Journal of Geodesy

, Volume 81, Issue 2, pp 157–170 | Cite as

Modeling long-period noise in kinematic GPS applications

  • Adrian A. Borsa
  • Jean-Bernard Minster
  • Bruce G. Bills
  • Helen A. Fricker
Original Article


We develop and test an algorithm for modeling and removing elevation error in kinematic GPS trajectories in the context of a kinematic GPS survey of the salar de Uyuni, Bolivia. Noise in the kinematic trajectory ranges over 15 cm and is highly autocorrelated, resulting in significant contamination of the topographic signal. We solve for a noise model using crossover differences at trajectory intersections as constraints in a least-squares inversion. Validation of the model using multiple realizations of synthetic/simulated noise shows an average decrease in root-mean-square-error (RMSE) by a factor of four. Applying the model to data from the salar de Uyuni survey, we find that crossover differences drop by a factor of eight (from an RMSE of 5.6  to 0.7 cm), and previously obscured topographic features are revealed in a plan view of the corrected trajectory. We believe that this algorithm can be successfully adapted to other survey methods that employ kinematic GPS for positioning.


Global positioning system (GPS) Noise Kinematic GPS Inverse theory salar de Uyuni ICESat 


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  1. Agnew DC (1992) The time-domain behavior of power-law noises. Geophys Res Lett 19(4):333–336Google Scholar
  2. Bock Y, Agnew DC, Fang P, Gengrich JF, Hager BH, Herring TA, Hudnut KW, King RW, Larsen SC, Minster J-B, Stark K, Wdowinski S, Wyatt FK (1993) Detection of crustal deformation from the Landers earthquake sequence using continuous geodetic measurements. Nature 361(6410):337–340CrossRefGoogle Scholar
  3. Bock Y, Nikolaidis RM, de Jonge PJ, Bevis M (2000) Instantaneous geodetic positioning at medium distances with the global positioning system. J Geophys Res 105:28223–28253CrossRefGoogle Scholar
  4. Borsa AA (2005) Geomorphology of the salar de Uyuni, Bolivia. Scripps Institution of Oceanography. La Jolla, University of California at San DiegoGoogle Scholar
  5. Chen G (1998) GPS kinematic positioning for the airborne laser altimetry at Long Valley, California. Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of TechnologyGoogle Scholar
  6. Dong D, Bock Y (1989) Global positioning system network analysis with phase ambiguity resolution applied to crustal deformation studies in California. J Geophys Res 94(B4):3949–3966Google Scholar
  7. Elósegui P, Davis JL, Jaldehag RTK, Johansson JM, Niell AE, Shapiro II (1995). Geodesy using the global positioning system: the effects of signal scattering on estimates of site position. J Geophys Res 100:9921–9934CrossRefGoogle Scholar
  8. Genrich JF, Bock Y (1992) Rapid resolution of crustal motion at short ranges with the global positioning system. J Geophys Res 97(B3):3261–3269Google Scholar
  9. Genrich JF, Bock Y (2006) Instantaneous geodetic positioning with 10–50 Hz GPS measurements: noise characteristics and implications for monitoring networks. J Geophys Res 111(B03403). Doi 10.1029/2005JB003617Google Scholar
  10. Georgiadou Y, Kleusberg A (1988) On carrier signal multipath effects in relative GPS positioning. Manuscripta Geodaetica 13:172–179Google Scholar
  11. Gutierrez R, Gibeaut JC, Smyth RC, Hepner TL, Andrews, JR, Weed C, Gutelius W, Mastin M (2001) Precise airborne lidar surveying for coastal research and geohazards applications. Int Arch Photogram Remote Sensing XXXIV-3/W4:185–192Google Scholar
  12. Herring T (2002) Documentation for the TRACK kinematic GPS analysis software, version 1.07. Massachusetts Institute of TechnologyGoogle Scholar
