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

Abstract

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.

Keywords

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

Notes

Acknowledgments

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).

References

  1. Arasaratnam I, Haykin S (2009) Cubature Kalman filters. IEEE Trans Autom Control 54(6):1254–1269CrossRefGoogle Scholar
  2. Gernot C, O’Keefe K, Lachapelle G (2008) Combined L1/L2C tracking scheme for weak signal environments. In: Proceedings of ION GNSS 2008, Institute of Navigation, Savannah, GA, 16–19 Sep, pp 1758–1772Google Scholar
  3. Im S-H, Song J-H, Jee G-I, Park C-G (2008) Comparison of GPS tracking loop performance in high dynamic condition with nonlinear filtering techniques. In: Proceedings of ION GNSS 2008, Institute of Navigation, Savannah, GA, 16–19, Sep, pp 2351–2360Google Scholar
  4. Jaakkola TS (2001) Tutorial on variational approximation methods. Advanced mean field methods: theory and practice. MIT Press, Cambridge, pp 129–159Google Scholar
  5. Jee GI (2005) GNSS receiver tracking loop optimization for combined phase, frequency and delay locked loops. In: European navigation conference (ENC-GNSS 2005), Munich, 19–22 JulyGoogle Scholar
  6. Jia B, Xin M (2013) High-degree cubature Kalman filter. Automatica 49(2):510–518CrossRefGoogle Scholar
  7. Macchi F, Petovello MG, Lachapelle G (2010) Combined acquisition and tracking methods for GPS L1 C/A and L1C signals. Int J Navig Obs 2010, Article ID 190465Google Scholar
  8. Mbalawata IS, Särkkä S, Vihola M, Haario H (2015) Adaptive metropolis algorithm using variational Bayesian adaptive Kalman filter. Comput Stat Data Anal 83:101–115CrossRefGoogle Scholar
  9. Petovello MG, Lachapelle G (2006) Comparison of vector-based software receiver implementations with application to ultra-tight GPS/INS integration. In: Proceedings of ION GNSS 2006, Institue of Navigation, Fort Worth, TX, 26–29 Sep, pp 1790–1799Google Scholar
  10. Psiaki, ML (2001) Smoother-based GPS signal tracking in a software receiver. In: Proceedings of ION GPS 2001, Salt Lake City, UT, 11–14 Sep, pp 2900–2913Google Scholar
  11. Psiaki ML, Jung H (2002) Extended Kalman filter methods for tracking weak GPS signals. In: Proceedings of ION GPS 2002, Portland, Oregon, 24–27 Sep, pp 2539–2553Google Scholar
  12. Salem D, O’Driscoll C, Lachapelle G (2009) Performance evaluation of combined L1/L5 Kalman filter-based tracking versus standalone L1/L5 tracking in challenging environments. J Glob Position Syst 8(2):135–147CrossRefGoogle Scholar
  13. Salem D, O’Driscoll C, Lachapelle G (2012) Methodology for comparing two carrier phase tracking techniques. GPS Solut 16(2):197–207CrossRefGoogle Scholar
  14. Särkkä S (2013) Bayesian filtering and smoothing. Volume 3 of Institute of Mathematical Statistics TextbooksGoogle Scholar
  15. Särkkä S, Nummenmaa A (2009) Recursive noise adaptive Kalman filtering by variational Bayesian approximations. IEEE Trans Autom Control 54(3):596–600CrossRefGoogle Scholar
  16. Tang X, Falco G, Falletti E, Presti LL (2013) Practical implementation and performance assessment of an extended Kalman filter-based signal tracking loop. In: International conference on localization and GNSS (ICL-GNSS), Torino, Italy, 25–27 June, pp 1–6Google Scholar
  17. Vilnrotter VA, Hinedi S, Kumar R (1989) A comparison of frequency estimation techniques for high dynamic trajectories. IEEE Trans Aerosp Electron Syst 25(4):559–577CrossRefGoogle Scholar
  18. Woessner W, Noronha J, Jovancevic A, Ganguly S (2006) A software defined real-time ultra-tightly coupled (UTC) GNSS-INS architecture. In: Proceedings of ION GNSS 2006, Fort Worth, TX, 26–29 Sep, pp 2695–2703Google Scholar
  19. Won J-H, Dotterbock D, Eissfeller B (2009) Performance comparison of different forms of Kalman filter approaches for a vector-based GNSS signal tracking loop. Navigation 57(3):185–199CrossRefGoogle Scholar
  20. Wu Y, Hu D, Wu M, Hu X (2006) A numerical-integration perspective on Gaussian filters. IEEE Trans Signal Process 54(8):2910–2921CrossRefGoogle Scholar
  21. Zarei J, Shokri E, Karimi HR (2014) Convergence analysis of cubature Kalman filter. In: European control conference (ECC), Strasbourg, France, 24–27 June, pp 1367–1372Google Scholar
  22. Zhang X-C, Guo C-J (2014) A new derivation of the cubature Kalman filters. Asian J Control 16(5):1501–1510CrossRefGoogle Scholar
  23. Ziedan NI, Garrison JL (2004) Extended Kalman filter-based tracking of weak GPS signals under high dynamic conditions. In: Proceedings of ION GNSS 2004, Long Beach, CA, 21–24 Sep, pp 20–31Google Scholar

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

Personalised recommendations