Abstract: Under the condition of uncertainty of integrated navigation in system state model and noise statistical characteristics, the standard Cubature Kalman Filter（CKF） algorithm robustness is poor, which easily leds to the decrease of the filtering precision, even appears the problem of filtering divergence, a H∞ robust adaptive CKF algorithm is put forward. The algorithm is based on the standard theory framework of the third-order CKF algorithm, under the condition that the observation equation is linear, simplified update of its measurement, and introduces numerical stability strong Singular Value Decomposition（SVD）, which decomposes the state covariance matrix to improve the numerical stability of the calculation. In the update process of the system state covariance matrix, H∞ filtering method is introduced, and based on the theory of matrix inequality, make adaptive selection for its constraints [γ], further to improve the filtering stability and the robustness of the system. The algorithm is used in numerical simulation experiment of GNSS/INS integrated navigation, the results verify the validity and superiority of the algorithm.

Key words: Singular Value Decomposition（SVD）, simplified cubature Kalman filter, H&infin, filter, adaptive optimization, GNSS/INS integrated navigation

摘要： 针对组合导航系统状态模型及噪声统计特性不确定的情况下，标准容积卡尔曼滤波（Cubature Kalman Filter，CKF）算法鲁棒性差，导致滤波精度下降甚至出现滤波发散的问题，提出一种H∞鲁棒自适应CKF算法。该算法基于标准的三阶CKF算法理论框架，在观测方程为线性的条件下，对其量测更新进行了简化，并引入数值稳定性较强的奇异值分解（Singular Value Decomposition，SVD）对系统状态协方差阵进行分解迭代，改善了计算的数值稳定性；在系统状态协方差阵更新过程中引入H∞ 滤波思想，并基于矩阵不等式的理论，对其约束条件[γ]进行了自适应选取，进一步改善了滤波的稳定性，提高了系统的鲁棒性。将该算法用于GNSS/INS组合导航的数值仿真实验，结果验证了该算法的有效性和优越性。

关键词: 奇异值分解, 简化的容积卡尔曼滤波, H&infin, 滤波, 自适应优化, GNSS/INS组合导航