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Journal of Geodesy

, Volume 89, Issue 11, pp 1145–1158 | Cite as

Particle filter-based estimation of inter-frequency phase bias for real-time GLONASS integer ambiguity resolution

  • Yumiao TianEmail author
  • Maorong Ge
  • Frank Neitzel
Original Article

Abstract

GLONASS could hardly reach the positioning performance of GPS, especially for fast and real-time precise positioning. One of the reasons is the phase inter-frequency bias (IFB) at the receiver end prevents its integer ambiguity resolution. A number of studies were carried out to achieve the integer ambiguity resolution for GLONASS. Based on some of the revealed IFB characteristics, for instance IFB is a linear function of the received carrier frequency and L1 and L2 have the same IFB in unit of length, most of recent methods recommend estimating the IFB rate together with ambiguities. However, since the two sets of parameters are highly correlated, as demonstrated in previous studies, observations over several hours up to 1 day are needed even with simultaneous GPS observations to obtain a reasonable solution. Obviously, these approaches cannot be applied for real-time positioning. Actually, it can be demonstrated that GLONASS ambiguity resolution should also be available even for a single epoch if the IFB rate is precisely known. In addition, the closer the IFB rate value is to its true value, the larger the fixing RATIO will be. Based on this fact, in this paper, a new approach is developed to estimate the IFB rate by means of particle filtering with the likelihood function derived from RATIO. This approach is evaluated with several sets of experimental data. For both static and kinematic cases, the results show that IFB rates could be estimated precisely just with GLONASS data of a few epochs depending on the baseline length. The time cost with a normal PC can be controlled around 1 s and can be further reduced. With the estimated IFB rate, integer ambiguity resolution is available immediately and as a consequence, the positioning accuracy is improved significantly to the level of GPS fixed solution. Thus the new approach enables real-time precise applications of GLONASS.

Keywords

GLONASS Integer ambiguity resolution Phase inter-frequency bias Particle filter Real-time applications 

Notes

Acknowledgments

The first author is financially supported by the China Scholarship Council (CSC) for his study at the Technische Universität Berlin and the German Research Center of Geosciences (GFZ).

