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 LiEmail author
  • Wen-Ge Yang
  • Dan Ding
  • Yu-Rong Liao
Short Paper


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.


Bayesian filtering Cubature Kalman filter Fifth-degree accuracy Cubature points 



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


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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

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