Advertisement

A New Adaptive Kalman Filter with Inaccurate Noise Statistics

  • Dingjie Xu
  • Zhemin WuEmail author
  • Yulong Huang
Short Paper

Abstract

In this paper, a new adaptive Kalman filter is proposed for a linear Gaussian state-space model with inaccurate noise statistics based on the variational Bayesian (VB) approach. Both the prior joint probability density function (PDF) of the one-step prediction and corresponding prediction error covariance matrix and the joint PDF of the mean vector and covariance matrix of measurement noise are selected as Normal-inverse-Wishart (NIW), from which a new NIW-based hierarchical Gaussian state-space model is constructed. The state vector, the one-step prediction and corresponding prediction error covariance matrix, and the mean vector and covariance matrix of measurement noise are jointly estimated based on the constructed hierarchical Gaussian state-space model using the VB approach. Simulation results show that the proposed filter has better estimation accuracy than existing state-of-the-art adaptive Kalman filters.

Keywords

Adaptive filtering Kalman filter Variational Bayesian Normal-inverse-Wishart distribution Inaccurate noise statistics 

Notes

References

  1. 1.
    C.M. Bishop, Pattern Recognition and Machine Learning (Springer, Berlin, 2007)zbMATHGoogle Scholar
  2. 2.
    X. Gao, D. You, S. Katayama, Seam tracking monitoring based on adaptive Kalman filter embedded elman neural network during high-power fiber laser welding. IEEE Trans. Ind. Electron. 59(11), 4315–4325 (2012)CrossRefGoogle Scholar
  3. 3.
    C. Hide, T. Moore, M. Smith, Adaptive Kalman filtering algorithms for integrating GPS and low cost INS, in Proceedings of Position Location Navigation Symposium. IEEE, Monterey, CA, USA, pp. 227–233 (2004)Google Scholar
  4. 4.
    Y.L. Huang, Y.G. Zhang, B. Xu, Z.M. Wu, J. Chambers, A new outlier-robust Student’s t based Gaussian approximate filter for cooperative localization. IEEE/AMSE Trans. Mech. 22(5), 2380–2386 (2017)CrossRefGoogle Scholar
  5. 5.
    Y.L. Huang, Y.G. Zhang, A new process uncertainty robust Student’s t based Kalman filter for SINS/GPS integration. IEEE Access 5(7), 14391–14404 (2017)CrossRefGoogle Scholar
  6. 6.
    Y.L. Huang, Y.G. Zhang, Z.M. Wu, N. Li, J. Chambers, A novel adaptive Kalman filter with inaccurate process and measurement noise covariance matrices. IEEE Trans. Autom. Control 63(2), 594–601 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Y.L. Huang, Y.G. Zhang, B. Xu, Z.M. Wu, J. Chambers, A new adaptive extended Kalman filter for cooperative localization. IEEE Trans. Aerosp. Electron. Syst. 54(1), 353–368 (2018)CrossRefGoogle Scholar
  8. 8.
    Y.L. Huang, Y.G. Zhang, Z.M. Wu, N. Li, J. Chambers, A novel robust Student’s t based Kalman filter. IEEE Trans. Aerosp. Electron. Syst. 53(3), 1545–1554 (2017)CrossRefGoogle Scholar
  9. 9.
    Y.L. Huang, Y.G. Zhang, N. Li, J. Chambers, A robust Gaussian approximate filter for nonlinear systems with heavy-tailed measurement noises, in 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (IEEE, Shanghai, China), pp. 4209–4213 (2016)Google Scholar
  10. 10.
    Y.L. Huang, Y.G. Zhang, N. Li, J. Chambers, A robust Gaussian approximate fixed-interval smoother for nonlinear systems with heavy-tailed process and measurement noises. IEEE Signal Proc. Lett. 23(4), 468–472 (2016)CrossRefGoogle Scholar
  11. 11.
    M. Karasalo, X.M. Hu, An optimization approach to adaptive Kalman filtering. Automatica 47(8), 1785–1793 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    X.R. Li, Y. Bar-Shalom, A recursive multiple model approach to noise identification. IEEE Trans. Aerosp. Electron. Syst. 30(3), 671–684 (1994)CrossRefGoogle Scholar
  13. 13.
    R. Mehra, Approaches to adaptive filtering. IEEE Trans. Autom. Control 17(5), 693–698 (1972)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    A. Mohamed, K.P. Schwarz, Adaptive Kalman filtering for INS/GPS. J. Geod. 73(4), 193–203 (1999)CrossRefzbMATHGoogle Scholar
  15. 15.
    K.P. Murphy, Conjugate Bayesian analysis of the Gaussian distribution. Technical report (2007)Google Scholar
  16. 16.
    D. Simon, Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches (Wiley, New York, 2006)CrossRefGoogle Scholar
  17. 17.
    A.P. Sage, G.W. Husa, Adaptive filtering with unknown prior statistics, in Proceedings of Joint Automatic Control Conference. Boulder, CO, pp. 760–769 (1969)Google Scholar
  18. 18.
    S. Särkkä, A. Nummenmaa, Recursive noise adaptive Kalman filtering by variational Bayesian approximations. IEEE Trans. Autom. Control. 54(3), 596–600 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    M.J. Yu, INS/GPS integration system using adaptive filter for estimating measurement noise variance. IEEE Trans. Aerosp. Electron. Syst. 48(2), 1786–1792 (2012)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Harbin Institute of TechnologyHarbinPeople’s Republic of China
  2. 2.Harbin Engineering UniversityHarbinPeople’s Republic of China

Personalised recommendations