Skip to main content
SpringerLink
Log in

Variational Bayesian-Based Adaptive Maximum Correntropy Generalized High-Degree Cubature Kalman Filter

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

In this paper, we propose a new filtering algorithm, the variational Bayesian-based adaptive maximum correntropy generalized high-degree cubature Kalman filter, which is designed to improve filtering accuracy under conditions of unknown measurement noise covariance and measurement outliers. Considering that the generalized high-degree cubature rule can solve the high dimensional nonlinear problem well, based on the generalized high-degree cubature Kalman filter, the variational Bayesian method is utilized to approximate the measurement noise covariance, and the maximum correntropy criterion is used to reduce the influence of the measurement outliers on the state estimation. Additionally, we introduce a resistance factor to correct measurement values and optimize the kernel bandwidth for different types of noise. Simulation experiments on target tracking and integrated navigation demonstrate that our proposed algorithm effectively suppresses unknown time-varying noise and non-Gaussian mutation noise, outperforming existing filtering algorithms in terms of estimation accuracy, robustness, and adaptability.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Data Availability

Data will be made available on reasonable request.

References

  1. F. Albu, L. T. T. Tran, S. Nordholm, The hybrid simplified Kalman filter for adaptive feedback cancellation, in 2018 International Conference on Communications (COMM), Bucharest, Romania (2018), pp. 45–50. https://doi.org/10.1109/ICComm.2018.8484823

  2. M. Ali, C.W. Ahn, M. Pant et al., An image watermarking scheme in wavelet domain with optimized compensation of singular value decomposition via artificial bee colony. Inf. Sci. 301, 44–60 (2016). https://doi.org/10.1016/j.ins.2014.12.042

    Article  Google Scholar 

  3. I. Arasaratnam, S. Haykin, Cubature Kalman filters. IEEE Trans. Autom. Control 6(54), 1254–1269 (2009). https://doi.org/10.1109/TAC.2009.2019800

    Article  MathSciNet  MATH  Google Scholar 

  4. A. Assa, F. Janabi-Sharifi, A Kalman filter-based framework for enhanced sensor fusion. IEEE Sens. J. 6(15), 3281–3292 (2015). https://doi.org/10.1109/JSEN.2014.2388153

    Article  Google Scholar 

  5. J. Bin, X. Ming, C.Y. Cheng, High-degree cubature Kalman filters. Automatica 4(49), 510–518 (2009). https://doi.org/10.1016/j.automatica.2012.11.014

    Article  MATH  Google Scholar 

  6. G.T. Cinar, J.C. Príncipe, Hidden state estimation using the correntropy filter with fixed point update and adaptive kernel size, in Proceedings of 2012 IEEE International Joint Conference on Neural Networks, IJCNN, July. (2012), pp. 1–6. https://doi.org/10.1109/IJCNN.2012.6252730

  7. N. Davari, A. Gholami, An asynchronous adaptive direct Kalman filter algorithm to improve underwater navigation system performance. IEEE Sens. J. 4(17), 1061–1068 (2016). https://doi.org/10.1109/JSEN.2016.2637402

    Article  Google Scholar 

  8. P. Dong, Z. Jing, H. Leung, K. Shen, Variational Bayesian adaptive cubature information filter based on Wishart distribution. IEEE Trans. Autom. Control 62(11), 6051–6057 (2017). https://doi.org/10.1109/TAC.2017.2704442

    Article  MathSciNet  MATH  Google Scholar 

  9. S. Fakoorian, R. Izanloo, A. Shamshirgaran, D. Simon, Maximum correntropy criterion Kalman filter with adaptive kernel size, in 2019 IEEE National Aerospace and Electronics Conference, NAECON, Dayton, OH, USA (2019), pp. 581–584. https://doi.org/10.1109/NAECON46414.2019.9057886

  10. Y. Guo, B. Xu, L. Wang, A robust SINS/USBL integrated navigation algorithm based on earth frame and right group error definition. IEEE Trans. Instrum. Meas. 71, 1–16 (2022). https://doi.org/10.1109/TIM.2022.3196425

    Article  Google Scholar 

  11. Y. Hao, A. Xu, X. Sui, Y. Wang, A modified extended kalman filter for a two-antenna GPS/INS vehicular navigation system. Sensors 18(11), 3809 (2018). https://doi.org/10.3390/s18113809

    Article  Google Scholar 

  12. J. He, C. Sun, B. Zhang, P. Wang, Maximum correntropy square-root cubature Kaman filter for non-gaussian measurement noise. IEEE Access 8, 70162–70170 (2020). https://doi.org/10.1109/ACCESS.2020.2986022

    Article  Google Scholar 

  13. B. Hou, Z. He, X. Zhou et al., Maximum correntropy criterion Kalman filter for-Jerk tracking model with non-Gaussian noise. Entropy 12(19), 648 (2017). https://doi.org/10.3390/e19120648

