基于变分贝叶斯理论的不确定厚尾噪声滤波方法

doi:10.16183/j.cnki.jsjtu.2020.99.014

上海交通大学学报 ›› 2020, Vol. 54 ›› Issue (9): 881-889.doi: 10.16183/j.cnki.jsjtu.2020.99.014

• 学报（中文） • 下一篇

基于变分贝叶斯理论的不确定厚尾噪声滤波方法

董祥祥, 吕润妍, 蔡云泽()

上海交通大学自动化系; 系统控制与信息处理教育部重点实验室;海洋智能装备与系统集成技术教育部实验室, 上海 200240

收稿日期:2020-01-06 出版日期:2020-09-28 发布日期:2020-10-10
通讯作者: 蔡云泽 E-mail:yzcai@sjtu.edu.cn
作者简介:董祥祥(1995-),女,山西省临汾市人,博士生,主要研究方向为状态估计与滤波
基金资助:
国家自然科学基金国家重大科研仪器研制项目(61627810);国家科技重大专项(2018YFB1305003)

A Variational Bayes-Based Filter with Uncertain Heavy-Tailed Noise

DONG Xiangxiang, LÜ Runyan, CAI Yunze*()

Department of Automation; Key Laboratory of System Control and Information Processing of the Ministry of Education; c. Key Laboratory of Marine Intelligent Equipment and System of the Ministry of Education, Shanghai Jiao Tong University, Shanghai 200240, China

Received:2020-01-06 Online:2020-09-28 Published:2020-10-10
Contact: CAI Yunze* E-mail:yzcai@sjtu.edu.cn

摘要/Abstract

摘要：

为了解决非线性滤波中量测噪声呈厚尾分布且统计特性不确定的问题,提出一种基于Pearson Type VII 分布的自适应滤波算法.针对传统鲁棒卡尔曼滤波器因尺度矩阵和自由度参数固定不变而无法自适应调整的问题,以容积卡尔曼滤波器为基础,选择Pearson Type VII 分布对厚尾噪声进行建模,将传统鲁棒滤波固定自由度参数的估计转化为Pearson Type VII 分布中可自适应调整的双自由度参数的估计,并通过 inverse Wishart和Gamma分布描述尺度矩阵、双自由度参数和辅助参数的先验分布,利用遗忘因子对各参数进行时间更新;基于变分贝叶斯理论,对系统状态、尺度矩阵、双自由度参数和辅助参数形成的联合后验概率密度函数进行变分迭代,实现对系统状态和未知厚尾噪声的联合估计.仿真结果表明,在不确定厚尾噪声条件下,本文算法的滤波精度高于传统鲁棒容积卡尔曼滤波.

关键词: 厚尾噪声, Pearson Type VII 分布, 变分贝叶斯, 联合估计, 容积卡尔曼滤波

Abstract:

An adaptive Pearson Type VII based filter was proposed to deal with measurement noise with heavy tailed distribution and uncertain statistical characteristics in nonlinear filtering. In view of the fact that the scale matrix and degree-of-freedom (DOF) parameters of traditional robust Kalman filter are fixed, which cannot adjust adaptively. The Pearson Type VII distribution was selected to model the heavy tailed noise to realize the adaptive estimation of 2-DOF parameters based on Cubature Kalman filter (CKF). Inverse Wishart and Gamma distributions were used to describe prior distributions of the scale matrix, 2-DOF parameters, and auxiliary parameters. Besides, time updating of these parameters was performed through a forgetting factor. Based on the variational Bayesian theory, the variational iteration of joint posterior probability density function formed by states together with the 2-DOF parameters and auxiliary parameters was performed, and the states and noise parameters were estimated simultaneously. The simulation results show that this algorithm has a higher filtering accuracy than the traditional robust CKF under the condition of uncertain heavy tailed noise.

Key words: heavy tailed noise, Pearson Type VII distribution, variational Bayesian (VB), joint estimation, Cubature Kalman filter (CKF)

中图分类号:

TP13

董祥祥, 吕润妍, 蔡云泽. 基于变分贝叶斯理论的不确定厚尾噪声滤波方法[J]. 上海交通大学学报, 2020, 54(9): 881-889.

DONG Xiangxiang, LÜ Runyan, CAI Yunze*. A Variational Bayes-Based Filter with Uncertain Heavy-Tailed Noise[J]. Journal of Shanghai Jiaotong University, 2020, 54(9): 881-889.

