Advertisement

GPS Solutions

, Volume 21, Issue 4, pp 1817–1828 | Cite as

On the estimation of higher-order ionospheric effects in precise point positioning

  • Simon BanvilleEmail author
  • Rafal Sieradzki
  • Mainul Hoque
  • Kinga Wezka
  • Tomasz Hadas
Original Article

Abstract

Higher-order ionospheric effects, if not properly accounted for, can propagate into geodetic parameter estimates. For this reason, several investigations have led to the development and refinement of formulas for the correction of second- and third-order ionospheric errors, bending effects and total electron content variations due to excess path length. Standard procedures for computing higher-order terms typically rely on slant total electron content computed either from global ionospheric maps (GIMs) or using GNSS observations corrected using differential code biases (DCBs) provided by an external process. In this study, we investigate the feasibility of estimating slant ionospheric delay parameters accounting for both first- and second-order ionospheric effects directly within a precise point positioning (PPP) solution. It is demonstrated that proper handling of the receiver DCB is critical for the PPP method to provide unbiased estimates of the position. The proposed approach is therefore not entirely free from external inputs since GIMs are required for isolating the receiver DCB, unless the latter is provided to the PPP filter. In terms of positioning performance, the PPP approach is capable of mitigating higher-order ionospheric effects to the same level as existing approaches. Due to the inherent risks associated with constraining slant ionospheric delay parameters in PPP during disturbed ionospheric conditions, the reliability of the method can be greatly enhanced when the receiver DCB is available a priori, such as for permanent GNSS stations.

Keywords

GNSS Ionosphere Higher-order corrections Precise point positioning (PPP) 

Notes

Acknowledgements

The authors would like to thank the International GNSS Service (IGS) for making GNSS data available and the Centre National d’Études Spatiales (CNES) for providing the satellite orbit and clock corrections used in this study. The project was conducted as a part of the International Association of Geodesy (IAG) working group 4.3.4 “Ionosphere and Troposphere Impact on GNSS Positioning.” This paper was published under the auspices of the NRCan Earth Sciences Sector as contribution number 20160445.

