GPS Solutions

, Volume 12, Issue 2, pp 87–97 | Cite as

Mitigation of higher order ionospheric effects on GNSS users in Europe

  • M. Mainul HoqueEmail author
  • N. Jakowski
Original Article


Current dual-frequency GPS measurements can only eliminate the first-order ionospheric term and may cause a higher-order range bias of several centimeters. This research investigates the second-order ionospheric effect for GNSS users in Europe. In comparison to previous studies, the electron density profiles of the ionosphere/plasmasphere are modeled as the sum of three Chapman layers describing electron densities of the ionospheric F2, F1 and E layers and a superposed exponential decay function describing the plasmasphere. The International Geomagnetic Reference Field model is used to calculate the geomagnetic field vectors at numerous points along the incoming ray paths. Based on extended simulation studies, we derive a correction formula to compute the average value of the longitudinal component of the earth’s magnetic field along the line-of-sight as a function of geographic latitude and longitude, and geometrical parameters such as elevation and azimuth angles. Using our correction formula in conjunction with the total electron content (TEC) along the line-of-sight, the second-order ionospheric term can be corrected to the millimeter level for a vertical TEC level of 1018 electrons/m2.


GNSS positioning Signal refraction Second-order ionospheric correction 



This work has been financially supported by the German State Government of Mecklenburg-Vorpommern under Grant V230-630-08-TIFA-334.


  1. Bassiri S, Hajj GA (1993) Higher-order ionospheric effects on the global positioning system observables and means of modeling them. Manuscripta Geodaetica 18(6):280–289Google Scholar
  2. Belehaki A, Jakowski N, Reinisch BW (2004) Plasmaspheric electron content derived from GPS TEC and digisonde ionograms. Adv Space Res 33(6):833–837CrossRefGoogle Scholar
  3. Bradley PA, Dudeney JR (1973) A simple model representation of the electron concentration of the ionosphere. J Atmos Terres Phys 35(12):2131–2146CrossRefGoogle Scholar
  4. Brunner FK, Gu M (1991) An improved model for the dual frequency ionospheric correction of GPS observations. Manuscripta Geodaetica 16(3):205–214Google Scholar
  5. Budden KG (1985) The propagation of radio waves: the theory of radio waves of low power in the ionosphere and magnetosphere. Cambridge University Press, Cambridge. ISBN 0 521 25461 2Google Scholar
  6. Davies K (1990) Ionospheric radio. Peter Peregrinus Ltd, London. ISBN 0 86341 186 XGoogle Scholar
  7. Decker RP (1972) Techniques for synthesizing median true height profiles from propagation parameters. J Atmos Terres Phys 34(3):451–464CrossRefGoogle Scholar
  8. 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):L23311. doi: 10.1029/2005GL024342CrossRefGoogle Scholar
  9. Hajj GA, Romans LJ (1998) Ionospheric electron density profiles obtained with the global positioning system: results from GPS/MET experiment. Radio Sci 33(1):175–190CrossRefGoogle Scholar
  10. Hawarey M, Hobiger T, Schuh H (2005) Effects of the 2nd order ionospheric terms on VLBI measurements. Geophys Res Lett 32(11):L11304. doi: 10.1029/2005GL022729CrossRefGoogle Scholar
  11. Hoque MM, Jakowski N (2006) Higher-order ionospheric effects in precise GNSS positioning. J Geodesy (in press). doi: 10.1007/s00190-006-0106-0Google Scholar
  12. Jakowski N (1996) TEC monitoring by using satellite positioning systems. In: Kohl H, Rüster R, Schlegel K (eds) Modern ionospheric science. EGS, Katlenburg-Lindau, ProduServ GmbH Verlagsservice, Berlin, pp 371–390, ISBN3-9804862-1-4Google Scholar
  13. Jakowski N, Wehrenpfennig A, Heise S, Reigber C, Lühr H, Grunwaldt L, Meehan T K (2002) GPS radio occultation measurements of the ionosphere from CHAMP: early results. Geophys Res Lett 29(10):1457. doi: 10.1029/2001 GL014364CrossRefGoogle Scholar
  14. Jakowski N, Leitinger R, Angling M (2004) Radio occultation techniques for probing the ionosphere. Ann Geophys 47(2/3):1049–1066Google Scholar
  15. Jakowski N, Stankov S M, Klaehn D, Beniguel Y, Rueffer J (2004) Operational service for monitoring and evaluating the space weather impact on precise positioning applications of GNSS. In: Proceedings of European Navigation Conference ENC-GNSS2004, Rotterdam, Paper No. GNSS2004–119Google Scholar
  16. 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 GL017639CrossRefGoogle Scholar
  17. Kelley MC (1989) The Earth’s Ionosphere, Plasmaphysics and Electrodynamics. Academic Press, New York (Appendix B)Google Scholar
  18. Klobuchar JA (1996) Ionospheric effects on GPS. In: Parkinson BW (ed) Global Positioning System: Theory and Applications, Vol I. American Institute of Aeronautics& Astronautics, pp 485–515. ISBN 156347106XGoogle Scholar
  19. Langley RB (1997) The GPS error budget. GPS World 8(3):51–56Google Scholar
  20. Lunt NL, Kersley L, Bailey GJ (1999) The influence of the protonosphere on GPS observations: model simulations. Radio Sci 34(3):725–732CrossRefGoogle Scholar
  21. Mandea M, Macmillan S (2000) International geomagnetic reference field—the eighth generation. Earth Planets Space 52(12):1119–1124Google Scholar
  22. Norman RJ (2003) An Inversion Technique for obtaining Quasi-Parabolic layer parameters from VI Ionograms. Proceedings IEEE Radar conference, pp. 363–367. doi: 10.1109/RADAR.2003.1278768Google Scholar
  23. Rishbeth H, Garriott OK (1969) Introduction to ionospheric physics. Academic Press, New YorkGoogle Scholar
  24. Rizos C (2002) Network RTK Research and Implementation—a geodetic perspective. J Global Position Syst 1(2):144–150CrossRefGoogle Scholar
  25. Sardon E, Zarraoa N (1997) Estimation of total electron content using GPS data: how stable are the differential satellite and receiver instrument biases. Radio Sci 32(5):1899–1910CrossRefGoogle Scholar
  26. Stankov SM, Jakowski N (2006) Topside ionospheric scale height analysis and modelling based on radio occultation measurements. J Atmos Sol-terr Phys 68:134–162. doi: 10.1016/j.jastp.2005.10.003CrossRefGoogle 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. Wang Z, Wu Y, Zhang K, Meng Y (2005) Triple-frequency method for high-order ionospheric refractive error modeling in GPS modernization. J Global Position Syst 4(1–2):291–295CrossRefGoogle Scholar
  29. Wilkes MV (1954) A table of Chapman’s grazing incidence integral Ch(x,χ). Proc Phys Soc 67B, pp. 304Google 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):5005–5017CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.German Aerospace Center (DLR)Institute of Communications and NavigationNeustrelitzGermany
  2. 2.International Postgraduate Programme Multi SensoricsCenter for Sensorsystems at University of SiegenSiegenGermany

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