Abstract:  To further improve the filtering accuracy and robustness of high-degree cubature Kalman filter when the random variable within non-Gaussian distribution, this paper presents a new filtering algorithm named Huber-based robust high-degree cubature Kalman filter algorithm. It is interpreted that the basic idea of Huber method acting on Kalman filter can be described as truncating the average from the perspective of recursive Bayesian approximation estimation. The observation vector is preprocessed by Huber method within the framework of the existed filtering, then the normal measurement update is implemented by using the preprocessed observation information, the robustness of the HCKF algorithm is realized consequently. The new method without approximating nonlinear measurements model by using the statistical linear regression model, the preponderance of high-degree cubature transform is fully used and the high precision is maintained while the robustness is ensured. Simulations in the context of univariate non-stationary growth model and the problem of reentry vehicle tracking demonstrate that the new method has superior performance in robustness and efficiency.

Key words: Huber method, Gaussian filter, high-degree cubature rule, robustness, filtering accuracy

摘要： 为提高随机变量非高斯分布时高阶容积卡尔曼滤波（High-degree Cubature Kalman Filter，HCKF）算法的鲁棒性，提出了一种基于Huber方法的鲁棒高阶容积卡尔曼滤波算法。从近似贝叶斯估计角度解释了Huber方法作用于卡尔曼滤波算法的本质是对新息进行截断平均，通过在现有滤波框架内利用Huber方法对观测量进行预处理，并将处理后的观测量进行标准的HCKF量测更新，实现了HCKF算法的鲁棒化。所提算法无需通过统计线性回归模型对系统的非线性量测模型进行近似，高阶容积变换的优势得到充分利用，从而在保持鲁棒性的前提下提高了算法的滤波精度。单变量非平稳增长模型和再入飞行器目标跟踪问题验证了该算法在鲁棒性和滤波精度方面的优势。

关键词: Huber方法, 高斯滤波, 高阶容积准则, 鲁棒性, 滤波精度