References

  1. Alber C, Ware R, Rocken C, Braun J (2000) Obtaining single path phase delays from GPS double differences. Geophys Res Lett 27(17):2661–2664CrossRefGoogle Scholar
  2. Al-Shaery A, Zhang S, Rizos C (2013) An enhanced calibration method of GLONASS inter-channel bias for GNSS RTK. GPS Solut. 17(2):165–173CrossRefGoogle Scholar
  3. Al-Shaery A, Zhang S, Lim S, Rizos C (2012) A comparative study of mathematical modelling for GPS/GLONASS real-time kinematic (RTK). In: Proceedings of ION GNSS 2012, pp 2231–2238Google Scholar
  4. Arulampalam MS, Maskell S, Gordon N, Clapp T (2002) A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans Signal Process 50(2):174–188CrossRefGoogle Scholar
  5. Banville S, Collins P, Lahaye F (2013) GLONASS ambiguity resolution of mixed receiver types without external calibration. GPS Solut 17(3):275–282CrossRefGoogle Scholar
  6. Blewitt G (1989) Carrier phase ambiguity resolution for the global positioning system applied to geodetic baselines up to 2000 km. J Geophys Res 94(B8):10187–10203CrossRefGoogle Scholar
  7. Dimov IT (2008) Monte Carlo methods for applied scientists. World Scientific, LondonGoogle Scholar
  8. Dong D, Bock Y (1989) Global positioning system network analysis with phase ambiguity resolution applied to crustal deformation studies in California. J Geophys Res 94:3949–3966CrossRefGoogle Scholar
  9. Doucet A, Godsill S, Andrieu C (2000) On sequential Monte Carlo sampling methods for Bayesian filtering. Stat Comput 10(3):197–208CrossRefGoogle Scholar
  10. Doucet A, Freitas N, Gordon N (2001) Sequential Monte Carlo methods in practice. Springer, New YorkCrossRefGoogle Scholar
  11. Ge M, Gendt G, Dick G, Zhang FP (2005) Improving carrier-phase ambiguity resolution in global GPS network solutions. J Geod 79:103–110. doi: 10.1007/s00190-005-0447-0
  12. Gordon NJ, Salmond DJ, Smith AF (1993) Novel approach to nonlinear/non-Gaussian Bayesian state estimation. In: IEE Proceedings-F (Radar and Signal Processing), vol 140, pp 107–113Google Scholar
  13. Gustafsson F, Gunnarsson F, Bergman N, Forssell U, Jansson J, Karlsson R, Nordlund PJ (2002) Particle filters for positioning, navigation, and tracking. IEEE Trans Signal Process 50(2):425–437CrossRefGoogle Scholar
  14. Gustafsson F (2010) Particle filter theory and practice with positioning applications. IEEE Aerosp Electron Syst Mag 25(7):53–82CrossRefGoogle Scholar
  15. Han S, Dai L, Rizos C (1999) A new data processing strategy for combined GPS/GLONASS carrier phase-based positioning. In: Proceedings of ION GPS 1999, pp 1619–1627Google Scholar
  16. Haug AJ (2012) Bayesian estimation and tracking: a practical guide. Wiley, New JerseyCrossRefGoogle Scholar
  17. Kitagawa G (1996) Monte Carlo filter and smoother for non-Gaussian nonlinear state space models. J Comput Graph Stat 5(1):1–25Google Scholar
  18. Leick A (1998) GLONASS satellite surveying. J Surv Eng 124(2):91–99CrossRefGoogle Scholar
  19. Li T, Wang J (2011) Comparing the mathematical models for GPS and GLONASS integration. In: International Global Navigation Satellite Systems Society Symposium-IGNSS, CD-ROM procs. SydneyGoogle Scholar
  20. Pratt M, Burke B, Misra P (1998) Single-epoch integer ambiguity resolution with GPS-GLONASS L1–L2 Data. In: Proceedings of ION GNSS 1998, pp 389–398Google Scholar
  21. Sleewagen J, Simsky A, Wilde WD, Boon F, Willems T (2012) Demystifying GLONASS inter-frequency carrier phase biases. InsideGNSS 7(3):57–61Google Scholar
  22. Takasu T, Yasuda A (2009) Development of the low-cost RTK-GPS receiver with an open source program package rtklib. In: Proceedings of international symposium on GPS/GNSS. JejuGoogle Scholar
  23. Teunissen PJ (1995) The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation. J Geod 70(1–2):65–82CrossRefGoogle Scholar
  24. Teunissen PJG (2004) Penalized GNSS ambiguity resolution. J Geod 78(4–5):235–244CrossRefGoogle Scholar
  25. Wang J (2000) An approach to GLONASS ambiguity resolution. J Geod 74(5):421–430CrossRefGoogle Scholar
  26. Wang J, Rizos C, Stewart MP, Leick A (2001) GPS and GLONASS integration: modeling and ambiguity resolution issues. GPS Solut 5(1):55–64CrossRefGoogle Scholar
  27. Wanninger L (2012) Carrier-phase inter-frequency biases of GLONASS receivers. J Geod 86(2):139–148CrossRefGoogle Scholar
  28. Wanninger L, Wallstab-Freitag S (2007) Combined processing of GPS, GLONASS, and SBAS code phase and carrier phase measurements. In: Proceedings of ION GNSS 2007, pp 866–875Google Scholar
  29. Zhang S, Zhang K, Wu S, Li B (2011) Network-based RTK positioning using integrated GPS and GLONASS observations. In: International global navigation satellite systems society symposium-IGNSS, CD-ROM procs. SydneyGoogle Scholar
  30. Zinoviev AE, Veitsel AV, Dolgin DA (2009) Renovated GLONASS: improved performances of GNSS receivers. In: Proceedings of ION GNSS 2009, pp 3271–3277Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Technische Universität BerlinBerlinGermany
  2. 2.German Research Centre for GeosciencesPotsdamGermany

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