Anisotropic Sparse Gauss-Hermite Quadrature Filter

In this paper, a new nonlinear filter based on the anisotropic sparse Gauss-Hermite quadrature (ASGHQ) is proposed. The sparse Gauss-Hermite quadrature (SGHQ) has been recently proposed and used in the nonlinear filtering to overcome the curse-of-dimensionality problem in the conventional Gauss-Hermite Quadrature (GHQ). SGHQ is more efficient to use since the number of SGHQ points increases polynomially with dimension whereas the number of GHQ points increases exponentially with dimension. In this paper, we propose to use ASGHQ to design a new nonlinear filter as an extension of SGHQ. The advantage of ASGHQ is that the design of quadrature incorporates the information of the system which is neglected by GHQ or SGHQ. As a result, the quadrature points in the filter algorithm can be further reduced and thus, this new nonlinear filter is particularly useful for high dimensional nonlinear filtering problems. In addition, the accuracy of ASGHQ is analyzed. The performance of this new filter is demonstrated by the application to the attitude estimation problem, which demonstrates much better performance than the extended Kalman filter (EKF), unscented Kalman filter (UKF) and more efficient than the filters based on SGHQ and GHQ.

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