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GPS satellite inter-frequency clock bias estimation using triple-frequency raw observations

  • Lei Fan
  • Chuang Shi
  • Min LiEmail author
  • Cheng Wang
  • Fu Zheng
  • Guifei Jing
  • Jun Zhang
Original Article
  • 116 Downloads

Abstract

This study proposes a unified uncombined model to estimate GPS satellite inter-frequency clock bias (IFCB) in both triple-frequency code and carrier-phase observations. In the proposed model, the formulae of both phase-based and code-based IFCBs are rigorously derived. Specifically, satellite phase-based IFCB refers to its time-variant part and it is modeled as a periodic function related to the sun–spacecraft–earth angle. A zero-mean condition of all available GPS satellites that support triple-frequency data is introduced to render satellite code-based IFCB estimable. Three months of data from 40 globally distributed stations of the International GNSS Service Multi-GNSS Experiment are used to test our method. The results show that the four-order periodic function is suitable for eliminating the 12-h, 6-h, 4-h, and 3-h periods that exist in the a posteriori phase residuals when no periodic function is used. For comparison, the geometry-free and ionosphere-free (GFIF) phase combination and differential code bias (DCB) products released by DLR (German Aerospace Center) and IGG (Institute of Geodesy and Geophysics, China) are also used to calculate the satellite phase-based and code-based IFCBs, respectively. The results show that (1) the average root mean square (RMS) of the phase-based IFCB difference between the proposed method and the GFIF phase combination is 4.3 mm; (2) the average RMS in the eclipse period increased by 50% compared with the average RMS in the eclipse-free period; (3) the mean monthly STD for code-based IFCB from the proposed method is 0.09 ns; and (4) the average RMS values of code-based IFCB differences between the proposed method and the DCB products released by DLR and IGG are 0.32 and 0.38 ns. This proposed model also provides a general approach for multi-frequency GNSS applications such as precise orbit and clock determination.

Keywords

GPS GNSS Inter-frequency clock bias Differential code bias Raw observations Geometry-free Ionosphere-free combination 

Notes

Acknowledgements

This work was sponsored by the National Natural Science Foundation of China (Grant Nos. 41804024, 41931075, 41804026, 41574027). The authors are grateful to the editors and reviewers for their valuable comments on improving our manuscript. We would also like to thank International GNSS Service (IGS) for providing GPS data and products, and German Aerospace Center (DLR) and Institute of Geodesy and Geophysics (IGG) for providing multi-frequency DCB products. The GPS observation data and IGS final orbit and clock products are obtained from the CDDIS (ftp://cddis.nasa.gov/pub/gps/data/). The GPS P1-C1 DCB products are achieved from the CODE (ftp.unibe.ch/aiub/CODE/2016/). The GPS multi-frequency DCB products are available at ftp://igs.ign.fr/pub/igs/products/mgex/dcb.

Author contributions

C. Shi, L. Fan, and J. Zhang designed the research; L. Fan, G. Jing, and M. Li performed the research; M. Li, C. Wang, and F. Zheng analyzed the data; and L. Fan wrote the paper.

