GPS Solutions

, Volume 11, Issue 2, pp 107–117 | Cite as

Affine distortion of small GPS networks with large height differences

  • Steffen SchönEmail author
Original Article


GPS is a promising tool for real-time monitoring of deformations of slopes or large structures. However, remaining systematic effects in GPS phase observations after double differencing and application of a priori models affect the resulting coordinates. They complicate the proper separation of the actual deformations from pseudo-deformations induced by the systematic effects. This paper shows that for small monitoring networks (baseline lengths <5 km) only affine distortions of the network geometry are generated by the remaining distance dependent systematic effects, e.g. unmodelled tropospheric and ionospheric propagation effects, or satellite orbit errors. Hence, a generic correction model is given by a three-dimensional affine transformation involving a maximum of 12 transformation parameters. For the determination of these parameters, four high quality GPS stations are necessary which are not affected by the actual deformations to be monitored. Based on the analysis of network geometries of synthetic GPS networks with large height differences and considering the physics of the GPS observations it is shown, however, that less than 12 parameters are sufficient for the computation of the corrections. The proposed 8 parameter model was applied to the GPS monitoring network of the Gradenbach landslide. For this small network with large height differences, it was shown that the distortions can be reduced by about 75%.


GPS Systematic errors Monitoring network Affine transformation 



The author is a recipient of a Feodor Lynen fellowship and acknowledges the financial support by the Alexander von Humboldt-Foundation. He warmly thanks Fritz K. Brunner for many fruitful discussions on systematic effects and affine correction models and Andreas Wieser for comments on the draft. The monitoring of the landslide Gradenbach is financed by the Austrian Academy of Sciences.


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Engineering Geodesy and Measurements Systems (EGMS)Graz University of TechnologyGrazAustria
  2. 2.Institut für ErdmessungLeibniz-Universität HannoverHannoverGermany

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