图/表 4

参考文献 18

[1]	杨峰, 郑丽涛, 王家琦, 等. 双层无迹卡尔曼滤波[J]. 自动化学报, 2019,45(7):1386-1391.
	YANG Feng, ZHENG Litao, WANG Jiaqi, et al. Double layer unscented Kalman filter[J]. Acta Automatica Sinica, 2019,45(7):1386-1391.
[2]	李建, 何黎明, 蔡云泽. 带有等式状态约束的多传感器数据融合算法[J]. 上海交通大学学报, 2014,48(7):893-898.
	LI Jian, HE Liming, CAI Yunze. Multi-sensor data fusion algorithm with state equality constraints[J]. Journal of Shanghai Jiao Tong University, 2014,48(7):893-898.
[3]	胡兵, 杨明, 郭林栋, 等. 基于地面快速鲁棒特征的智能车全局定位方法[J]. 上海交通大学学报, 2019,53(2):81-86.
	HU Bing, YANG Ming, GUO Lindong, et al. Glo-bal localization for intelligent vehicles using ground SURF[J]. Journal of Shanghai Jiao Tong University, 2019,53(2):81-86.
[4]	LI K L, CHANG L B, HU B Q. A variational Bayesian-based unscented Kalman filter with both adaptivity and robustness[J]. IEEE Sensors Journal, 2016,16(18):6966-6976.
[5]	AGAMENNONI G, NEBOT E M. Robust estimation in non-linear state-space models with state-dependent noise[J]. IEEE Transactions on Signal Processing, 2014,62(8):2165-2175.
[6]	CHEN B D, LIU X, ZHAO H Q, et al. Maximum correntropy Kalman filter[J]. Automatica, 2017,76:70-77.
[7]	LI X R, JILKOV V P. Survey of maneuvering target tracking. Part V. Multiple-model methods[J]. IEEE Transactions on Aerospace and Electronic Systems, 2005,41(4):1255-1321.
[8]	DONG P, JING Z L, LEUNG H, et al. Variational Bayesian adaptive cubature information filter based on Wishart distribution[J]. IEEE Transactions on Automatic Control, 2017,62(11):6051-6057.
[9]	IZANLOO R, FAKOORIAN S A, YAZDI H S, et al. Kalman filtering based on the maximum correntropy criterion in the presence of non-Gaussian noise [C]//2016 Annual Conference on Information Science and Systems (CISS). Princeton, NJ, USA: IEEE, 2016: 500-505.
[10]	BILIK I, TABRIKIAN J. MMSE-based filtering in presence of non-Gaussian system and measurement noise[J]. IEEE Transactions on Aerospace and Electronic Systems, 2010,46(3):1153-1170.
[11]	TZIKAS D G, LIKAS A C, GALATSANOS N P. The variational approximation for Bayesian inference[J]. IEEE Signal Processing Magazine, 2008,25(6):131-146.
[12]	潘泉, 胡玉梅, 兰华, 等. 信息融合理论研究进展: 基于变分贝叶斯的联合优化[J]. 自动化学报, 2019,45(7):1207-1223.
	PAN Quan, HU Yumei, LAN Hua, et al. Information fusion progress: Joint optimization based on variational Bayesian theory[J]. Acta Automatica Sinica, 2019,45(7):1207-1223.
[13]	PICHé R, S?RKKā S, HARTIKAINEN J. Recursive outlier-robust filtering and smoothing for nonli-near systems using the multivariate Student-t distribution [C]//2012 IEEE International Workshop on Machine Learning for Signal Processing. Santander, Spain: IEEE, 2012: 1-6.
[14]	YUN P, WU P L, HE S. Pearson type VII distribution-based robust Kalman filter under outliers interference[J]. IET Radar, Sonar & Navigation, 2019,13(8):1389-1399.
[15]	HUANG Y L, ZHANG Y G, SHI P, et al. Robust Kalman filters based on Gaussian scale mixture distributions with application to target tracking[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019,49(10):2082-2096.
[16]	ARASARATNAM I, HAYKIN S. Cubature Kalman filters[J]. IEEE Transactions on Automatic Control, 2009,54(6):1254-1269.
[17]	SUN J Y, KABAN A, GARIBALDI J M. Robust mixture modeling using the Pearson type VII distribution [C]//The 2010 International Joint Conference on Neural Networks (IJCNN). Barcelona, Spain: IEEE, 2010: 1-7.
[18]	GOLUB G H, VAN LOAN C F. Matrix computations[M]. 4th ed. Baltimore: The Johns Hopkins University Press, 2013.

滤波算法	MRMSE
滤波算法	s_x/m	v_x/(m·s^-1)	s_y/m	v_y/(m·s^-1)	ω/[(°)·s^-1]
Robust CKF	43.4444	16.8042	36.5075	15.0647	0.0283
VBCKF Pearson	33.7801	14.7821	30.0664	14.0835	0.0276
VBCKF Pearson-R	50.9088	18.8177	45.5194	17.5744	0.0297
VBCKF Pearson-r	44.2491	17.9638	39.9166	16.5867	0.0294

基于变分贝叶斯理论的不确定厚尾噪声滤波方法

A Variational Bayes-Based Filter with Uncertain Heavy-Tailed Noise

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