References

  1. Blewitt G (1990) An automatic editing algorithm for GPS data. Geophys Res Lett 17(3):199–202.  https://doi.org/10.1029/GL017i003p00199 CrossRefGoogle Scholar
  2. Boehm J, Niell A, Tregoning P, Schuh H (2006) Global mapping function (GMF): a new empirical mapping function based on numerical weather model data. Geophys Res Lett.  https://doi.org/10.1029/2005GL025546 CrossRefGoogle Scholar
  3. Ciraolo L, Azpilicueta F, Brunini C, Meza A, Radicella S (2007) Calibration errors on experimental slant total electron content (TEC) determined with GPS. J Geod 81(2):111–120.  https://doi.org/10.1007/s00190-006-0093-1 CrossRefGoogle Scholar
  4. Dow JM, Neilan R, Rizos C (2009) The international GNSS service in a changing landscape of global navigation satellite systems. J Geod 83(3–4):191–198.  https://doi.org/10.1007/s00190-008-0300-3 CrossRefGoogle Scholar
  5. Elmowafy A, Deo M, Rizos C (2016) On biases in precise point positioning with multi-constellation and multi-frequency GNSS data. Meas Sci Technol 27(3):035102.  https://doi.org/10.1088/0957-0233/27/3/035102 CrossRefGoogle Scholar
  6. Fan L, Li M, Wang C, Shi C (2017) BeiDou satellite’s differential code biases estimation based on uncombined precise point positioning with triple-frequency observable. Adv Space Res 59(3):804–814.  https://doi.org/10.1016/j.asr.2016.07.014 CrossRefGoogle Scholar
  7. Feltens J, Schaer S (1998). IGS products for the ionosphere. In: Proceedings of the 1998 IGS analysis centers workshop, ESOC, Darmstadt, Germany, 9–11 Feb 1998Google Scholar
  8. Ge M, Gendt G, Rothacher M, Shi C, Liu J (2008) Resolution of GPS carrier-phase ambiguities in precise point positioning (PPP) with daily observations. J Geod 82(7):389–399.  https://doi.org/10.1007/s00190-007-0187-4 CrossRefGoogle Scholar
  9. Geng J, Bock Y (2013) Triple-frequency GPS precise point positioning with rapid ambiguity resolution. J Geod 87(5):449–460.  https://doi.org/10.1007/s00190-013-0619-2 CrossRefGoogle Scholar
  10. Guo J, Geng J (2017) GPS satellite clock determination in case of inter-frequency clock biases for triple-frequency precise point positioning. J Geod 92(10):1133–1142.  https://doi.org/10.1007/s00190-017-1106-y CrossRefGoogle Scholar
  11. Hernandez-Pajares M, Juan JM, Sanz J, Orus R, Garcia-Rigo A, Feltens J, Komjathy A, Schaer SC, Krankowski A (2009) The IGS VTEC maps: a reliable source of ionospheric information since 1998. J Geod 83(3–4):263–275.  https://doi.org/10.1007/s00190-008-0266-1 CrossRefGoogle Scholar
  12. IGS R-S (2013). RINEX: the receiver independent exchange format (RINEX) Version 3.02. Technical report, IGS Central BureauGoogle Scholar
  13. Kouba J (2009a) A guide to using International GNSS Service (IGS) products. International GNSS, Geodetic Survey Division of Natural Resources Canada, OttawaGoogle Scholar
  14. Kouba J (2009b) A simplified yaw-attitude model for eclipsing GPS satellites. GPS Solut 13(1):1–12.  https://doi.org/10.1007/s10291-008-0092-1 CrossRefGoogle Scholar
  15. Li H, Zhou X, Wu B, Wang J (2012a) Estimation of the inter-frequency clock bias for the satellites of PRN25 and PRN01. Sci China 55(11):2186–2193.  https://doi.org/10.1007/s11433-012-4897-0 CrossRefGoogle Scholar
  16. Li Z, Yuan Y, Li H, Ou J, Huo X (2012b) Two-step method for the determination of the differential code biases of COMPASS satellites. J Geod 86(11):1059–1076.  https://doi.org/10.1007/s00190-012-0565-4 CrossRefGoogle Scholar
  17. Li Y, Gao Y, Li B (2015) An impact analysis of arc length on orbit prediction and clock estimation for PPP ambiguity resolution. GPS Solut 19(2):201–213.  https://doi.org/10.1007/s10291-014-0380-x CrossRefGoogle Scholar
  18. Li H, Li B, Xiao G, Wang J, Xu T (2016) Improved method for estimating the inter-frequency satellite clock bias of triple-frequency GPS. GPS Solut 20(4):751–760.  https://doi.org/10.1007/s10291-015-0486-9 CrossRefGoogle Scholar
