Seventh-degree spherical simplex-radial cubature Kalman filter

This paper proposes a new seventh-degree spherical simplex-radial rule based on the seventh-degree spherical simplex rule and seventh-degree radial rule, then a new seventh-degree spherical simplex-radial cubature Kalman filter (SSRCKF) is developed by using the proposed cubature rule to numerically compute the Gaussian weighted integrals involved in the Gaussian filter (GF). The proposed filter has higher filtering accuracy than the existing SSRCKF. Besides, the proposed seventh-degree SSRCKF has almost consistent filtering accuracy with the Gauss-Hermite quadrature filter (GHQF) but less computation burden than the GHQF. A numerical simulation example including high nonlinearities, large process noise and large initial estimation errors shows the superiority and effectiveness of the proposed filter.