Abstract: The traditional Cubature Kalman Filter（CKF） has problems of low accuracy and even divergence when dealing with highly nonlinear systems, and High-Degree Cubature Kalman Filter（HCKF） increases the accuracy while greatly increasing the computational complexity, at the same time, negative weight affects the stability of the algorithm in high-dimensional systems. In view of the above problems, this paper proposes an Adaptive Mixed-degree Spherical Simplex-Radial Cubature Kalman Filter（AMSSRCKF）, which adopts Mixed-degree Spherical Simplex-Radial（MSSR） sampling to obtain higher accuracy than CKF, and combines with the strong tracking filter algorithm of multiple fading factors to improve the robustness of the algorithm. The algorithm is applied to the simulation of the integrated navigation system, the results show that AMSSRCKF can effectively suppress the impact of the sudden change of the system state and improve the positioning accuracy and robustness of the integrated navigation system.

Key words: Cubature Kalman Filter（CKF）, mix-degree, spherical simplex-radial, adaptive, suboptimal multiple fading factor, integrated navigation

摘要： 传统的容积卡尔曼滤波（CKF）在处理强非线性系统时存在精度低甚至发散的问题，高阶容积卡尔曼滤波（HCKF）提高精度的同时也会大幅度提高计算复杂度，同时在高维系统中存在负权值影响算法的稳定性。针对以上问题提出了一种自适应混合阶球面最简相径容积卡尔曼滤波（AMSSRCKF），该算法采用混合阶最简相径容积规则（MSSR）采样获得了比CKF更高的精度，同时结合了多重渐消因子强跟踪滤波算法，提高了算法的鲁棒性。最后，将该算法应用于组合导航系统仿真，结果表明，AMSSRCKF可以有效抑制系统状态突变的影响，提高了组合导航系统的定位精度和鲁棒性。

关键词: 容积卡尔曼滤波, 混合阶, 球面最简相径, 自适应, 多重渐消因子, 组合导航