A Novel Adaptive Kalman Filter Based on Credibility Measure

Quanbo Ge; Xiaoming Hu; Yunyu Li; Hongli He; Zihao Song

doi:10.1109/JAS.2023.123012

Volume 10 Issue 1

Jan. 2023

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2023 > 10(1): 103-120

Q. B. Ge, X. M. Hu, Y. Y. Li, H. L. He, and Z. H. Song, “A novel adaptive Kalman filter based on credibility measure,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 1, pp. 103–120, Jan. 2023. doi: 10.1109/JAS.2023.123012

Citation:

Q. B. Ge, X. M. Hu, Y. Y. Li, H. L. He, and Z. H. Song, “A novel adaptive Kalman filter based on credibility measure,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 1, pp. 103–120, Jan. 2023. doi: 10.1109/JAS.2023.123012

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A Novel Adaptive Kalman Filter Based on Credibility Measure

doi: 10.1109/JAS.2023.123012

Quanbo Ge^1
,,
Xiaoming Hu^{2
,
,},
Yunyu Li^3
,,
Hongli He^4
,,
Zihao Song^5
,

1.
School of Automation, Nanjing University of Information Science and Technology, Nanjing 210044, and also with Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing University of Information Science & Technology, Nanjing 210044, China
2.
KTH Royal Institute of Technology, Stockholm 10044, Sweden
3.
School of Automation, Hangzhou Dianzi University, Hangzhou 310000, China
4.
Testing Institute, Chinese Flight Test Establishment, Xi’an 710000, China
5.
School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang 330000, China

Funds: This work was supported by the National Natural Science Foundation of China (62033010) and Aeronautical Science Foundation of China (2019460T5001)

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Author Bio:
Quanbo Ge (Member, IEEE) received the B.S. in computer and applications and M.S. degrees in applied mathematics from the College of Computer and Information Engineering, Henan University, in 2002 and 2005, respectively, and the Ph.D. degree in power electronics and power transmission from Shanghai Maritime University, in 2008. He was a Professor with the Institute of Systems Science and Control Engineering, the School of Automation, Hangzhou Dianzi University. From 2008 to 2010, he was a Lecturer and became an Associate Professor with the School of Automation, Hangzhou Dianzi University, in 2010. From 2009 to 2013, he was a Postdoctoral Fellow with the State Key Laboratory of Industrial Control Technology, Zhejiang University. From 2012 to 2013, he was a Visiting Scholar with the Optimization for Signal Processing and Communication Group, the Department of Electrical and Computer Engineering, Twin Cities Campus, University of Minnesota, USA. He is currently a Professor with the School of Automation, Nanjing University of Information Science and Technology, Nanjing, China. His research interests include information fusion, autonomous unmanned system, man-mechanic hybrid system, and machine vision

Xiaoming Hu (Member, IEEE) received the B.S. degree in automatic control from the University of Science and Technology of China in 1983, and the M.S. and Ph.D. degrees in systems and control from the Arizona State University, USA in 1986 and in 1989, respectively. He served as a Research Assistant at the Institute of Automation, the Chinese Academy of Sciences, from 1983 to 1984. From 1989 to 1990 he was a Gustafsson Postdoctoral Fellow at KTH Royal Institute of Technology, Sweden, where he is currently Professor of optimization and systems theory. His main research interests are in nonlinear dynamical systems, nonlinear observation and filtering, and multi-agent systems

Yunyu Li received the B.S. degree in automation and the M.S. degree in control science and engineering from the School of Automation, Hangzhou Dianzi University in 2017 and 2020, respectively. His main research interest is multi-source information fusion

Hongli He received the B.S. degree in computer science and the M.S. degree in control engineering from Northwestern Polytechnical University in 1998 and 2007, respectively. She is currently a Professional Researcher in Chinese Flight Test Establishment and a Super Expert of Flight Test Center. She is now also a First-Class Expert of AVIC Group. Her research interest includes photoelectric testing and data processing of flight. She has obtained more than 10 provincial and ministerial science and technology progress awards

Zihao Song received the B.S. degree in automation from the School of Electrical and Automation Engineering, Anhui University of Science and Technology in 2018. He is currently a master student in control science and engineering at the School of Electrical and Automation Engineering, East China Jiaotong University. His main research interest is multi-source information fusion
Corresponding author: Xiaoming Hu, e-mail: hu@kth.se
Received Date: 2022-08-01
Revised Date: 2022-09-26
Accepted Date: 2022-10-19

Available Online: 2022-12-07

Abstract

Abstract

It is quite often that the theoretic model used in the Kalman filtering may not be sufficiently accurate for practical applications, due to the fact that the covariances of noises are not exactly known. Our previous work reveals that in such scenario the filter calculated mean square errors (FMSE) and the true mean square errors (TMSE) become inconsistent, while FMSE and TMSE are consistent in the Kalman filter with accurate models. This can lead to low credibility of state estimation regardless of using Kalman filters or adaptive Kalman filters. Obviously, it is important to study the inconsistency issue since it is vital to understand the quantitative influence induced by the inaccurate models. Aiming at this, the concept of credibility is adopted to discuss the inconsistency problem in this paper. In order to formulate the degree of the credibility, a trust factor is constructed based on the FMSE and the TMSE. However, the trust factor can not be directly computed since the TMSE cannot be found for practical applications. Based on the definition of trust factor, the estimation of the trust factor is successfully modified to online estimation of the TMSE. More importantly, a necessary and sufficient condition is found, which turns out to be the basis for better design of Kalman filters with high performance. Accordingly, beyond trust factor estimation with Sage-Husa technique (TFE-SHT), three novel trust factor estimation methods, which are directly numerical solving method (TFE-DNS), the particle swarm optimization method (PSO) and expectation maximization-particle swarm optimization method (EM-PSO) are proposed. The analysis and simulation results both show that the proposed TFE-DNS is better than the TFE-SHT for the case of single unknown noise covariance. Meanwhile, the proposed EM-PSO performs completely better than the EM and PSO on the estimation of the credibility degree and state when both noise covariances should be estimated online.
- Credibility,
- expectation maximization-particle swarm optimization method (EM-PSO),
- filter calculated mean square errors (MSE),
- inaccurate models,
- Kalman filter,
- Sage-Husa,
- true MSE (TMSE)

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References

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A trust factor, which evaluated online, is designed to express the creditable degree of the Kalman filter. Exactly, it also indicates the closeness of true mean square errors (TMSE) and filter calculated mean square errors (FMSE) matching degree of the used system model
The necessary and sufficient condition for accurate noise estimation is P_zk^f = P_zk^m, P_zk^f - P_zk^m is presented for noise covariances estimation. Where P_zk^f and P_zk^m, represents the filter FMSE and the TMSE , respectively. It also indicates the relationship between TMSE and FMSE. Under this case, the equivalence between the filter TMSE and FMSE becomes a necessary and sufficient condition for noise covariances estimation
The directly numerical solving way is presented to estimate the noise covariances, meanwhile, the Sage-Husa technology is also introduced to estimate the trust factor. Afterward, the evaluation of the trust factor is also discussed for the case with two unknown noise covariances. When the directly numerical solving way is used to solve this problem, it is found that the method is unavailable to deal with two unknown covariances
The optimization method proposed in this paper is successfully used to deal with the estimation with two unknown noise covariances. the optimization solution is proposed to synchronously estimate the two noise covariances. The corresponding optimization model is constructed, and the particle swarm optimization method is introduced to solve the optimization problem. The results show that the estimation accuracy and the convergence can be improved

A Novel Adaptive Kalman Filter Based on Credibility Measure

doi: 10.1109/JAS.2023.123012

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