, which shows better results than the Extended Kalman Filter (EKF).