Abstract:

For a nonlinear system, the Cubature Kalman Filter（CKF） is a useful method to deal with the state estimation problems and can obtain good performance under Gaussian noise. However, its performance often degrades dramatically when the noises are contaminated by some heavy-tailed noises. To cope with this problem, the Huber methodology is applied to the framework of CKF to improve its robustness instead of the traditional Minimum Mean Square Error（MMSE） criterion. In the proposed filter, a linear regression model is formulated by linearizing the measurement equation, and the fixed-point algorithm is used to solve the Huber-based minimization problem. Hence the Fixed-Point Iterated Huber-based robust Cubature Kalman Filter（FP-IHCKF） is derived, in which the prior information and measurement information are reformulated using the Huber methodology. The effectiveness and robustness of the proposed filter are demonstrated through numerical simulation study on a re-entry target tracking problem.

Key words: nonlinear filter, Cubature Kalman Filter（CKF）, Huber methodology, robustness, fixed-point algorithm

摘要：

对于非线性系统而言，容积卡尔曼滤波（Cubature Kalman Filter，CKF）算法是处理状态估计问题的一种有效方法，并且其在高斯噪声下可以获得良好的估计性能。然而，当噪声被重尾噪声污染时，其性能通常会急剧下降。为解决此问题，将Huber方法应用于CKF框架中，取代了传统的最小均方误差（Minimum Mean Square Error，MMSE）准则，以提高算法的鲁棒性。在所提算法中，通过将量测方程线性化构造了线性回归模型，并采用固定点迭代的方法求解基于Huber方法的最小化问题。因此，推导了基于固定点迭代的Huber鲁棒CKF（FP-IHCKF）算法，在该算法中先验信息和量测信息通过Huber方法进行了重构。通过对再入目标跟踪问题进行仿真，验证了所提算法的有效性和鲁棒性。

关键词: 非线性滤波, 容积卡尔曼滤波（CKF）, Huber方法, 鲁棒性, 固定点算法