GPS Solutions

, 22:46 | Cite as

Accurate ionospheric delay model for real-time GPS-based positioning of LEO satellites using horizontal VTEC gradient estimation

  • Alfredo Renga
  • Flavia Causa
  • Urbano Tancredi
  • Michele Grassi
Original Article


Ionospheric delays compensation is a mandatory step for precise absolute and relative positioning of Low Earth Orbit Satellites (LEO) by GPS measurements. The most frequently used ionosphere model for real-time GPS-based navigation in LEO is an isotropic model proposed by Lear, which uses the Vertical Total Electron Content (VTEC) above the receiver and a mapping function for TEC evaluation along a given ray path. Based on significant assessed results available for ground-based GPS receivers, we propose the use of a different model relying on the thin shell assumption and a bilinear horizontal variation of the VTEC as a function of latitude and longitude in the shell. It is expected that this model is capable of better describing horizontal gradients in the ionosphere, thus improving ionospheric delay estimation, especially in intense ionospheric conditions. This model is referred to as Linear Thin Shell (LTS). LTS performance in estimating undifferenced and double-differenced ionospheric delays is checked by comparing measured and predicted delays computed using flight data from the GRACE mission. Results show that the LTS always outperforms the isotropic model, especially in case of high solar activity. Moreover, the LTS model provides a higher performance uniformity over a wide range of ionospheric delays, thus ensuring good performance in different conditions. The results obtained demonstrate that the LTS model improves the ionosphere delays estimation accuracy by 20 and 40% for undifferenced and double-differenced delays, respectively. This suggests the LTS model can effectively contribute to improving precision in LEO positioning applications.


Ionospheric path delay Space-borne GPS receivers Vertical Total Electron Content gradient Formation flying Relative navigation Large baseline Double differences Real-time positioning 