  19. Li P, Zhang X, Ge M, Schuh H (2018) Three-frequency BDS precise point positioning ambiguity resolution based on raw observables. J Geod 28(5):1–13.  https://doi.org/10.1007/s00190-018-1125-3 CrossRefGoogle Scholar
  20. Liu J, Ge M (2003) PANDA software and its preliminary result of positioning and orbit determination. Wuhan Univ J Nat Sci 8(2B):603–609.  https://doi.org/10.1007/BF02899825 CrossRefGoogle Scholar
  21. Liu T, Zhang B, Yuan Y, Li Z, Wang N (2019) Multi-GNSS triple-frequency differential code bias (DCB) determination with precise point positioning (PPP). J Geod 93(5):765–784.  https://doi.org/10.1007/s00190-018-1194-3 CrossRefGoogle Scholar
  22. Montenbruck O, Hugentobler U, Dach R, Steigenberger P, Hauschild A (2012) Apparent clock variations of the Block IIF-1 (SVN62) GPS satellite. GPS Solut 16(3):303–313.  https://doi.org/10.1007/s10291-011-0232-x CrossRefGoogle Scholar
  23. Montenbruck O, Hauschild A, Steigenberger P, Hugentobler U, Teunissen P, Nakamura S (2013) Initial assessment of the COMPASS/BeiDou-2 regional navigation satellite system. GPS Solut 17(2):211–222.  https://doi.org/10.1007/s10291-012-0272-x CrossRefGoogle Scholar
  24. Montenbruck O, Hauschild A, Steigenberger P (2014) Differential code bias estimation using multi-GNSS observations and global ionosphere maps. Navigation 31(3):191–201.  https://doi.org/10.1002/navi.64 CrossRefGoogle Scholar
  25. Montenbruck O, Steigenberger P, Prange L, Deng Z, Zhao Q, Perosanz F, Romero I, Noll C, Stürze A, Weber G (2017) The Multi-GNSS Experiment (MGEX) of the international GNSS service (IGS)—achievements, prospects and challenges. Adv Space Res 59(7):1671–1697.  https://doi.org/10.1016/j.asr.2017.01.011 CrossRefGoogle Scholar
  26. Odijk D, Zhang B, Khodabandeh A, Odolinski R, Teunissen P (2016) On the estimability of parameters in undifferenced, uncombined GNSS network and PPP-RTK user models by means of S-system theory. J Geod 90(1):15–44.  https://doi.org/10.1007/s00190-015-0854-9 CrossRefGoogle Scholar
  27. Pan L, Zhang X, Li X, Liu J, Li X (2017) Characteristics of inter-frequency clock bias for Block IIF satellites and its effect on triple-frequency GPS precise point positioning. GPS Solut 21(2):811–822.  https://doi.org/10.1007/s10291-016-0571-8 CrossRefGoogle Scholar
  28. Pan L, Zhang X, Guo F, Liu J (2018a) GPS inter-frequency clock bias estimation for both uncombined and ionospheric-free combined triple-frequency precise point positioning. J Geod 93(4):473–487.  https://doi.org/10.1007/s00190-018-1176-5 CrossRefGoogle Scholar
  29. Pan L, Zhang X, Li X, Liu J, Guo F, Yuan Y (2018b) GPS inter-frequency clock bias modeling and prediction for real-time precise point positioning. GPS Solut 22(3):76.  https://doi.org/10.1007/s10291-018-0741-y CrossRefGoogle Scholar
  30. Petit G, Luzum B and Al E (2010). IERS conventions (2010). IERS Technical Note 36: 1–95. http://www.iers.org/TN36/
  31. Rodriguez-Solano CJ, Hugentobler U, Steigenberger P (2012) Adjustable box-wing model for solar radiation pressure impacting GPS satellites. Adv Space Res 49(7):1113–1128.  https://doi.org/10.1016/j.asr.2012.01.016 CrossRefGoogle Scholar
  32. Roma-Dollase D, Hernández-Pajares M, Krankowski A, Kotulak K, Ghoddousi-Fard R, Yuan Y, Li Z, Zhang H, Shi C, Wang C, Feltens J, Vergados P, Komjathy A, Schaer S, García-Rigo A, Gómez-Cama JM (2018) Consistency of seven different GNSS global ionospheric mapping techniques during one solar cycle. J Geod 92(6):691–706.  https://doi.org/10.1007/s00190-017-1088-9 CrossRefGoogle Scholar
  33. Saastamoinen J (1972) Atmospheric correction for the troposphere and stratosphere in radio ranging satellites. Use Artif Satell Geod 15(6):247–251.  https://doi.org/10.1029/GM015p0247 CrossRefGoogle Scholar
