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

doi:10.16183/j.cnki.jsjtu.2020.99.014

Abstract

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)

CLC Number:

TP13

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.

Figures/Tables 4

References 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