  13. Hofton MA, Blair JB, Minster J-B, Ridgway JR, Williams NP, Bufton JL, Rabine DL (2000) An airborne scanning laser altimetry survey of Long Valley, California. Int J Remote Sensing 21(12):2413–2437CrossRefGoogle Scholar
  14. Krabill WB, Martin CF (1987) Aircraft positioning using global positioning system carrier phase data. Navigation 34(1):1–21Google Scholar
  15. Krabill WB, Thomas R, Jezek K, Kuivenen K, Manizade S (1995) Greenland ice sheet thickness changes measured by laser altimetry. Geophys Res Lett 22(17):2341–2344CrossRefGoogle Scholar
  16. Macmillan DS (1995) Atmospheric gradients from very long baseline interferometry observations. Geophys Res Lett 22(9):1041–1044CrossRefGoogle Scholar
  17. Mader GL (1986) Dynamic positioning using GPS carrier phase measurements. Manuscripta Geodaetica 11:272–277Google Scholar
  18. Mader GL, Lucas JR (1989) Verification of airborne positioning using global positioning system carrier phase measurements. J Geophys Res 94(B8):10175–10181Google Scholar
  19. Mader GL, MacKay JR (1997) Calibration of GPS antennas. 1996 Analysis Center Workshop, International GPS Service Central Bureau, Jet Propulsion Laboratory, Pasadena, CaliforniaGoogle Scholar
  20. Mao A, Harrison CGA, Dixon TH (1999) Noise in GPS coordinate time series. J Geophys Res 104(B2):2797–2816CrossRefGoogle Scholar
  21. Parker RL (1994) Geophysical inverse theory. Princeton University Press, PrincetonGoogle Scholar
  22. Phillips HA, Allison I, Coleman R, Hyland G, Morgan PJ, Young NW (1998) Comparison of ERS satellite radar altimeter heights with GPS-derived heights on the Amery Ice Shelf, East Antarctica. Ann Glaciol 27:19–24Google Scholar
  23. Pilgrim B, Kaplan DT (1998) A comparison of estimators for 1/f noise. Physica D 114:108–122CrossRefGoogle Scholar
  24. Prescott WH, Savage JC, Svarc JL, Manaker D (2001) Deformation across the Pacific-North American plate boundary near San Fransisco, California. J Geophys Res 106(B4):6673–6682CrossRefGoogle Scholar
  25. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in C. Cambridge University Press, New YorkGoogle Scholar
  26. Ridgway JR, Minster J-B, Williams NP, Bufton JL, Krabill WB (1997) Airborne laser altimeter survey of Long Valley, California. Geophys J Int 131:267–280CrossRefGoogle Scholar
  27. Rowlands DD, Pavlis DE, Lemoine FG, Neumann GA, Luthcke SB (1999) The use of laser altimetry in the orbit and attitude determination of Mars Global Surveyor. Geophys Res Lett 26:1191–1194CrossRefGoogle Scholar
  28. Saka MH, Kavzoglu T, Ozsamli C, Alkan RM (2004) Sub-meter accuracy for stand alone GPS positioning in hydrographic surveying. J Navigation 57:135–144CrossRefGoogle Scholar
  29. Williams SDP, Bock Y, Fang P, Jamason P, Nikolaidis RM, Miller M, Johnson DJ (2004) Error analysis of continuous GPS positioin time series. J Geophys Res 109(B03412): Doi:10.1029/2003JB002741Google Scholar
  30. Zhang J, Bock Y, Johnson H, Fang P, Williams S, Genrich J, Wdowinski S, Behr J (1997) Southern California permanent GPS geodetic array: error analysis of daily position estimates and site velocities. J Geophys Res 102(B8):18035–18055CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Adrian A. Borsa
    • 1
  • Jean-Bernard Minster
    • 1
  • Bruce G. Bills
    • 1
    • 2
  • Helen A. Fricker
    • 1
  1. 1.Institute of Geophysics and Planetary Physics, Scripps Institution of OceanographyUniversity of California at San DiegoLa JollaUSA
  2. 2.Planetary Geodynamics LaboratoryNASA Goddard Space Flight CenterGreenbeltUSA

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