  34. Sardon E, Zarraoa N (1997) Estimation of total electron content using GPS data: how stable are the differential satellite and receiver instrumental biases? Radio Sci 32(5):1899–1910.  https://doi.org/10.1029/97rs01457 CrossRefGoogle Scholar
  35. Schaer S, Steigenberger P (2006) Determination and use of GPS differential code bias values. In: Proceedings of IGS workshop, Darmstadt, 8–11 MayGoogle Scholar
  36. Schmid R, Dach R, Collilieux X, Jäggi A, Schmitz M, Dilssner F (2016) Absolute IGS antenna phase center model igs08.atx: status and potential improvements. J Geod 90(4):1–22.  https://doi.org/10.1007/s00190-015-0876-3 CrossRefGoogle Scholar
  37. Schönemann E, Becker M, Springer T (2011) A new approach for GNSS analysis in a multi-GNSS and multi-signal environment. J Geod Sci 1(3):204–214.  https://doi.org/10.2478/v10156-010-0023-2 CrossRefGoogle Scholar
  38. Schönemann E, Springer T, Dilssner F, Enderle W and Zandbergen R (2014) GNSS analysis in a multi-GNSS and multi-signal environment. In: Proceedings of IGS workshop, Pasadena, Califorlia, USA, 23–27 JuneGoogle Scholar
  39. Shi C, Fan L, Li M, Liu Z, Gu S, Zhong S, Song W (2016) An enhanced algorithm to estimate BDS satellite’s differential code biases. J Geod 90(2):161–177.  https://doi.org/10.1007/s00190-015-0863-8 CrossRefGoogle Scholar
  40. Torre AD, Caporali A (2014) An analysis of intersystem biases for multi-GNSS positioning. GPS Solut 19(2):297–307.  https://doi.org/10.1007/s10291-014-0388-2 CrossRefGoogle Scholar
  41. Wang N, Yuan Y, Li Z, Montenbruck O, Tan B (2015) Determination of differential code biases with multi-GNSS observations. J Geod 90(3):209–228.  https://doi.org/10.1007/s00190-015-0867-4 CrossRefGoogle Scholar
  42. Wu JT, Wu SC, Hajj GA, Bertiger WI, Lichten SM (1993) Effects of antenna orientation on GPS carrier phase. Manuscr Geod 18(2):91–98Google Scholar
  43. Ye S, Zhao L, Song J, Chen D, Jiang W (2017) Analysis of estimated satellite clock biases and their effects on precise point positioning. GPS Solut 22(1):16.  https://doi.org/10.1007/s10291-017-0680-z CrossRefGoogle Scholar
  44. Zhang B, Ou J, Yuan Y, Li Z (2012) Extraction of line-of-sight ionospheric observables from GPS data using precise point positioning. Sci China Earth Sci 55(11):1919–1928.  https://doi.org/10.1007/s11430-012-4454-8 CrossRefGoogle Scholar
  45. Zhang B, Teunissen PJG, Yuan Y (2017a) On the short-term temporal variations of GNSS receiver differential phase biases. J Geod 91(5):563–572.  https://doi.org/10.1007/s00190-016-0983-9 CrossRefGoogle Scholar
  46. Zhang X, Wu M, Liu W, Li X, Yu S, Lu C, Wickert J (2017b) Initial assessment of the COMPASS/BeiDou-3: new-generation navigation signals. J Geod 91(10):1225–1394.  https://doi.org/10.1007/s00190-017-1020-3 CrossRefGoogle Scholar
  47. Zhao L, Ye S, Chen D (2019) Numerical investigation on the effects of third-frequency observable on the network clock estimation model. Adv Space Res 63(9):2930–2937.  https://doi.org/10.1016/j.asr.2018.03.004 CrossRefGoogle Scholar
  48. Zumberge J, Heflin M, Jefferson D, Watkins M, Webb F (1997) Precise point positioning for the efficient and robust analysis of GPS data from large networks. J Geophys Res Solid Earth 102(B3):5005–5017.  https://doi.org/10.1029/96JB03860 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Lei Fan
    • 1
  • Chuang Shi
    • 1
  • Min Li
    • 2
    Email author
  • Cheng Wang
    • 3
  • Fu Zheng
    • 1
  • Guifei Jing
    • 4
  • Jun Zhang
    • 1
  1. 1.School of Electronic and Information EngineeringBeihang UniversityBeijingChina
  2. 2.GNSS Research CenterWuhan UniversityWuhanChina
  3. 3.Institute of Innovative Research in Frontier Science and TechnologyBeihang UniversityBeijingChina
  4. 4.BeiDou Belt and Road SchoolBeihang UniversityBeijingChina

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