In this paper, a novel robust Student’s t-based Kalman filter (RSTKF) is proposed to solve the problem of a linear system with heavy-tailed process and measurement noises (HPMN) and colored measurement noise (CMN). The above problem is transformed into the filtering problem of a linear system with HPMN and white measurement noise after using the measurement differencing method and state augmentation approach. The augmentation state vector, the scale matrix and the auxiliary random variables are jointly estimated based on the variational Bayesian approach. Simulation results are provided to demonstrate the superiority of the proposed RSTKF by comparing with the existing filtering algorithms for systems with HPMN and CMN.

中文翻译：

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一种带有彩色测量噪声的新型学生基于 t 的卡尔曼滤波器

在本文中，提出了一种新颖的鲁棒基于学生 t 的卡尔曼滤波器 (RSTKF) 来解决具有重尾过程和测量噪声 (HPMN) 和有色测量噪声 (CMN) 的线性系统的问题。使用测量差分方法和状态增强方法后，将上述问题转化为具有HPMN和测量白噪声的线性系统的滤波问题。基于变分贝叶斯方法联合估计增强状态向量、尺度矩阵和辅助随机变量。通过与 HPMN 和 CMN 系统的现有滤波算法进行比较，仿真结果证明了所提出的 RSTKF 的优越性。