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2020影响因子

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## 留言板

 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
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

## 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)
###### 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 $\delta_0$

•  [1] 潘泉, 胡玉梅, 兰华, 孙帅, 王增福, 杨峰. 信息融合理论研究进展: 基于变分贝叶斯的联合优化. 自动化学报, 2019, 45(7): 1207-1223Pan Quan, Hu Yu-Mei, Lan Hua, Sun Shuai, Wang Zeng-Fu, Yang Feng. Information fusion progress: Joint optimization based on variational Bayesian theory. Acta Automatica Sinica, 2019, 45(7): 1207-1223 [2] 罗小元, 潘雪扬, 王新宇, 关新平. 基于自适应 Kalman 滤波的智能电网假数据注入攻击检测. 自动化学报, 在线出版, 2022, DOI: 10.16383/j.aas.c190636Luo Xiao-Yuan, Pan Xue-Yang, Wang Xin-Yu, Guan Xin-Ping. Detection of false data injection attack in smart grid via adaptive Kalman filtering. Acta Automatica Sinica, to be published, 2020, DOI: 10.16383/j.aas.c190636 [3] Wang G Q, Wang X D, Zhang Y G. Variational Bayesian IMM-filter for JMSs with unknown noise covariances. IEEE Transactions on Aerospace and Electronic Systems, 2020, 56(2): 1652-1661 [4] Arasaratnam I, Haykin S. Cubature Kalman filters. IEEE Transactions on Automatic Control, 2009, 54(6): 1254-1269 [5] Dang L J, Chen B D, Wang S Y, Ma W T, Ren P J. Robust power system state estimation with minimum error entropy unscented Kalman filter. IEEE Transactions on Instrumentation and Measurement, 2020, 69(11): 8797-8808 [6] 葛泉波, 王贺彬, 杨秦敏, 张兴国, 刘华平. 基于改进高斯混合模型的机器人运动状态估计. 自动化学报, 2022, 48(8): 1972-1983Ge Quan-Bo, Wang He-Bin, Yang Qin-Min, Zhang Xing-Guo, Liu Hua-Ping. Estimation of robot motion state based on improved Gaussian mixture model. Acta Automatica Sinica, 2022, 48(8): 1972-1983 [7] Huang Y L, Zhang Y G, Xu B, Wu Z M, Chambers J A. A new outlier-robust student's t based Gaussian approximate filter for cooperative localization. IEEE-ASME Transactions on Mechatronics, 2017, 22(5): 2380-2386 [8] Bai M M, Huang Y L, Zhang Y G, Chen F. A novel heavy-tailed mixture distribution based robust Kalman filter for cooperative localization. IEEE Transactions on Industrial Informatics, 2021, 17(5): 3671-3681 [9] 朱兵, 李星, 刘强, 李作虎. 鲁棒Kalman滤波及其在水下组合导航中的应用. 导航定位与授时, 2021, 8(1): 96-103Zhu Bing, Li Xing, Liu Qiang, Li Zuo-Hu. Robust Kalman filter and its application in underwater intergrated navigation. Navigation Positioning and Timing, 2021, 8(1): 96-103 [10] Huang Y L, Zhang Y G, Shi P, Wu Z M, Qian J H, Chambers J A. Robust Kalman filters based on Gaussian scale mixture distributions with application to target tracking. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 49(10): 2082-2096 [11] 王国庆, 杨春雨, 马磊. 基于多变量 Laplace 分布的非线性系统分布式鲁棒状态估计. 电子学报, 在线出版, 2022, DOI: 10.12263/dzxb.20220141Wang Guo-Qing, Yang Chun-Yu, Ma Lei. Distributed robust state estimation for nonlinear systems based on multivariate Laplace distribution. Acta Electronica Sinica, to be published, 2022, DOI: 10.12263/dzxb.20220141 [12] Chen B D, Liu X, Zhao H Q, Principe J C. Maximum correntropy Kalman filter. Automatica, 2017, 76: 70-77 [13] Chen B D, Dang L J, Gu Y T, Zheng N N, Principe J C. Minimum error entropy Kalman filter. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(9): 5819-5829 [14] Huang Y L, Zhang Y G, Zhao Y X, Shi P, Chambers J A. A novel outlier-robust Kalman filtering framework based on statistical similarity measure. IEEE Transactions on Automatic Control, 2021, 66(6): 2677-2692 [15] Bai M M, Huang Y L, Zhang Y G, Chambers J A. Statistical similarity measure-based adaptive outlier-robust state estimator with applications. IEEE Transactions on Automatic Control, 2022, 67(8): 4354-4361 [16] Wang G Q, Zhang Y G, Wang X D. Maximum correntropy Rauch-Tung-Striebel smoother for nonlinear and non-Gaussian systems. IEEE Transactions on Automatic Control, 2021, 66(3): 1270-1277 [17] Wang G Q, Zhang Y G, Wang X D. Iterated maximum correntropy unscented Kalman filters for non-Gaussian systems. Signal Processing, 2019, 163: 87-94 [18] Wang G Q, Li N, Zhang Y G. Maximum correntropy unscented Kalman and information filters for non-Gaussian measurement noise. Journal of the Franklin Institute, 2017, 354(18): 8659-8677 [19] Wang G Q, Li N, Zhang Y G. Distributed maximum correntropy linear and nonlinear filters for systems with non-Gaussian noises. Signal Processing, 2021, 182: Article No. 107937 [20] 王健, 鲁金瑞, 郑栋, 李璇, 张涛. 