GPS Solutions

, Volume 21, Issue 1, pp 111–122 | Cite as

Analysis of a variational Bayesian adaptive cubature Kalman filter tracking loop for high dynamic conditions

  • Zhi-yong Miao
  • Yun-long Lv
  • Ding-jie Xu
  • Feng Shen
  • Shun-wan Pang
Original Article


Under high dynamic conditions, a robust tracking loop is essential for accuracy positioning with the global position system. In previous studies, the extended Kalman filter (EKF)-based tracking loop technology has been proven better than the traditional tracking loop technology under high dynamic conditions. However, the performance of EKF may degrade because under high dynamic conditions, the statistics of measurement noise may change with time. In order to improve the robustness of the tracking loop under high dynamic conditions, the variational Bayesian adaptive cubature Kalman filter (VBACKF) algorithm with different types of measurement noise variances is proposed and used to track the carrier and code in this study. In the proposed algorithm, the measurement noise is considered as random variables and dynamically estimated by variational Bayesian theory. We take into consideration the two-measurement model with measurements in-phase and quadra-phase prompt (IP and QP), and the six-measurement model with measurements in-phase and quadra-phase prompt, early and late (IP, QP, IE, QE, IL and QL), and compare the proposed method with the EKF- and CKF-based tracking loops. The analytical and simulation results show that the VBACKF-based tracking loop performs better than both the EKF- and CKF-based tracking loops. Furthermore, the influence on the tracking loop of the different numbers of measurements used in the measurement model is also investigated. The results show that the phase, code and frequency tracking performances of EKF-, CKF- and VBACKF-based six measurements outperform those of the corresponding filter-based two measurements under dynamic conditions.


High dynamic conditions Global position system Tracking loop Extended Kalman filter Variational Bayesian adaptive cubature Kalman filter Cubature Kalman filter 



This work was supported by the National Natural Science Foundation of China (Grant Nos. 61102107 and 61374208) and by the China Fundamental Research Funds for the Central Universities (Grant No. HEUCFX41310).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Zhi-yong Miao
    • 1
  • Yun-long Lv
    • 1
  • Ding-jie Xu
    • 2
  • Feng Shen
    • 1
  • Shun-wan Pang
    • 1
  1. 1.College of AutomationHarbin Engineering UniversityHarbinChina
  2. 2.School of Electrical Engineering and AutomationHarbin Institute of TechnologyHarbinChina

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