Cauchy kernel-based maximum correntropy Kalman filter

Abstract

Non-Gaussian noise processing is a difficult and hot spot in the study of filters. A currently effective method to deal with non-Gaussian noise is replacing the minimum mean square error criterion with the maximum correntropy criterion. Based on the maximum correntropy criterion, maximum correntropy Kalman filter, which usually uses the Gaussian kernel function to define the distance between vectors, is developed. However, when the non-Gaussian noise is multi-dimensional, maximum correntropy Kalman filter tends to break down due to the appearance of singular matrices. To overcome the drawback, a novel filter named Cauchy kernel-based maximum correntropy Kalman filter is proposed, which utilises the Cauchy kernel function to define the distance between vectors. Due to the insensitive feature to the kernel bandwidth and thick-tailed characteristic of the Cauchy kernel function, Cauchy kernel-based maximum correntropy Kalman filter can effectively avoid filter faults and has a better stability. Simulation results demonstrate the excellent performance of the proposed algorithm by comparing it with other conventional methods, such as Kalman filter, ideal Kalman filter, Huber-based filter, Gaussian sum filter and maximum correntropy Kalman filter.

Keywords:

• Kalman filter
• maximum correntropy
• Cauchy kernel function
• CKKF

Acknowledgments

The authors express their appreciation to the Associate Editor and anonymous reviewers for their helpful suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [grant number 61773021, 61903086 and 61903366], the National Natural Science Foundation of Hunan Province [grant number 2019JJ20018, 2019JJ50745 and 2020JJ4280], Technical Field Fund of Foundation Strengthening Program [grant number 2019-JCJQ-JJ-217]. The Civil Space Pre-research Foundation [grant number D020213] and Pre-research Project of National University of Defense Technology [grant number ZK18-03-18].

Notes on contributors

Jiongqi Wang

Jiongqi Wang received his B.S. degree in Applied Mathematics from Zhejiang University, Hangzhou, China, in 2002 and the M.S. and PhD degree in System Science from National University of Defense Technology, in 2004 and 2008, respectively. He is a Professor in the College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, China.

He has published more than 80 refereed journal papers and 30 international conference papers, coauthored 5 monographs and 27 patents. He conducts several outstanding research awards from National Natural Science Foundation of China and Ministry of Education of China. He also serves as a reviewer of several refereed journals and conferences. He interests in measurement data analysis, parameter estimation, system identification, and space target state filter and its applications.

Donghui Lyu

Donghui Lyu received the B.S. degree in Information and Computing Sciences from University of Science and Technology Beijing, Beijing, China, in 2014.

Now, he has been studying in the National University of Defense Technology as a postgraduate. His current research interests include Kalman filter, signal processing, and integrated navigation.

Zhangming He

Zhangming He obtained his B.S. and M.S. degrees in Applied Mathematics from the National University of Defense Technology, Changsha, China, in 2008 and 2010, respectively. From 2013 to 2014, he was a visiting scholar in Institute for Automatic Control and Complex Systems, University of Duisburg-Essen, Duisburg, Germany.

He obtained his PhD degree in System Science from National University of Defense Technology, in 2015. Since 2015, he is a Lecturer in the College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, China. Dr Zhangming He interests in fault diagnosis and prognosis, signal processing, and system identification.

Haiyin Zhou

Haiyin Zhou obtained his B.S. degree in Applied Mathematics from Wuhan University, Wuhan, China, in 1986, his M.S. degree from Hunan University, Changsha, China in 1989 and his PhD degree in Systems Engineering from National University of Defense Technology, Changsha, China, in 2003.

Since 2009, he is a Professor in the College of Liberal Arts and Sciences, National University of Defense Technology. He serves as a part-time researcher in Beijing Institute of Control Engineering, Beijing, China. He has published more than 80 refereed journal papers and 10 international conference papers, coauthored 4 monographs and 6 patents.

Prof. Haiyin Zhou interests in data-driven diagnosis approaches, power system dynamics and controls, advanced signal processing, and data information fusion and its application.

Dayi Wang

Dayi Wang received the PhD degree in Aerospace Engineering from the Harbin Institute of Technology in 2003.

From 2003 to 2015, he was a researcher with the Beijing Institute of Spacecraft System Engineering, China Academy of Space Technology. From 2011 to 2015, he was the Deputy Director of the State Key Laboratory of Spatial Intelligent Control Technology and the chief scientist for the 973-Project. He was authorised with 34 patents, 2 monographs and more than 69 papers.

Researcher Dayi Wang won the National Outstanding Youth Fund of the National Natural Science Foundation of China. He conducted innovative research in the field of spacecraft autonomous navigation and control and solved a series of key technical issues.