Anisotropic Sparse Gauss-Hermite Quadrature Filter

Anisotropic sparse Gauss-Hermite quadrature filter (ASGHQF) is designed. The accuracy of the ASGHQ is guaranteed by some theorems. The ASGHQF is designed to place more GHQ points in directions with larger uncertainties according to the state covariance information, and to do this the eigenvalues of the covariance matrix are used as the metric of uncertainty. To show the efficiency of the ASGHQ, it is first applied to a numerical integration problem, and then to the spacecraft attitude estimation problem. It is found that all point-based Gaussian approximation filters share the same filtering algorithm. The primary advantage of the ASGHQF is that it is more flexible to use than the sparse Gauss-Hermite quadrature filter (SGHQF) and GHQF, allowing the designer to tune the importance vector to balance the computational load with the accuracy requirement.