A Novel Robust Gaussian-Student's t Mixture Distribution Based Kalman Filter
A Novel Robust Gaussian-Student's t Mixture Distribution Based Kalman Filter
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基于鲁棒高斯-Student混合分布的卡尔曼滤波器
DOI：
10.1109/tsp.2019.2916755
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发表时间：
2019-07-01
影响因子：
5.4
通讯作者：
Chambers, Jonathon A.
中科院分区：
文献类型：
--
作者：
Huang, Yulong;Zhang, Yonggang;Chambers, Jonathon A.
本文提出了一种新的高斯-学生t混合（GSTM）分布来模拟非平稳重尾噪声。通过引入一个Bernoulli随机变量，将GSTM分布表示为一个分层高斯分布，并在此基础上构造了一个新的分层线性高斯状态空间模型.基于变分贝叶斯方法构造的分层线性高斯状态空间模型，提出了一种新的基于GSTM分布的鲁棒卡尔曼滤波器。卡尔曼滤波器和鲁棒的基于学生t的卡尔曼滤波器（RSTKF）与固定的分布参数的两个现有的特殊情况下，该滤波器。新的GSTM分布式卡尔曼滤波器具有重要的优势比RSTKF的混合参数的自适应更直接的自由度参数的学习。仿真结果表明，对于带有非平稳重尾噪声的线性状态空间模型，该滤波器具有比Kalman滤波器和RSTKF更好的估计精度。
In this paper, a novel Gaussian-Student's t mixture (GSTM) distribution is proposed to model non-stationary heavytailed noises. The proposed GSTM distribution can be formulated as a hierarchical Gaussian form by introducing a Bernoulli random variable, based on which a new hierarchical linear Gaussian state-space model is constructed. A novel robust GSTM distribution based Kalman filter is proposed based on the constructed hierarchical linear Gaussian state-space model using the variational Bayesian approach. The Kalman filter and robust Student's t based Kalman filter (RSTKF) with fixed distribution parameters are two existing special cases of the proposed filter. The novel GSTM distributed Kalman filter has the important advantage over the RSTKF that the adaptation of the mixing parameter is much more straightforward than learning the degrees of freedom parameter. Simulation results illustrate that the proposed filter has better estimation accuracy than those of the Kalman filter andRSTKF for a linear state-space model with non-stationary heavy-tailed noises.