Skip to main content

Volume 52 Supplement 10

Special Issue: Application of GPS and other space geodetic techniques to Earth Sciences (1)

An extended weight model for GPS phase observations


Low elevation data may be included in the processing of small scale engineering GPS applications, in order to improve satellite geometry and reduce the required observation time. Careful weighting of the phase observations is needed then, because of increased noise and systematic errors. The measured carrier-to-noise-power-density ratio (C/N0) has proven to be an excellent tool for the estimation of the random errors of the phase observables. In this paper an extended weight model using robust estimation is presented, in particular the Danish Method. This model combines the information inherent in C/N0 and the residuals of the double differenced phase observations in order to model random errors and signal distortion effects.


  1. Allnutt, J. E., Satellite-to-Ground Radio wave Propagation, 421 pp., Peter Peregrinus Ltd., London, UK, 1989.

    Google Scholar 

  2. Axelrad, P., C. Comp, and P. MacDoran, Use of Signal-To-Noise Ratio for Multipath Error Correction in GPS Differential Phase Measurements: Methodology and Experimental Results, Proc. ION GPS-94, Salt Lake City, Utah, 655–666, 1994.

  3. Baarda, W., A Testing Procedure for Use in Geodetic Networks, 97 pp., Netherlands Geodetic Commission, New Series Vol. 2/5, 1968.

  4. Brunner, F. K., H. Hartinger, and L. Troyer, GPS signal diffraction modelling: The stochastic SIGMA-A model, J. Geod., 73, 259–267, 1999.

    Article  Google Scholar 

  5. Eissfeller, B., Ein dynamisches Fehlermodell für GPS Autokorrelation-sempfänger, Schriftenreihe Studiengang Vermessungswesen, Universit’t der Bundeswehr, München, Heft 55, 1997.

  6. Hartinger, H. and F. K. Brunner, Variances of GPS phase observations: The SIGMA-ϵ model, GPS Solutions, 2/4, 35–43, 1999.

    Article  Google Scholar 

  7. Jørgensen, P. C., K. Kubik, P. Frederiksen, and W. Weng, Ah, robust estimation!, Aust. J. Geod. Photo. Surv., 42, June, 19–32, 1985.

    Google Scholar 

  8. Krarup, T, J. Juhl, and K. Kubik, Götterdämmerung over least squares adjustment, Proc. 14th Congress of the International Society of Photogrammetry, Hamburg, Vol. B3, 369–378, 1980.

  9. Langley, R., GPS receiver system noise, GPS World, June, 40–45, 1997.

  10. Xu, P., Consequences of constant parameters and confidence intervals of robust estimation, Boll. Geod. Sc. Affini, 52, 231–249, 1993.

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Andreas Wieser.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Wieser, A., Brunner, F.K. An extended weight model for GPS phase observations. Earth Planet Sp 52, 777–782 (2000).

Download citation


  • Phase Error
  • Weight Model
  • Signal Distortion
  • Phase Observation
  • Double Difference