In view of the problem that the utilization efficiency of points is low in sparse Gauss-Hermite quadrature filter(SGHQF), an adaptive anisotropic SGHQF(AASGHQF) based on observable degree analysis of state parameters is proposed. A mechanism for controlling accuracy level of each dimension is presented by utilizing the state parameters’ observable degree and the anisotropic importance vector, which can distribute the quadrature points nonuniformly and reasonably. The AASGHQF is applied to the CNS/SAR/SINS nonlinear integrated navigation system and compared with the UKF and the SGHQF. Simulation results show that the AASGHQF is more accurate than the UKF and has very close performance with the SGHQF. In addition, the AASGHQ points are decreased substantially and the computation efficiency is higher compared with the SGHQF.