GPS Solutions

, 22:85 | Cite as

Revisit the calibration errors on experimental slant total electron content (TEC) determined with GPS

  • Wenfeng Nie
  • Tianhe XuEmail author
  • Adria Rovira-GarciaEmail author
  • José Miguel Juan Zornoza
  • Jaume Sanz Subirana
  • Guillermo González-Casado
  • Wu Chen
  • Guochang Xu
Original Article


The calibration errors on experimental slant total electron content (TEC) determined with global positioning system (GPS) observations is revisited. Instead of the analysis of the calibration errors on the carrier phase leveled to code ionospheric observable, we focus on the accuracy analysis of the undifferenced ambiguity-fixed carrier phase ionospheric observable determined from a global distribution of permanent receivers. The results achieved are: (1) using data from an entire month within the last solar cycle maximum, the undifferenced ambiguity-fixed carrier phase ionospheric observable is found to be over one order of magnitude more accurate than the carrier phase leveled to code ionospheric observable and the raw code ionospheric observable. The observation error of the undifferenced ambiguity-fixed carrier phase ionospheric observable ranges from 0.05 to 0.11 total electron content unit (TECU) while that of the carrier phase leveled to code and the raw code ionospheric observable is from 0.65 to 1.65 and 3.14 to 7.48 TECU, respectively. (2) The time-varying receiver differential code bias (DCB), which presents clear day boundary discontinuity and intra-day variability pattern, contributes the most part of the observation error. This contribution is assessed by the short-term stability of the between-receiver DCB, which ranges from 0.06 to 0.17 TECU in a single day. (3) The remaining part of the observation errors presents a sidereal time cycle pattern, indicating the effects of the multipath. Further, the magnitude of the remaining part implies that the code multipath effects are much reduced. (4) The intra-day variation of the between-receiver DCB of the collocated stations suggests that estimating DCBs as a daily constant can have a mis-modeling error of at least several tenths of 1 TECU.


Ionospheric observable Total electron content Integer ambiguity resolution Receiver DCB 



The study is funded by National Key Research and Development Program of China (2016YFB0501902), National Natural Science Foundation of China (41574025, 41574013, 41731069), Spanish Ministry of Science and Innovation project (CGL2015-66410-P), The Hong Kong RGC Joint Research Scheme (E-PolyU501/16) and State Key Laboratory of Geo-Information Engineering (SKLGIE2015-M-2-2).


