一种高斯-重尾切换分布鲁棒卡尔曼滤波器

为降低实际应用中由强未知干扰和仪器故障对观测造成的影响，减轻随机和未建模干扰对系统的侵蚀，从而提升系统在非高斯噪声环境下的状态估计精度，提高滤波器的鲁棒性能，提出了一种基于高斯-重尾切换分布的鲁棒卡尔曼滤波器(Gaussian-heavy-tailed switching distribution based robust Kalman filter, GHTSRKF)。首先，通过自适应学习高斯分布和一种重尾分布之间的切换概率将噪声建模为GHTS(Gaussian-heavy-tailed switching)分布，所设计的GHTS分布可以通过在线调整高斯分布和新的重尾分布之间的切换概率来对非平稳重尾噪声进行建模，具有虚拟协方差的高斯分布用于处理协方差矩阵不准确的高斯噪声。其次，引入两个分别服从Categorical分布与伯努利分布的辅助参数将GHTS分布表示为一个分层高斯形式，进一步利用变分贝叶斯方法推导了GHTSRKF。最后，利用一个仿真场景对几种不同的RKFs(robust Kalman filters)进行了对比验证。结果表明，所提出的GHTSRKF算法的估计精度对初始状态的选...

A Gaussian-heavy-tailed switching distribution robust Kalman filter

To mitigate the influence of strong unknown disturbances and instrument faults on observations in practical applications, and to alleviate the degradation caused by random and unmodeled interferences on the system, so as to improve the state estimation accuracy of the system in non-Gaussian noise environment and the robustness of the filter, a Gaussian-heavy-tailed switching distribution based robust Kalman filter (GHTSRKF) is proposed. Firstly, the noises are modeled as a GHTS（Gaussian-heavy-tailed switching）distribution by adaptively learning the switching probability between the Gaussian distribution and the newly designed heavy-tailed distribution. The designed GHTS distribution can model non-stationary heavy tail noise by adjusting the switching probability between the Gaussian distribution and the new heavy-tailed distribution online. The Gaussian distribution with a virtual covariance is used to deal with Gaussian noise with inaccurate covariance matrix. Secondly, two auxiliary parameters following the category distribution and the Bernoulli distribution are introduced to express the GHTS distribution as a hierarchical Gaussian form. Furthermore, the GHTSRKF is derived by utilizing the variational Bayesian method. Finally, a simulation scenario is used to compare and verify several different robust Kalman filters (RKFs). The results show that the accuracy of the proposed GHTSRKF algorithm is insensitive to the selection of initial state and exhibits higher estimation accuracy compared to other RKFs. Its root mean square errors（RMSEs）are closest to those of KF with true noise covariances（KFTNC）with accurate noise information. Compared with existing filters, GHTSRKF has better estimation performance when the system and measurement noise are unknown time-varying Gaussian noise, thus verifying the effectiveness of GHTSRKF.