In many engineering systems, the distribution of measurement noise is unknown and non-Gaussian, such as skewed, multimodal, time-varying distributions and we can not obtain these prior statistics in advance. How to achieve state estimation via this kind of non-Gaussian measurement noises without prior statistic information is a challenging problem. In this paper, a novel Gaussian mixture regression model (GMRM) is proposed to model the unknown non-Gaussian measurement likelihood for Bayesian update to achieve nonlinear state estimation. Without any prior assumption or limitation of measurement noises’ statistics and distributions, the GMRM can still describe the measurement likelihood accurately based on a group of parameters which are adjusted by maximizing the evidence lower bound. Based on the optimized GMRM, a new variational Bayesian Gaussian mixture filter is proposed by using the variational Bayesian approach. To eliminate the influence of the initialization of the introduced parameters, a learning scheme is proposed to adaptively optimize their hyper-parameters based on the historical measurements. Finally, simulation examples are employed to illustrate the effectiveness of the filter.

在许多工程系统中，测量噪声的分布是未知的和非高斯分布的，例如偏斜、多峰、时变分布，我们无法提前获得这些先验统计数据。如何在没有先验统计信息的情况下通过这种非高斯测量噪声来实现状态估计是一个具有挑战性的问题。在本文中，提出了一种新的高斯混合回归模型（GMRM）来对未知的非高斯测量似然进行建模，以实现贝叶斯更新以实现非线性状态估计。在没有任何先验假设或对测量噪声的统计和分布的限制的情况下，GMRM仍然可以根据一组通过最大化证据下界调整的参数来准确描述测量似然。基于优化的GMRM，利用变分贝叶斯方法提出了一种新的变分贝叶斯高斯混合滤波器。为了消除引入参数初始化的影响，提出了一种基于历史测量值自适应优化超参数的学习方案。最后，通过仿真实例来说明滤波器的有效性。