References

  1. Bassiri S, Hajj GA (1993) Higher-order ionospheric effects on the global positioning system observables and means of modeling them. Manuscr Geodaet 18(6):280–289Google Scholar
  2. Brunner FK, Gu M (1991) An improved model for the dual frequency ionospheric correction of GPS observations. Manuscr Geodaet 16(3):205–214Google Scholar
  3. Collins P, Bisnath S, Lahaye F, Héroux P (2010) Undifferenced GPS ambiguity resolution using the decoupled clock model and ambiguity datum fixing. Navigation 57(2):123–135CrossRefGoogle Scholar
  4. Elmas ZG, Aquino M, Marques HA, Monico JFG (2011) Higher order ionospheric effects in GNSS positioning in the European region. Ann Geophys 29:1383–1399. doi: 10.5194/angeo-29-1383-2011 CrossRefGoogle Scholar
  5. Fritsche M, Dietrich R, Knöfel C, Rülke A, Vey S, Rothacher M, Steigenberger P (2005) Impact of higher-order ionospheric terms on GPS estimates. Geophys Res Lett 32(23):L23–311. doi: 10.1029/2005GL024342 CrossRefGoogle Scholar
  6. Hawarey M, Hobiger T, Schuh H (2005) Effects of the 2nd order ionospheric terms on VLBI measurements. Geophys Res Lett 32(11):L11304. doi: 10.1029/2005GL022729 CrossRefGoogle Scholar
  7. Hernández-Pajares M, Juan JM, Sanz J, Orús R (2007) Second-order ionospheric term in GPS: implementation and impact on geodetic estimates. J Geophys Res 112:B08417. doi: 10.1029/2006JB004707 CrossRefGoogle Scholar
  8. Hernández-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 83:263. doi: 10.1007/s00190-008-0266-1 CrossRefGoogle Scholar
  9. Hernández-Pajares M, Aragón-Ángel À, Defraigne P, Bergeot N, Prieto-Cerdeira R, Garcia-Rigo A (2014) Distribution and mitigation of higher-order ionospheric effects on precise GNSS processing. J Geophys Res 119:3823–3837. doi: 10.1002/2013JB010568 CrossRefGoogle Scholar
  10. Hoque MM, Jakowski N (2008) Estimate of higher order ionospheric errors in GNSS positioning. Radio Sci 43:RS5008. doi: 10.1029/2007RS003817 CrossRefGoogle Scholar
  11. Hoque MM, Jakowski N (2012) New correction approaches for mitigating ionospheric higher order effects in GNSS applications. In: Proceedings of ION GNSS 2012, Nashville, Tennessee, USA, September 17–21, pp 3444–3453Google Scholar
  12. Jakowski N, Porsch F, Mayer G (1994) Ionosphere-induced-ray-path bending effects in precise satellite positioning systems. Z Satellitengestützte Position Navig Kommun SPN 1(94):6–13Google Scholar
  13. Kedar S, Hajj G, Wilson B, Heflin M (2003) The effect of the second order GPS ionospheric correction on receiver positions. Geophys Res Lett 30(16):1829. doi: 10.1029/2003.GL017639 CrossRefGoogle Scholar
  14. Kouba J (2015) A guide to using international GNSS service (IGS) products, September 2015 update. http://kb.igs.org/hc/en-us/articles/201271873-A-Guide-to-Using-the-IGS-Products
  15. Kouba J, Héroux P (2001) Precise point positioning using IGS orbit and clock products. GPS Solut 5(2):12–28. doi: 10.1007/PL00012883 CrossRefGoogle Scholar
  16. Loyer S, Perosanz F, Mercier F, Capdeville H, Marty JC (2012) Zero-difference GPS ambiguity resolution at CNES–CLS IGS analysis center. J Geod 86:991. doi: 10.1007/s00190-012-0559-2 CrossRefGoogle Scholar
  17. Marques HA, Monico JFG, Aquino M (2011) RINEX_HO: second- and third-order ionospheric corrections for RINEX observation files. GPS Solut 15(3):305. doi: 10.1007/s10291-011-0220-1 CrossRefGoogle Scholar
  18. Odijk D (2003) Ionosphere-free phase combinations for modernized GPS. J Surv Eng 129(4):165–173. doi: 10.1061/(ASCE)0733-9453 CrossRefGoogle Scholar
  19. Odijk D, Zhang B, Khodabandeh A, Odolinski R, Teunissen PJG (2016) On the estimability of parameters in undifferenced, uncombined GNSS network and PPP-RTK user models by means of S-system theory. J Geod 90:15–44. doi: 10.1007/s00190-015-0854-9 CrossRefGoogle Scholar
  20. Petit G, Luzum B, Conventions IERS (2010) IERS technical note 36. Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am MainGoogle Scholar
  21. Petrie EJ, Hernández-Pajares M, Spalla P, Moore P, King MA (2011) A review of higher order ionospheric refraction effects on dual frequency GPS. Surv Geophys 32:197–253. doi: 10.1007/s10712-010-9105-z CrossRefGoogle Scholar
  22. Pireaux S, Defraigne P, Wauters L, Bergeot N, Baire Q, Bruyninx C (2010) Higher-order ionospheric effects in GPS time and frequency transfer. GPS Solut 14(3):267–277. doi: 10.1007/s10291-009-0152-1 CrossRefGoogle Scholar
  23. Rebischung P, Altamimi Z, Ray J, Garayt B (2016) The IGS contribution to ITRF2014. J Geod 90:611. doi: 10.1007/s00190-016-0897-6 CrossRefGoogle Scholar
  24. Rovira-Garcia A, Juan JM, Sanz J, González-Casado G, Ibáñez D (2016) Accuracy of ionospheric models used in GNSS and SBAS: methodology and analysis. J Geod 90:229. doi: 10.1007/s00190-015-0868-3 CrossRefGoogle Scholar
  25. Schaer S (1999) Mapping and predicting the Earth’s ionosphere using the Global Positioning System. Ph.D. Dissertation Astronomical Institute, University of Berne, Berne, Switzerland, 25 MarchGoogle Scholar
  26. Schaer S, Gurtner W, Feltens F (1998) IONEX: the IONosphere map exchange format version 1. In: Proceedings of the 1998 IGS analysis centers workshop, Darmstadt, Germany, 9–11 FebruaryGoogle Scholar
  27. Strangeways HJ, Ioannides RT (2002) Rigorous calculation of ionospheric effects on GPS Earth–Satellite paths using a precise path determination method. Acta Geod Geoph Hung 37(2–3):281–292CrossRefGoogle Scholar
  28. Zehentner N, Mayer-Gürr T (2016) Precise orbit determination based on raw GPS measurements. J Geod 90:275–286. doi: 10.1007/s00190-015-0872-7 CrossRefGoogle Scholar
  29. Zhang W, Zhang DH, Xiao Z (2009) The influence of geomagnetic storms on the estimation of GPS instrumental biases. Ann Geophys 27:1613C1623. doi: 10.5194/angeo-27-1613-2009 Google Scholar
  30. 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 102(B3):5005–5017. doi: 10.1029/96JB03860 CrossRefGoogle Scholar

Copyright information

© Her Majesty the Queen in Right of Canada 2017

Authors and Affiliations

  • Simon Banville
    • 1
    Email author
  • Rafal Sieradzki
    • 2
  • Mainul Hoque
    • 3
  • Kinga Wezka
    • 4
  • Tomasz Hadas
    • 5
  1. 1.Canadian Geodetic Survey, Natural Resources Canada (NRCan)OttawaCanada
  2. 2.University of Warmia and MazuryOlsztynPoland
  3. 3.Institute of Communications and NavigationGerman Aerospace Center (DLR)WesslingGermany
  4. 4.Technical University of BerlinBerlinGermany
  5. 5.Wroclaw University of Environmental and Life SciencesWrocławPoland

Personalised recommendations