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

JCR Impact Factor: 15.3, Top 1 (SCI Q1)

CiteScore: 23.5, Top 2% (Q1)
Google Scholar h5-index: 77， TOP 5

Turn off MathJax

Article Contents

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

Citation:

PDF( 2027 KB)

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)

More Information

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)

FullText(HTML)

References(34)

References

[1]	R. E. Kalman, “A new approach to linear filtering and prediction problems,” Trans. ASME-J. Basic Eng, vol. 82, pp. 35–45, 1960. doi: 10.1115/1.3662552
[2]	Q.-B. Ge, T. Shao, Z.-S. Duan, and C.-L. Wen, “Performance analysis of the Kalman filter with mismatched noise covariances,” IEEE. Trans. Autom. Control, vol. 61, no. 12, pp. 4014–4019, 2016. doi: 10.1109/TAC.2016.2535158
[3]	L. E. Andersson, L.Imsland, E. F. Brekke, and F. Scibilia, “On Kalman filtering with linear state equality constraints,” Automatica, vol. 101, pp. 467–470, 2019. doi: 10.1016/j.automatica.2018.12.010
[4]	Q.-B. Ge, T.-X. Chen, H.-L. He, and Z.-T. Hu, “Cramer-Rao lower bound-based observable degree analysis,” Science China (Information Sciences), vol. 62, no. 5, pp. 050209:1–3, 2019.
[5]	L. F. Zhang, S. P. Wang, M. S. Selezneva, and K. A. Neusypin, “A new adaptive Kalman filter for navigation systems of carrier-based aircraft,” Chinese J. Aeronautics, vol. 35, no. 1, pp. 416–425, 2022. doi: 10.1016/j.cja.2021.04.014
[6]	C.-Y. Zhang, “Research on adaptive filtering method,” J. Aeronautics, vol. 19, no. 1, pp. 97–100, 1998.
[7]	D. Zhao, S.-X. Ding, H. R. Karimi, Y.-Y. Li, and Y.-Q. Wang, “On robust Kalman filter for two-dimensional uncertain linear discrete time-varying systems: A least squares method,” Automatica, vol. 99, pp. 203–212, 2019. doi: 10.1016/j.automatica.2018.10.029
[8]	M. B. Luca, S. Azou, G. Burel, and A. Serbanescu, “On exact Kalman filtering of polynomial systems,” IEEE Trans. Circuits Syst. I Reg. Papers, vol. 53, no. 6, pp. 1329–1340, 2006. doi: 10.1109/TCSI.2006.870899
[9]	Q.-B. Ge, Z.-C. Ma, J.-L. Li, Q.-M. Yang, Z.-Y. Lu, and H. Li, “Adaptive cubature Kalman filter with the estimation of correlation between multiplicative noise and additive measurement noise,” Chinese J. Aeronautics, vol. 35, no. 5, pp. 40–52, 2022. doi: 10.1016/j.cja.2021.05.004
[10]	Q.-B. Ge, T. Shao, S.-D. Chen, and C.-L. Wen, “Carrier tracking estimation analysis by using the extended strong tracking filtering,” IEEE Trans. Industrial Electronics, vol. 64, no. 2, pp. 1415–1424, 2017. doi: 10.1109/TIE.2016.2610403
[11]	L. Zhao and K. Wu, “New adaptive Kalman filtering algorithm and application,” Piezoelectric and Acousto-Optic, vol. 31, no. 6, pp. 908–911, 2009.
[12]	A. P. Sage and G. W. Husa, “Algorithms for sequential adaptive estimation of prior statistics,” in Proc. 8th IEEE Symp. Adaptive Processes, 1969, pp. 17–19.
[13]	S. Sarkka and A. Nummenmaa, “Recursive noise adaptive Kalman filtering by variational Bayesian approximations,” IEEE Trans. Automatic Control, vol. 54, no. 3, pp. 596–600, 2009. doi: 10.1109/TAC.2008.2008348
[14]	J. Sun, Z. Jie, and X. Gu, “Variational Bayesian two-stage Kalman filter for systems with unknown inputs,” Procedia Engineering, vol. 29, no. 4, pp. 2265–2273, 2012.
[15]	Y. Huang, Y. Zhang, Z. Wu, L. Ning, and J. Chambers, “A novel adaptive Kalman filter with inaccurate process and measurement noise covariance matrices,” IEEE Trans. Automatic Control, vol. 63, no. 2, pp. 594–601, 2018. doi: 10.1109/TAC.2017.2730480
[16]	M. Zorzi, “Robust Kalman filtering under model perturbations,” IEEE Trans. Automatic Control, vol. 62, no. 6, pp. 2902–2907, 2017. doi: 10.1109/TAC.2016.2601879
[17]	Z.-W. Zhou and H.-T. Fang, “L₂-stability of discrete-time Kalman filter with random coefficients under incorrect covariance,” ACTA Automatica Sinica, vol. 39, no. 1, pp. 43–52, 2013. doi: 10.1016/S1874-1029(13)60005-1
