Advertisement

Circuits, Systems, and Signal Processing

, Volume 37, Issue 9, pp 4090–4108 | Cite as

A Novel Fifth-Degree Cubature Kalman Filter Approaching the Lower Bound on the Number of Cubature Points

  • Zhao-Ming Li
  • Wen-Ge Yang
  • Dan Ding
  • Yu-Rong Liao
Short Paper

Abstract

In this paper, a novel fifth-degree cubature Kalman filter, which approaches the lower bound on the number of cubature points, is proposed to reduce the computational complexity while maintaining the fifth-degree filtering accuracy. The Gaussian weighted integral of a nonlinear function is approximated using a numerical cubature rule, whose number of cubature points needed is only one more than the theoretical lower bound, and the filter is deduced under the Bayesian filtering framework by this rule. Furthermore, a square-root version of the proposed fifth-degree cubature Kalman filter is given, and it acquires higher computational efficiency and ensures the numerical stability of the filter. Three numerical simulations are taken, and the results show that the proposed filters maintain the fifth-degree filtering accuracy, while needing the least amount of computation and achieving the best real-time performance.

Keywords

Bayesian filtering Cubature Kalman filter Fifth-degree accuracy Cubature points 

Notes

Acknowledgements

This work was supported by the National High Technology Research and Development Program of China (Grant No. 2015AA7026085).

References

  1. 1.
    I. Arasaratnam, S. Haykin, Cubature Kalman filters. IEEE Trans. Autom. Control 54(6), 1254–1269 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    J.G. Chen, N. Wang, L.L. Ma, B.G. Xu, Extended target probability hypothesis density filter based on cubature Kalman filter. IET Radar Sonar Navig. 9(3), 324–332 (2015)CrossRefGoogle Scholar
  3. 3.
    L. James, L.D. David, Higher-dimensional integration with Gaussian weight for applications in probabilistic design. SIAM J. Sci. Comput. 26(2), 613–624 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    B. Jia, M. Xin, Y. Cheng, High-degree cubature Kalman filters. Automatica 49(2), 510–518 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    S. Julier, J. Uhlmann, A new method for nonlinear transformation of means and covariances in filters and estimators. IEEE Trans. Autom. Control 45(3), 477–482 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    A.K. Singh, S. Bhaumik, Higher degree cubature quadrature Kalman filter. Int. J. Control Autom. Syst. 13(5), 1097–1105 (2015)CrossRefGoogle Scholar
  7. 7.
    A.H. Stroud, Approximate Calculation of Multiple Integrals (Prentice-Hall, Englewood Cliffs, 1971)zbMATHGoogle Scholar
  8. 8.
    S.Y. Wang, J.C. Feng, C.K. Tse, Spherical simplex-radial cubature Kalman filter. IEEE Signal Process. Lett. 21(1), 43–46 (2014)CrossRefGoogle Scholar
  9. 9.
    K. Xiong, H.Y. Zhang, C.W. Chan, Performance evaluation of UKF-based nonlinear filtering. Automatica 42(2), 261–270 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    J. Zarei, E. Shokri, Convergence analysis of non-linear filtering based on cubature Kalman filter. IET Sci. Meas. Technol. 9(3), 294–305 (2015)CrossRefGoogle Scholar
  11. 11.
    L.J. Zhang, H.B. Yang, H.P. Lu, S.F. Zhang, H. Cai, S. Qian, Cubature Kalman filtering for relative spacecraft attitude and position estimation. Acta Astronaut. 105(1), 254–264 (2014)CrossRefGoogle Scholar
  12. 12.
    X.C. Zhang, Cubature information filters using high-degree and embedded cubature rules. Circuits Syst. Signal Process. 33(6), 1799–1818 (2014)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Company of Postgraduate ManagementAcademy of EquipmentHuairou District, BeijingChina
  2. 2.Department of Optical and Electrical EquipmentAcademy of EquipmentHuairou District, BeijingChina

Personalised recommendations