Scaling parameters selection principle for the scaled unscented Kalman filter

doi:10.21629/JSEE.2018.03.17

Journal of Systems Engineering and Electronics ›› 2018, Vol. 29 ›› Issue (3): 601-610.doi: 10.21629/JSEE.2018.03.17

• Control Theory and Application • Previous Articles Next Articles

Scaling parameters selection principle for the scaled unscented Kalman filter

Yongfang NIE^1,²(), Tao ZHANG^1,*()

¹ Department of Automation, Tsinghua University, Beijing 100084, China
² Department of Strategic Missile and Underwater Weapon, Naval Submarine Academy, Qingdao 266071, China

Received:2017-08-07 Online:2018-06-28 Published:2018-07-02
Contact: Tao ZHANG E-mail:nyf14@mails.tsinghua.edu.cn;taozhang@mail.tsinghua.edu.cn
About author:NIE Yongfang was born in 1976. She received her M.S degree in weapon system engineering from Naval Aeronautical Engineering Institute in 2002. She was a lecturer with Naval Submarine Academy from 2002 to 2014. Now, she is also a Ph.D. student in control science and engineering at Tsinghua University. Her current research activity focuses on simultaneous localization and mapping for autonomous underwater vehicles. E-mail: nyf14@mails.tsinghua.edu.cn|ZHANG Tao was born in 1969. He received his B.S. degree, M.S. degree and Ph.D. degree from Tsinghua University, Beijing, China, in 1993, 1995 and 1999 respectively. He received his second Ph.D. degree from Saga University, Saga, Japan, in 2002. He is currently a professor and the deputy head of the Department of Automation, School of Information Science and Technology, Tsinghua University, Beijing, China. He is the author or coauthor of more than 200 papers and three books. His current research includes robotics, control theory, artificial intelligence, navigation and control of spacecraft, fault diagnosis and reliability analysis, body signal extraction and recognition. E-mail: taozhang@mail.tsinghua.edu.cn
Supported by:
the National Natural Science Foundation of China(61703228);This work was supported by the National Natural Science Foundation of China (61703228)

Abstract

Abstract:

The paper deals with the state estimation of the widely used scaled unscented Kalman filter (UKF). In particular, the stress is laid on the scaling parameters selection principle for the scaled UKF. Several problems caused by recommended constant scaling parameters are highlighted. On the basis of the analyses, an effective scaled UKF is proposed with self-adaptive scaling parameters, which is easy to understand and implement in engineering. Two typical strong nonlinear examples are given and their simulation results show the effectiveness of the proposed principle and algorithm.

Key words: nonlinear filtering, scaled unscented Kalman filter, scaling parameter selection principle

Yongfang NIE, Tao ZHANG. Scaling parameters selection principle for the scaled unscented Kalman filter[J]. Journal of Systems Engineering and Electronics, 2018, 29(3): 601-610.

Figures/Tables 12

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References 25

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Filter	Mean	Covariance	Parameter
EKF	0	0	—
EKF2	n	2n	—
UKF1	n	(3-n)n	$ a = \sqrt {3/n}, \beta = 3/n-1, k = 0$
UKF2	n	2n²	a=10^-3, β=2, k=0
CKF	n	0	—

κ	MSE (β = 0)	MSE (β = 2)
κ=0	69.905 0	78.462 3
κ=1	35.363 5	56.641 5
κ=2	41.835 9	65.735 2
κ=3	42.032 8	66.355 7

κ	MSE (β = 0)	MSE (β = 2)
κ=0	56.419 8	37.779 9
κ=1	34.401 7	29.880 9
κ=2	62.194 3	31.618 3
κ=3	43.622 8	42.168 3
κ=4	100.988 8	46.790 2
κ=5	40.782 8	32.233 6
κ=6	35.781 1	29.792 4
κ=7	50.805 8	24.477 3
κ=8	44.785 1	32.977 5
κ=9	36.406 1	24.003 0

Example	Parameter	Default UKF	UKF_G
Example1	MSE	38.951 8	8.473 2
Example1	time/s	0.047	0.092
Example2	MSE	22.859 6	9.843 5
Example2	time/s	0.072	0.106

[1]	Junyi Zuo, Yingna Jia, and Quanxue Gao. Simplified unscented particle filter for nonlinear/non-Gaussian Bayesian estimation [J]. Journal of Systems Engineering and Electronics, 2013, 24(3): 537-.
[2]	Zhan Ronghui, Xin Qin & Wan Jianwei. Modified unscented particle filter for nonlinear Bayesian tracking [J]. Journal of Systems Engineering and Electronics, 2008, 19(1): 7-14.
[3]	Zhan Ronghui, Wang Ling, Wan Jianwei & Sun Zhongkang. Passive target tracking using marginalized particle filter [J]. Journal of Systems Engineering and Electronics, 2007, 18(3): 503-508.

Scaling parameters selection principle for the scaled unscented Kalman filter

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