[18]	T. Shao, Q.-B. Ge, Z.-S. Duan, and J. Yu, “Relative closeness ranking of Kalman filtering with multiple mismatched measurement noise covariances,” IET Control Theory Appl, vol. 12, no. 8, pp. 1133–1140, 2018. doi: 10.1049/iet-cta.2017.1088
[19]	S. Gibson and B. Ninness, “Robust maximum-likelihood estimation of multivariable dynamic systems,” Automatica, vol. 41, no. 10, pp. 1667–1682, 2005. doi: 10.1016/j.automatica.2005.05.008
[20]	Z. Zhao, J. Wang, X. Cheng, and Y. Qi, “Particle swarm optimized particle filter and its application in visual tracking,” in Proc. 6th. Natural. Comput. Conf., 2010, pp. 2673–2676.
[21]	J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proc. ICNN. Conf. Neural Networks, 1995, pp. 1942–1948.
[22]	B.-D. Chen, X. Liu, H.-Q. Zhao, and J. C. Principe, “Maximum correntropy Kalman filter,” Automatica, vol. 76, pp. 70–77, 2017. doi: 10.1016/j.automatica.2016.10.004
[23]	Z.-Z. Wu, M.-Y. Fu, Y. Xu, and R.-Q. Lu, “A distributed Kalman filtering algorithm with fast finite-time convergence for sensor networks,” Automatica, vol. 95, pp. 63–72, 2018. doi: 10.1016/j.automatica.2018.05.012
[24]	M.-M. Wang, Q.-B. Ge, C.-X. Li, and C.-Y. Sun, “Charging diagnosis of power battery based on adaptive STCKF and BLS for electric vehicles,” IEEE Trans. Vehicular Technology, vol. 71, no. 8, pp. 8251–8265, 2022. doi: 10.1109/TVT.2022.3171766
[25]	D. Etter, M. Hicks, and K. Cho, “Recursive adaptive filter design using an adaptive genetic algorithm,” in Proc. IEEE. ICASSP. Conf, 1982, pp. 635–638.
[26]	N. Benvenuto and M. Marchesi, “Digital filters design by simulated annealing,” IEEE Trans. Circuits Syst, vol. 36, no. 3, pp. 459–460, 1989. doi: 10.1109/31.17597
[27]	K. Watanabe, F. Campelo, and H. Igarashi, “Topology optimization based on immune algorithm and multigrid method,” IEEE Trans. Magn, vol. 43, no. 4, pp. 1637–1640, April. 2007. doi: 10.1109/TMAG.2006.892259
[28]	S. Qian, Y. Ye, B. Jiang, and J. Wang, “Constrained multiobjective optimization algorithm based on immune system model,” IEEE Trans. Cybern, vol. 46, no. 9, pp. 2056–2069, 2016. doi: 10.1109/TCYB.2015.2461651
[29]	Q. Song, Y. Wu, and Y.-C. Soh, “Robust adaptive gradient-descent training algorithm for recurrent neural networks in discrete time domain,” IEEE Trans. Neural Networks, vol. 19, no. 11, pp. 1841–1853, 2008. doi: 10.1109/TNN.2008.2001923
[30]	R. A. Redner and H. F. Walker, “Mixture densities, maximum likelihood and the EM algorithm,” SIAM Review, vol. 26, no. 2, pp. 195–239, 1984. doi: 10.1137/1026034
[31]	Y. Zhang, P. Zhou, and G. Cui, “Multi-model based PSO method for burden distribution matrix optimization with expected burden distribution output behaviors,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 6, pp. 1506–1512, 2018.
[32]	Y. Wang and X. Zuo, “An effective cloud workflow scheduling approach combining PSO and idle time slot-aware rules,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 5, pp. 1079–1094, 2021. doi: 10.1109/JAS.2021.1003982
[33]	Z. Lv, L. Wang, Z. Han, and J. Zhao, “Surrogate-assisted particle swarm optimization algorithm with Pareto active learning for expensive multi-objective optimization,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 3, pp. 838–849, 2019. doi: 10.1109/JAS.2019.1911450
[34]	L.-F. Xu, Z.-S. Huang, Z.-Z. Yang, and W.-L. Ding, “Mixed particle swarm optimization algorithm with multistage disturbances,” J. Software, vol. 30, no. 6, pp. 1835–1852, 2019.

Supplements(0)

Cited By

Proportional views

Proportional views

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Figures(12) / Tables(8)

Get Citation

PDF

XML

Article Metrics

Article views (660) PDF downloads(98)

Highlights

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

Abstract

References

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Highlights

Export File

Citation

Format

Content