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基于高斯–广义双曲混合分布的非线性卡尔曼滤波

王国庆 杨春雨 马磊 代伟

王国庆, 杨春雨, 马磊, 代伟. 基于高斯–广义双曲混合分布的非线性卡尔曼滤波. 自动化学报, 2022, 48(x): 1001−1013 doi: 10.16383/j.aas.c220400
引用本文: 王国庆, 杨春雨, 马磊, 代伟. 基于高斯–广义双曲混合分布的非线性卡尔曼滤波. 自动化学报, 2022, 48(x): 1001−1013 doi: 10.16383/j.aas.c220400
Wang Guo-Qing, Yang Chun-Yu, Ma Lei, Dai Wei. Nonlinear Kalman filter based on Gaussian-generalized-hyperbolic mixing distribution. Acta Automatica Sinica, 2022, 48(x): 1001−1013 doi: 10.16383/j.aas.c220400
Citation: Wang Guo-Qing, Yang Chun-Yu, Ma Lei, Dai Wei. Nonlinear Kalman filter based on Gaussian-generalized-hyperbolic mixing distribution. Acta Automatica Sinica, 2022, 48(x): 1001−1013 doi: 10.16383/j.aas.c220400

基于高斯–广义双曲混合分布的非线性卡尔曼滤波

doi: 10.16383/j.aas.c220400
基金项目: 国家自然科学基金 (62003348, 62073327, 62203448, 61973306, 61873272), 江苏省自然科学基金 (BK20200633, BK20200631, BK20200086) 资助
详细信息
    作者简介:

    王国庆:中国矿业大学信息与控制工程学院副教授. 分别于2014年和2019年获得中国矿业大学学士学位和哈尔滨工程大学博士学位. 2017年 ~ 2019年美国哥伦比亚大学访问学者. 主要研究方向为鲁棒状态估计, 分布式信息融合及其在导航中的应用. E-mail: wangguoqing0632@163.com

    杨春雨:中国矿业大学信息与控制工程学院教授. 于2009年获得东北大学博士学位. 2014年 ~ 2016年美国密歇根大学访问学者. 主要研究方向为奇异摄动系统, 工业过程运行控制, 物理信息系统和鲁棒控制. 本文通信作者. E-mail: chunyuyang@cumt.edu.cn

    马磊:中国矿业大学信息与控制工程学院讲师. 于2019年获得南京理工大学博士学位. 2017年 ~ 2018年英国布鲁奈尔大学访问学者. 主要研究方向为奇异摄动系统, 切换系统和网络控制系统. E-mail: maleinjust@126.com

    代伟:中国矿业大学信息与控制工程学院教授. 于2015年获得东北大学博士学位. 主要研究方向为复杂工业过程建模、优化与控制, 数据挖掘和机器学习. E-mail: weidai@cumt.edu.cn

Nonlinear Kalman Filter Based on Gaussian-generalized-hyperbolic Mixing Distribution

Funds: Supported by National Natural Science Foundation of China (62003348, 62073327, 62203448, 61973306, 61873272) and Natural Science Foundation of Jiangsu Province (BK20200633, BK20200631, BK20200086)
More Information
    Author Bio:

    WANG Guo-Qing Associate Professor at the School of Information and Control Engineering, China University of Mining and Technology. He received his bachelor degree from China University of Mining and Technology in 2014, and Ph.D. degree from Harbin Engineering University in 2019. From 2017 to 2019, he was a visiting scholar with the Columbia University, USA. His research interest coves robust state estimation, distributed information fusion, and applications in navigation technology

    YANG Chun-Yu Professor at the School of Information and Control Engineering, China University of Mining and Technology. He received his Ph.D. degree from Northeastern University in 2009. From 2014 to 2016, he was a visiting scholar with the University of Michigan, USA. His research interest covers singularly perturbed systems, industrial process operational control, cyber-physical systems, and robust control. Corresponding author of this paper

    MA Lei Lecturer at the School of Information and Control Engineering, China University of Mining and Technology. He received his Ph.D. degree from Nanjing University of Science and Technology in 2019. From 2017 to 2018, he was a visiting scholar with the Brunel University, London, UK. His research interest covers singularly perturbed systems, switched systems, and networked control systems

