GPS Solutions

, 22:50 | Cite as

Geometry of GPS relative positioning

  • R. Santerre
  • A. Geiger
Original Article


GPS positioning is often assimilated to trilateration and even to triangulation methods. Both comparisons are wrong because GPS observations are pseudoranges containing clock errors. The geometric interpretations of GPS relative positioning and trilateration method are presented. Receiver clock parameter is also analyzed from a geometric point of view. The generalization of positioning solutions is made without and with observations redundancy. The geometry of the propagation of systematic errors into positioning solutions is also shown, especially the tropospheric (and the ionospheric) delay.


Relative positioning GPS Geometry Receiver clock parameter Tropospheric delay 



The first author would like to acknowledge NSERC (Natural Sciences and Engineering Research Council of Canada) for financial support of his GPS research.


  1. Allan AL (2007) Principles of geospatial surveying. CRC Press, Boca RatonGoogle Scholar
  2. ANM (1938) Admiralty navigation manual, vol 3—chapter 13: errors in position linesGoogle Scholar
  3. Apostol TM, Mnatsakanian MA (2006) Solids circumscribing spheres. Math Assoc Am 113:521–522CrossRefGoogle Scholar
  4. Beutler G, Bauersima I, Gurtner W, Rothacher M, Schildknecht T, Geiger A (1988) Atmospheric refraction and some other important biases in GPS carrier phase observations. Atmospheric effects on geodetic space measurements, School of Surveying Monograph No. 12. UNSW, Sydney, pp 15–43Google Scholar
  5. Eberly DH (2008) Distance from linear component to tetrahedron.
  6. Font-Llagunes JM, Batlle JA (2009) New method that solves the three-point resection problem using straight lines intersection. J Surv Eng 135(2):39–45CrossRefGoogle Scholar
  7. Fresnel J (1996) Méthodes modernes en géométrie. Hermann, ParisGoogle Scholar
  8. Geiger A (1988) Simulating disturbances in GPS by continuous satellite distribution. J Surv Eng 114(4):182–194CrossRefGoogle Scholar
  9. Morales JJ, Khalife JJ, Kassas ZM (2016) GNSS vertical dilution of precision reduction using terrestrial signals of opportunity. In: Proceedings of ITM ION 2016, Institute of Navigation, Monterey, California, USA, 25–28 Jan, pp 664–669Google Scholar
  10. Santerre R, Geiger A (1998) Geometrical interpretation of GPS positioning with single, double and triple difference carrier phase observations. In: Proceedings of the symposium on geodesy for geotechnical and structural engineering, Eisenstadt, Austria, 20–22 April, pp 465–470Google Scholar
  11. Santerre R, Geiger A, Banville S (2017) Geometry of GPS dilution of precision: revisited. GPS Solut 21(4):1747–1763CrossRefGoogle Scholar
  12. Vanicek P, Langley RB, Wells DE, Delikaraoglou D (1984) Geometrical aspects of differential GPS positioning. Bull Géod 58:37–52CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Département des Sciences GéomatiquesUniversité LavalQuebecCanada
  2. 2.Institute of Geodesy and PhotogrammetryETHZurichSwitzerland

Personalised recommendations