  1. Allain DJ, Mitchell CN (2009) Ionospheric delay corrections for single-frequency GPS receivers over Europe using tomographic mapping. GPS Solut 13(2):141–151. CrossRefGoogle Scholar
  2. Allende-Alba G, Montenbruck O (2016) Robust and precise baseline determination of distributed spacecraft in LEO. Adv Space Res 57(1):46–63. CrossRefGoogle Scholar
  3. Allien A, Taillandier C, Capo C, Priselow K, Legenne J, Marechal J, Jeannot M (2011) User guide for EGNOS application developers, 2nd edn. Office for Official Publications of the European Communities, LuxembourgGoogle Scholar
  4. Banville S, Zhang W, Ghoddousi-Fard R, Langley RB (2012) Ionospheric monitoring using “integer-levelled” observations. In: Proceedings of ION GNSS 2013, Institute of Navigation, Nashville, Tennessee, USA, 16–20 September, pp 2692–2701Google Scholar
  5. Dach R, Schaer S, Arnold D, Prange L, Susnik A, Villiger A, Jäggi A (2016) CODE final product series for the IGS. Accessed 14 June 2017
  6. Ebinuma T, Bishop RH, Lightsey EG (2003) Integrated hardware investigations of precision spacecraft rendezvous using the global positioning system. J Guid Control Dyn 26(3):425–433. CrossRefGoogle Scholar
  7. Farrell J (2008) Aided navigation: gps with high rate sensors, 1st edn. McGraw-Hill Inc, New YorkGoogle Scholar
  8. Gill E, D’Amico S, Montenbruck O (2007) Autonomous formation flying for the PRISMA mission. J Spacecr Rockets 44(3):671–681. CrossRefGoogle Scholar
  9. Howe BM, Runciman K, Secan JA (1998) Tomography of the ionosphere: four-dimensional simulations. Radio Sci 33(1):109–128. CrossRefGoogle Scholar
  10. Huang Z, Yuan H (2013) Analysis and improvement of ionospheric thin shell model used in SBAS for China region. Adv Space Res 51(11):2035–2042. CrossRefGoogle Scholar
  11. Jin R, Jin S, Feng G (2012) M_DCB: matlab code for estimating GNSS satellite and receiver differential code biases. GPS Solut 16(4):541–548. CrossRefGoogle Scholar
  12. Klobuchar JA (1987) Ionospheric time-delay algorithm for single-frequency GPS users. IEEE Trans Aerosp Electron Syst AES 23(3):325–331. CrossRefGoogle Scholar
  13. Klobuchar JA (1996) Ionospheric effects on GPS. In: Parkinson BW, Spilker JJ (eds) Global positioning system: theory and applications, vol I. American Institute of Aeronautics and Astronautics Inc., Washington, pp 485–515Google Scholar
  14. Komjathi A, Langley RB (1996) An assessment of predicted and measured ionospheric total electron content using a regional GPS network. In: Proceedings of ION NTM 1996, Santa Monica, California USA, 22–23 January, pp 615–624Google Scholar
  15. Krieger G, Moreira A, Fiedler H, Hajnsek I, Werner M, Marwan Y, Zink M (2007) TanDEM-X: a satellite formation for high-resolution SAR interferometry. IEEE Trans Geosci Remote 45(11):3317–3340. CrossRefGoogle Scholar
  16. Kroes R, Montenbruck O, Bertiger W, Visser P (2005) Precise GRACE baseline determination using GPS. GPS Solut 9(1):21–31. CrossRefGoogle Scholar
  17. Lear WM (1988) GPS navigation for low earth orbiting vehicles. NASA 87-FM-2, Rev. 1, JSC-32031, Lyndon B. Johnson Space Center, Mission planning and analysis divisionGoogle Scholar
  18. Leung S, Montenbruck O (2005) Real-time navigation of formation-flying spacecraft using global-positioning-system measurements. J Guid Control Dyn 28(2):226–235. CrossRefGoogle Scholar
  19. Liu J, Cannon ME, Alves P, Petrovello MG, Lachapelle G, MacGougan G, deGroot L (2003) A performance comparison of single and dual frequency GPS ambiguity resolution strategies. GPS Solut 7(2):87–100. CrossRefGoogle Scholar
  20. Mannucci AJ, Iijima BA, Lindqwister UJ, Pi X, Sparks L, Wilson BD (1999) GPS and ionosphere. In: Ross Stone W (ed) The review of radio science 1996–1999. Oxford University Press, New York, pp 625–665Google Scholar
  21. Mitch RH, Psiaki ML, Tong DM (2013) Local ionosphere model estimation from dual-frequency global navigation satellite system observables. Radio Sci 48(6):671–684. CrossRefGoogle Scholar
  22. Mohiuddin S, Psiaki ML (2008) Carrier-phase differential global positioning system navigation filter for high-altitude spacecraft. J Guid Control Dyn 31(4):801–814. CrossRefGoogle Scholar
  23. Montenbruck O (2003) Kinematic GPS positioning of LEO satellites using ionosphere-free single frequency measurements. Aerosp Sci Technol 7:396–405. CrossRefGoogle Scholar
  24. Montenbruck O, D’Amico S (2013) GPS based relative navigation. In: D’Errico M (ed) Distributed space missions for earth system monitoring. Springer, New York, pp 185–223CrossRefGoogle Scholar