    Dai Wei Professor at the School of Information and Control Engineering, China University of Mining and Technology. He received his Ph. D. degree from Northeastern University in 2015. His research interest covers modeling, optimization and control of the complex industrial process, data mining, and machine learning

  • 摘要: 本文研究带非平稳厚尾非高斯量测噪声的非线性系统状态估计问题. 考虑到广义双曲分布包含多种常见厚尾分布特例, 且其混合分布为共轭的广义逆高斯分布, 本文选用广义双曲分布建模厚尾噪声; 进而引入伯努利变量构建高斯–广义双曲混合分布来建模非平稳厚尾噪声, 并利用该分布的高斯分层结构得到系统的概率模型. 随后采用变分贝叶斯方法实现对系统状态以及噪声参数的后验估计, 得到针对此类噪声系统的卡尔曼滤波 (Kalman filter, KF) 框架, 现有的几种鲁棒滤波均是本文方法的特例. 机器人跟踪仿真实验表明, 本文所提算法与同类算法相比具有更好的估计精度和数值稳定性, 且对于初始参数具有较好的鲁棒性.
  • 图  1  本文系统的图模型

    Fig.  1  Graph model of the system used in this paper

    图  2  基于传感器网络的机器人跟踪示意图

    Fig.  2  The illustration of tracking a robot with the sensor network

    图  3  仿真中产生一维噪声的幅值以及概率密度函数

    Fig.  3  The amplitude and probability density functions of the one-dimensional noise used in the simulation

    图  4  本文所提算法与同类方法的${RMSE}_{\rm pos}$

    Fig.  4  The ${RMSE}_{\rm pos}$ of the proposed algorithms and related ones

    图  5  本文所提算法与同类方法的${RMSE}_{\rm vel}$

    Fig.  5  The ${RMSE}_{\rm vel}$ of the proposed algorithms and related ones

    图  6  本文算法在迭代次数$ N$不同时的$ {RMSE}_{\rm pos}$

    Fig.  6  The $ {RMSE}_{ \rm pos}$ of the proposed algorithms with different iteration number $ N$

    图  7  本文算法在迭代次数$N$不同时的$ {RMSE}_{\rm vel}$

    Fig.  7  The $ {RMSE}_{\rm vel}$ of the proposed algorithms with different iteration number $N$

    图  8  本文算法在$\omega_0$$\eta_0$不同时的${RMSE}_{\rm {pos}}$

    Fig.  8  The ${RMSE}_{\rm {pos}}$ of the proposed algorithms with different $\omega_0$ and $\eta_0$

    图  9  本文算法在$\omega_0$$\eta_0$不同时的$ {RMSE}_{\rm vel}$

    Fig.  9  The $ {RMSE}_{\rm vel}$ of the proposed algorithms with different $\omega_0$ and $\eta_0$

    图  10  本文算法在$\delta_0$不同时的$ {RMSE}_{\rm pos}$

    Fig.  10  The $ {RMSE}_{\rm pos}$ of the proposed algorithms with different $\delta_0$

    图  11  本文算法在$\delta_0$不同时的$ {RMSE}_{\rm vel}$

    Fig.  11  The ${RMSE}_{\rm vel}$ of the proposed algorithms with different $\delta_0$

    表  1  广义双曲分布的几种特殊分布

    Table  1  Several special cases of generalized hyperbolic distribution

    分布名称关键参数
    高斯分布$\delta\rightarrow+\infty$或者$\delta\rightarrow-\infty$
    正态逆高斯分布$\delta=-0.5$
    双曲分布$\delta=1$
    K 分布$\omega=0$
    广义双曲学生 t 分布$\eta=0$
    下载: 导出CSV

    表  2  不同算法总运行时间

    Table  2  The total simulation time of different algorithms

    算法名称仿真时间 (s)
    UKF15.28
    STUKF139.66
    MCUKF22.51
    RSE-ML151.75
    SEUKF146.92
    OUKF14.67
    G-GHUKF1167.36
    G-GHUKF2165.32
    G-GHUKF3166.65
    G-GHUKF4145.77
    下载: 导出CSV
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  • 收稿日期:  2022-05-16
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