水下复杂环境下基于 SINS/USBL/DVL 多源信息融合的组合导航算法. 导航定位与授时, 2022, 9(1): 76-84Wang Jian, Lu Jin-Rui, Zheng Dong, Li Xuan, Zhang Tao. Integrated navigation algorithm based on SINS/USBL/DVL multi-souce information fusion in underwater complex environment. Navigation Positioning and Timing, 2022, 9(1): 76-84 [21] Huang Y L, Zhang Y G, Li N, Wu Z M, Chambers J A. A novel robust student's t-based Kalman filter. IEEE Transactions on Aerospace and Electronic Systems, 2017, 53(3): 1545-1554 [22] Huang Y L, Zhang Y G, Li N, Chambers J A. A robust Gaussian approximate filter for nonlinear systems with heavy tailed measurement noises. In: Proceedings of the 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). Shanghai, China: IEEE, 2016. 4209−4213 [23] Wang G Q, Yang C Y, Ma X P. A novel robust nonlinear Kalman filter based on multivariate Laplace distribution. IEEE Transactions on Circuits and Systems II: Express Briefs, 2021, 68(7): 2705-2709 [24] Xue C, Huang Y L, Zhu F C, Zhang Y G, Chambers J A. An outlier-robust Kalman filter with adaptive selection of elliptically contoured distributions. IEEE Transactions on Signal Processing, 2022, 70: 994-1009 [25] Wang G Q, Yang C Y, Ma L, Dai W. Centralized and distributed robust state estimation over sensor networks using elliptical distribution. IEEE Internet of Things Journal, to be published, 2022, DOI: 10.1109/JIOT.2022.3181683 [26] Huang Y L, Zhang Y G, Zhao Y, Chambers J A. A novel robust Gaussian-student's t mixture distribution based Kalman filter. IEEE Transactions on Signal Processing, 2019, 67(13): 3606-3620 [27] Zhu H, Zhang G R, Li Y F, Leung H. A novel robust Kalman filter with unknown non-stationary heavy-tailed noise. Automatica, 2021, 127: Article No. 109511 [28] Bai M M, Huang Y L, Chen B D, Zhang Y G. A movel robust Kalman filtering framework based on normal-skew mixture distribution. IEEE Transactions on Systems, Man, and Cybernetics: Systems, to be published, 2021, DOI: 10.1109/TSMC.2021.3098299 [29] Nakabayashi A, Ueno G. Nonlinear filtering method using a switching error model for outlier-contaminated observations. IEEE Transactions on Automatic Control, 2020, 65(7): 3150-3156 [30] Breymann W, Lüthi D. ghyp: A package on generalized hyperbolic distributions [Online], available: https://cran.microsoft.com/snapshot/2015-09-28/web/packages/ghyp/vignettes/Generalized_Hyperbolic_Distribution.pdf, May 16, 2022 [31] Babacan S D, Nakajima S. Do M N. Bayesian group-sparse modeling and variational inference. IEEE Transactions on Signal Processing, 2014, 62(11): 2906-2921 [32] Zhang Y, Chu J, Chan S, Chan B. The generalised hyperbolic distribution and its subclass in the analysis of a new era of cryptocurrencies: Ethereum and its financial risk. Physica A: Statistical Mechanics and its Applications, 2019, 526: Article No. 120900. [33] Särkkä S, Hartikainen J. Non-linear noise adaptive Kalman filtering via variational Bayes. In: Proceedings of the 2013 IEEE International Workshop on Machine Learning for Signal Processing (MLSP). Southampton, UK: IEEE, 2013. 1−6 [34] Yang X S, Zhang W A, Yu L, Yang F W. Sequential Gaussian approximation filter for target tracking with nonsynchronous measurements. IEEE Transactions on Aerospace and Electronic Systems, 2019, 55(1): 407-418

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• 文章访问数:  101
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##### 出版历程
• 收稿日期:  2022-05-16
• 录用日期:  2022-08-07
• 网络出版日期:  2022-09-26

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