  1. Banville S, Zhang W, Ghoddousi-Fard R, Langley RB (2012) Ionospheric monitoring using integer-leveled observations. In: Proceedings of ION ITM 2012, Institute of Navigation, Nashville, Tennessee, USA, September 17–21, pp 2692–2701Google Scholar
  2. Bossler JD, Goad CC, Bender PL (1980) Using the global positioning system (GPS) for geodetic positioning. Bull Géodésique 54(4):553–563CrossRefGoogle Scholar
  3. Braasch M (1996) Multi-path effects. In: Parkinson BW, Spilker JJ (eds) Global positioning system: theory and applications, vol 1. Progress in astronautics and aeronautics. American Institute of Aeronautics and Astronautics, Reston, pp 547–568Google Scholar
  4. Brunini C, Azpilicueta FJ (2009) Accuracy assessment of the GPS-based slant total electron content. J Geodesy 83(8):773–785CrossRefGoogle Scholar
  5. Ciraolo L, Azpilicueta F, Brunini C, Meza A, Radicella S (2007) Calibration errors on experimental slant total electron content (TEC) determined with GPS. J Geodesy 81(2):111–120CrossRefGoogle Scholar
  6. Collins P, Lahaye F, Heroux P, Bisnath S (2008) Precise point positioning with ambiguity resolution using the decoupled clock model. In: Proceedings of ION GNSS 2008, Institute of Navigation, Savannah, Georgia, USA, September 16–19, pp 1315–1322Google Scholar
  7. Coster A, Williams J, Weatherwax A, Rideout W, Herne D (2013) Accuracy of GPS total electron content: GPS receiver bias temperature dependence. Radio Sci 48(2):190–196. CrossRefGoogle Scholar
  8. Dow JM, Neilan RE, Rizos C (2009) The international GNSS service in a changing landscape of global navigation satellite systems. J Geodesy 83(3–4):191–198CrossRefGoogle Scholar
  9. Ge M, Gendt M, Rothacher M, Shi C, Liu J (2008) Resolution of GPS carrier phase ambiguities in precise point positioning (PPP) with daily observations. J Geodesy 82(7):389–399CrossRefGoogle Scholar
  10. Geng J, Shi C, Ge M, Dodson AH, Lou Y, Zhao Q, Liu J (2012) Improving the estimation of fractional-cycle biases for ambiguity resolution in precise point positioning. J Geodesy 86(8):579–589CrossRefGoogle Scholar
  11. Hatch R (1982) The synergism of GPS code and carrier measurements. In: Proceedings of the third international symposium on satellite Doppler positioning, Physical Sciences Laboratory of New Mexico State University, Feb 8–12, pp 1213–1231Google Scholar
  12. Hernández-Pajares M, Juan J, Sanz J, Orus R, Garcia-Rigo A, Feltens J, Komjathy A, Schaer S, Krankowski A (2009) The IGS VTEC maps: a reliable source of ionospheric information since 1998. J Geodesy 83(3–4):263–275CrossRefGoogle Scholar
  13. Hernández-Pajares M, Roma Dollase D, Krankowski A, García Rigo A, Orús Pérez R (2016) Comparing performances of seven different global VTEC ionospheric models in the IGS context. In International GNSS service workshop (IGS 2016), Sydney, Australia, February 8–12, pp 1–13Google Scholar
  14. Juan J, Hernández-Pajares M, Sanz J, Ramos-Bosch P, Aragon-Angel A, Orús R, Ochieng W, Feng S, Coutinho P, Samson J, Tossaint M (2012) Enhanced precise point positioning for GNSS Users. IEEE Trans Geosci Remote Sens 50(10):4213–4222CrossRefGoogle Scholar
  15. Laurichesse D, Mercier F (2007) Integer Ambiguity resolution on undifferenced GPS phase measurements and its application to PPP. In: Proceedings of ION GNSS 2007, Institute of Navigation, Fort Worth, Texas, USA, September 25–28, pp 839–848Google Scholar
  16. Li M, Yuan Y, Wang N, Liu T, Chen Y (2017) Estimation and analysis of the short-term variations of multi-GNSS receiver differential code biases using global ionosphere maps. J Geodesy. Google Scholar
  17. Liu T, Yuan Y, Zhang B, Wang N, Tang B, Cheng Y (2017) Multi-GNSS precise point positioning (MGPPP) using raw observations. J Geodesy 91(3):253–268CrossRefGoogle Scholar
  18. Liu T, Zhang B, Yuan Y, Li M (2018) Real-time precise point positioning (RTPPP) with raw observations and its application in real-time regional ionospheric VTEC modeling. J Geodesy. Google Scholar
  19. Manucci AJ, Iijima BA, Lindqwister UJ, Pi X, Sparks L, Wilson BD (1999) GPS and ionosphere. URSI reviews of radio science. Jet Propulsion Laboratory, PasadenaGoogle Scholar
  20. Melbourne WG (1985) The case for ranging in GPS-based geodetic systems. In: Proceedings of the first international symposium on precise positioning with the Global Positioning System Rockville, Maryland, April 15–19, pp 373–386Google Scholar
  21. Nie W, Xu T, Rovira-Garcia A, Zornoza JM, Subirana JS, González-Casado G, Chen W, Xu G (2018) The impacts of the ionospheric observable and mathematical model on the global ionosphere model. Remote Sens 10(2):169CrossRefGoogle Scholar
  22. Rovira-Garcia A, Juan JM, Sanz J, González-Casado G (2015) A world-wide ionospheric model for fast precise point positioning. IEEE Trans Geosci Remote Sens 53(8):4596–4604. CrossRefGoogle Scholar
  23. Rovira-Garcia A, Juan JM, Sanz J, González-Casado G, Ibáñez-Segura D (2016a) Accuracy of ionospheric models used in GNSS and SBAS: methodology and analysis. J Geodesy 90(3):229–240. CrossRefGoogle Scholar
  24. Rovira-Garcia A, Juan JM, Sanz J, González-Casado G, Bertran E (2016b) Fast precise point positioning: a system to provide corrections for single and multi-frequency Navigation. Navigation 63(3):231–247. CrossRefGoogle Scholar
  25. Sanz J, Juan J, Hernández-Pajares M (2013) GNSS data processing, vol I: fundamentals and algorithms. ESA Communications, Noordwijk (ESTEC TM-23/1, ISBN 978-92-9221-886-7)Google Scholar
  26. Sanz J, Juan JM, Rovira-Garcia A, González-Casado G (2017) GPS differential code biases determination: methodology and analysis. GPS Solut 21(4):1549–1561. CrossRefGoogle Scholar
  27. 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):1899–1910CrossRefGoogle Scholar
  28. Sardon E, Rius A, Zarraoa N (1994) Estimation of the transmitter and receiver differential biases and the ionospheric total electron content from global positioning system observations. Radio Sci 29(3):577–586. CrossRefGoogle Scholar
  29. Wilson BD, Mannucci AJ (1993) Instrumental biases in ionospheric measurement derived from GPS data. In: Proceedings of ION GPS 1993, Institute of Navigation, Salt Lake City, UT, September 22–24, pp 1343–1351Google Scholar
  30. Wübbena G (1985) Software developments for geodetic positioning with GPS using TI-4100 code and carrier measurements. In: Proceedings of the first international symposium on precise positioning with the global positioning system, Rockville, Maryland, April 15–19Google Scholar
  31. Zhang B (2016) Three methods to retrieve slant total electron content measurements from ground-based GPS receivers and performance assessment. Radio Sci 51(7):972–988CrossRefGoogle Scholar
  32. Zhang B, Teunissen PJ (2015) Characterization of multi-GNSS between-receiver differential code biases using zero and short baselines. Sci Bull 60(21):1840–1849CrossRefGoogle Scholar
  33. 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):1919–1928CrossRefGoogle Scholar
  34. Zhang B, Teunissen PJ, Yuan Y (2017) On the short-term temporal variations of GNSS receiver differential phase biases. J Geodesy 91(5):563–572CrossRefGoogle Scholar
  35. Zumberge JF, Heflin MB, Jefferson DC, Watkins MM, Webb FH (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. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Space SciencesShandong UniversityWeihaiChina
  2. 2.State Key Laboratory of Geo-information EngineeringXi’anChina
  3. 3.Department of Land Surveying and Geo-InformaticsThe Hong Kong Polytechnic UniversityHong KongChina
  4. 4.Research Group of Astronomy and Geomatics (gAGE)Universitat Politecnica de Catalunya (UPC)BarcelonaSpain

Personalised recommendations