  25. Montenbruck O, Ramos-Bosch P (2008) Precision real-time navigation of LEO satellites using global positioning system measurements. GPS Solut 12(3):187–198. CrossRefGoogle Scholar
  26. Nava B, Coïsson P, Radicella SM (2008) A new version of the NeQuick ionosphere electron density model. J Atmos Solar-Terr Phys 70(15):1856–1862. CrossRefGoogle Scholar
  27. Odijk D (2003) Ionosphere-free phase combinations for modernized GPS. J Sur Eng ASCE 129(4):165–173. CrossRefGoogle Scholar
  28. Odijk D, Teunissen PJG (2010) Improving the speed of CORS Network RTK ambiguity resolution. In: Proceedings of ION PLANS 2010, Indian Wells, California, USA, 4–6 May, pp 79–84.
  29. Rawer K (1988) Synthesis of ionospheric electron density profiles with Epstein functions. Adv Space Res 8(4):191–199. CrossRefGoogle Scholar
  30. Sardón 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. CrossRefGoogle Scholar
  31. Shi C, Gu S, Lou Y, Ge M (2012) An improved approach to model ionospheric delays for single-frequency Precise Point Positioning. Adv Space Res 49(12):1698–1708. CrossRefGoogle Scholar
  32. Skone S, Cannon ME (1998) Auroral zone ionospheric considerations for WADGPS. J Navig 45(2):117–127. CrossRefGoogle Scholar
  33. Spilker JJ (1996) GPS navigation data. In: Parkinson BW, Spilker JJ (eds) Global positioning system: theory and applications, vol I. American Institute of Aeronautics and Astronautics Inc., Washington, pp 230–257Google Scholar
  34. Tancredi U, Renga A, Grassi M (2011) Ionospheric path delay models for spaceborne GPS receivers flying in formation with large baselines. Adv Space Res 48(3):507–520. CrossRefGoogle Scholar
  35. Tancredi U, Renga A, Grassi M (2014a) Real-time relative positioning of spacecraft over long baselines. J Guid Control Dyn 37(1):47–58. CrossRefGoogle Scholar
  36. Tancredi U, Renga A, Grassi M (2014b) Geometric total electron content models for topside ionospheric sounding. In: Proceedings of EESMS 2014—2014 IEEE workshop on environmental energy and structural monitoring systems, 17–18 September, pp 163–168.
  37. Tancredi U, Renga A, Grassi M (2014c) Novel closed-loop approaches for precise relative navigation of widely separated GPS receivers in LEO. Acta Astronaut 93:243–251. CrossRefGoogle Scholar
  38. Tancredi U, Allende-Alba G, Renga A, Montenbruck O, Grassi M (2015) Relative positioning of spacecraft in intense ionospheric conditions by GPS. Aerosp Sci Technol 43:191–198. CrossRefGoogle Scholar
  39. Tapley BD, Bettadpur S, Watkins M, Reigber C (2004) The gravity recovery and climate experiment: mission overview and early results. Geophys Res Lett. Google Scholar
  40. Teunissen PJG (1997) The geometry-free GPS ambiguity search space with a weighted ionosphere. J Geodesy 71(6):370–383. CrossRefGoogle Scholar
  41. van Barneveld PWL, Montenbruck O, Visser PN (2007) Differential ionospheric effects in GPS based navigation of formation flight satellites. In: Proceedings of 3rd international symposium on formation flying, Mission and Technology 2008, ESA/ESTEC, Noordwijk, The Netherlands, 23–25 April, pp 1–8Google Scholar
  42. Verhagen S, Odijk D, Teunissen PJG, Huisman L (2010) Performance improvement with low-cost multi-GNSS receivers. In: Proceedings of NAVITEC 2010, Noordwijk, The Netherlands, 8–10 December, pp 1–8.
  43. Verhulst T, Stankov SM (2015) Ionospheric specification with analytical profilers: evidences of non-Chapman electron density distribution in the upper ionosphere. Adv Space Res 55(8):2058–2069. CrossRefGoogle Scholar
  44. Zhang W, Langley RB, Komjathi A, Banville S (2013) Eliminating potential errors caused by the thin shell assumption: an extended 3D UNB ionospheric modelling technique. In: Proceedings of ION GNSS 2013, Institute of Navigation, Nashville, Tennessee, USA, 16–20 September, pp 2447–2462Google Scholar
  45. Zhong J, Lei J, Dou X, Yue X (2016a) Assessment of vertical TEC mapping functions for space-based GNSS observations. GPS Solut 20(3):353–362. CrossRefGoogle Scholar
  46. Zhong J, Lei J, Yue X, Dou X (2016b) Determination of differential code bias of GNSS receiver onboard low earth orbit satellite. IEEE Trans Geosci Remote 54(8):4896–4905. CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.University of Naples “Federico II”NaplesItaly
  2. 2.European Patent OfficeMunichGermany

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