    Article  Google Scholar 

  14. P.J. Huber, Robust estimation of a location parameter, in Breakthroughs in Statistics: Methodology and Distribution (1992), pp. 492–518. https://doi.org/10.1007/978-1-4612-4380-9_35

  15. R. Izanloo, S. A. Fakoorian, H. S. Yazdi, D. Simon, Kalman filtering based on the maximum correntropy criterion in the presence of non-Gaussian noise, in Proceedings of 50th Annual Conference on Information Sciences and Systems (Princeton, USA, 2016), pp. 500–505. https://doi.org/10.1109/CISS.2016.7460553

  16. J. Lan, X.R. Li, Multiple conversions of measurements for nonlinear estimation. IEEE Trans. Signal Process. 65(18), 4956–4970 (2017). https://doi.org/10.1109/TSP.2017.2716901

    Article  MathSciNet  MATH  Google Scholar 

  17. Y. Li, Y. Wang, F. Albu et al., A general zero attraction proportionate normalized maximum correntropy criterion algorithm for sparse system identification. Symmetry 9(10), 229–232 (2017). https://doi.org/10.3390/sym9100229

    Article  MATH  Google Scholar 

  18. D. Liu, X. Chen, Y. Xu et al., Maximum correntropy generalized high-degree cubature Kalman filter with application to the attitude determination system of missile. Aerosp. Sci. Technol. 95, 105–114 (2019). https://doi.org/10.1016/j.ast.2019.105441

    Article  Google Scholar 

  19. H. Ren, R. Lu, J. Xiong, Y. Wu, P. Shi, Optimal filtered and smoothed estimators for discrete-time linear systems with multiple packet dropouts under Markovian communication constraints. IEEE Trans. Cybern. 50(9), 4169–4181 (2020). https://doi.org/10.1109/TCYB.2019.2924485

    Article  Google Scholar 

  20. H. Ren, R. Lu, J. Xiong, Y. Xu, Optimal estimation for discrete-time linear system with communication constraints and measurement quantization. IEEE Trans. Syst. Man Cybern. Syst. 50(5), 1932–1942 (2020). https://doi.org/10.1109/TSMC.2018.2792009

    Article  Google Scholar 

  21. S. Särkkä, J. Hartikainen, Non-linear noise adaptive Kalman filtering via variational Bayes, in Proceedings of 2013 IEEE International Workshop on Machine Learning for Signal Processing (Southampton, UK, 2013), pp. 1–6. https://doi.org/10.1109/MLSP.2013.6661935

  22. B. Wang, Q. Ren, Z. Deng et al., A self-calibration method for northogonal angles between gimbals of rotational inertial navigation system. IEEE Trans. Ind. Electron. 4(62), 2353–2362 (2014). https://doi.org/10.1109/TIE.2014.2361671

    Article  Google Scholar 

  23. G. Wang, N. Li, Y. Zhang, Maximum correntropy unscented Kalman and information filters for non-Gaussian measurement noise. J. Frankl. Inst. 354(18), 8659–8677 (2017). https://doi.org/10.1016/j.jfranklin.2017.10.023

    Article  MathSciNet  MATH  Google Scholar 

  24. G. Wang, Z. Gao, Y. Zhang, B. Ma, Adaptive maximum correntropy Gaussian filter based on variational Bayes. Sensors 18(6), 1960 (2018). https://doi.org/10.3390/s18061960

    Article  Google Scholar 

  25. S. Wang, J. Feng, K.T. Chi, Spherical simplex-radial cubature Kalman filter. IEEE Signal Process. Lett. 1(21), 43–46 (2013). https://doi.org/10.1109/LSP.2013.2290381

    Article  Google Scholar 

  26. X.C. Zhang, Cubature information filters using high-degree and embedded cubature rules. Circuits System Signal Process 3(33), 1799–1818 (2014)

    Article  MathSciNet  Google Scholar 

Download references

Funding

This research was supported by funds from the National Natural Science Foundation of China under Grant Numbers 41906005, 41705081, National Key Research and Development Project of China under Grant Numbers 2017YFB0202701, and National Basic Research Program of China under Grant Number 2019-JCJQ-ZD-149-00.

Author information

Authors and Affiliations

  1. Naval Submarine Academy, Qingdao, 266199, China

    Baoheng Liu, Xiaochuan Zhang & Shuyang Jia

  2. Laoshan Laboratory, Qingdao, 266237, China

    Baoheng Liu, Xiaochuan Zhang, Shuyang Jia, Sichen Zou & Deyan Tian

Authors
  1. Baoheng Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaochuan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shuyang Jia
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Sichen Zou
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Deyan Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Baoheng Liu.

Ethics declarations

Conflict of interest

The authors declare no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, B., Zhang, X., Jia, S. et al. Variational Bayesian-Based Adaptive Maximum Correntropy Generalized High-Degree Cubature Kalman Filter. Circuits Syst Signal Process 42, 7073–7098 (2023). https://doi.org/10.1007/s00034-023-02436-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-023-02436-w

Keywords

Search

Navigation