Journal of Geodesy

, Volume 82, Issue 1, pp 47–57 | Cite as

Atmospheric turbulence theory applied to GPS carrier-phase data

  • Steffen SchönEmail author
  • Fritz K. Brunner
Original Article


Turbulent irregularities in the lower atmosphere cause physical correlations between Global Positioning System (GPS) carrier-phase measurements. Based on turbulence theory, a variance–covariance model is developed in this paper that reflects these correlations. The main result shows that the obtained fully-populated variance–covariance matrices depend not only on the satellite-station geometry, but also on the prevailing atmospheric conditions, which are parameterised by, e.g., the von Karman spectrum of refractivity fluctuations and the wind velocity vector. It is shown that the amount of the correlation between two GPS carrier-phase observations is inversely related to the separation distance of the corresponding ray paths through the turbulent atmosphere. Furthermore, the wind velocity and direction play a key role in the correlation.


GPS Physical correlations Turbulence theory Atmospheric refractivity fluctuations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abramowitz M, Segun IA (eds) (1972) Handbook of mathematical functions. Dover, New YorkGoogle Scholar
  2. Andrews LC, Phillips RL (1998) Laser beam propagation through random media. The International Society of Optical Engineering Press, BellinghamGoogle Scholar
  3. Armstrong JW, Sramek RA (1982) Observations of the tropospheric phase scintillations at 5 GHz on vertical paths. Radio Sci 17(6):1579–1586Google Scholar
  4. Bischoff W, Heck B, Howind J, Teusch A (2005) A procedure for testing the assumption of homoscedasticity in least-squares residuals: a case study of GPS carrier-phase observations. J Geod 78(7–8):397–404 doi:10.1007/s00190-004-0390-5CrossRefGoogle Scholar
  5. Bischoff W, Heck B, Howind J, Teusch A (2006) A procedure for estimating the variance function of linear models and for checking the appropriateness of estimated variances: a case study of GPS carrier phase observations. J Geod 79(12):694–704 doi:10.1007/s00190-006-0024-1CrossRefGoogle Scholar
  6. Beutler G, Bauersima I, Gurtner W, Rothacher M (1987) Correlations between simultaneous GPS double difference carrier phase observations in the multistation mode: Implementation considerations and first experiences. Manusc Geod 12(1):40–44Google Scholar
  7. Born M, Wolf E (2003) Principles of optics electromagnetic theory of propagation, interference and diffraction of light, 7th (expanded) edn. Cambridge University Press, CambridgeGoogle Scholar
  8. Brunner FK (1982) The effects of atmospheric turbulence on telescopic observations. Bull Géod 56(4):341–355 doi:10.1007/ BF02525733CrossRefGoogle Scholar
  9. Davis JL (1992) The effect of turbulence on atmospheric gradient parameter estimated from ground-based radiometric and space geodetic measurements. Geophys Res Lett 19(1):2183–2186Google Scholar
  10. Dravskikh AF, Finkelstein AM (1979) Tropospheric limitations in phase and frequency coordinate measurements in astronomy. Astrophys Space Sci 60(2):251–265CrossRefGoogle Scholar
  11. Edwards CD (1989) The effect of spatial and temporal wet-troposphere fluctuations on connected element interferometry. TDA Progress report 42–97:47–57, Jet Propulsion Laboratory, PasadenaGoogle Scholar
  12. El-Rabbany A (1994) The effect of physical correlations on the ambiguity resolution and accuracy estimation in GPS differential positioning. Tech Report 170, Department of Surveying Engineering, University of New Brunswick, FrederictonGoogle Scholar
  13. Emardson TR, Jarlemark PO (1999) Atmospheric modelling in GPS analysis and its effect on the estimated geodetic parameters. J Geod 73(6):322–331 doi:10.1007/s001900050249CrossRefGoogle Scholar
  14. Hartinger H, Brunner FK (1999) Variances of GPS phase observations: the SIGMA-ɛ model. GPS Solutions 2(4):35–43 doi:10.1007/PL00012765CrossRefGoogle Scholar
  15. Howind J, Kutterer H, Heck B (1999) Impact of temporal correlations on GPS-derived relative point positions. J Geod 73(5):246–258 doi:10.1007/s001900050241CrossRefGoogle Scholar
  16. Gradinarsky LP (2002) Sensing atmospheric water vapor using radio waves. Dept. Radio and Space Science, School of Electrical Engineering, Chalmer University of Technology, GöteborgGoogle Scholar
  17. Ishimaru A (1978) Wave propagation and scattering in random media, Vol II. Academic, New YorkGoogle Scholar
  18. Stotskii AA, Elgered KG, Stotskaya IM (1998) Structure analysis of path delay variations in the neutral atmosphere. Astron Astrophys Trans 17(1):59–68CrossRefGoogle Scholar
  19. Tatarskii VI (1971) The effect of the turbulent atmosphere on wave propagation (translated from Russian by the Israel Program of Scientific Translation), JerusalemGoogle Scholar
  20. Taylor GI (1938) The spectrum of turbulence. Proc R S 164(A919):476–490Google Scholar
  21. Tiberius C, Kenselaar F (2003) Variance component estimation and precise GPS positioning: case study. J Surv Eng 129(1):11–18 doi: 10.1061/(ASCE)0733–9453(2003)129:1(11)CrossRefGoogle Scholar
  22. Tiberius C, Jonkman N, Kenselaar F (1999) The stochastics of GPS observables. GPS World 10(2):49–54Google Scholar
  23. Teunissen P, Jonkman N, Tiberius C (1998) Weighting GPS dual frequency observations: bearing the cross of cross-correlation. GPS Solutions 2(2):28–37 doi:10.1007/PL00000033CrossRefGoogle Scholar
  24. Treuhaft RN, Lanyi GE (1987) The effect of the dynamic wet troposphere on radio interferometric measurements. Radio Sci 22(2):251–265Google Scholar
  25. Wang J, Satirapod C, Rizos C (2002) Stochastic assessment of GPS carrier phase measurements for precise static relative positioning. J Geod 76(2):95–104 doi:10.1007/s00190-001-0225-6CrossRefGoogle Scholar
  26. Wheelon AD (2001) Electromagnetic scintillation—I. Geometrical optics. Cambridge University Press, CambridgeGoogle Scholar
  27. Williams S, Bock Y, Fang P (1998) Integrated satellite interferometry: tropospheric noise, GPS estimates and implication for interferometric synthetic aperture radar products. J Geophys Res 103(B11):27051–27067CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Institut für Erdmessung (IfE)Leibniz Universität HannoverHannoverGermany
  2. 2.Engineering Geodesy and Measurements Systems (EGMS)Graz University of TechnologyGrazAustria

Personalised recommendations