Skip to main content

Volume 52 Supplement 10

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

Minimal Detectable Biases of GPS observations for a weighted ionosphere


The theory and application of statistical quality control is well established in precise positioning, navigation and geodesy. Quality control is made up of several contributing factors, one of which is internal reliability. Internal reliability describes the ability to find biases in observational data and is represented by the Minimal Detectable Bias (MDB). The MDB provides a diagnostic tool to infer the strength with which positioning models can be validated. In this contribution closed-form expressions will be given for the MDBs of GPS code and carrier observations for three different baseline models: the geometry-free model and two variants of the geometry-based model. These expressions apply toany numberofcarrier frequencies. The expressions take into account the presence of ionospheric disturbances by weighting these effects. As such, they are applicable to baselines of any length.


  1. Baarda, W., Statistical Concepts in Geodesy, Netherlands Geodetic Commission, Publications on Geodesy, New Series, vol. 2, no. 4, 74 pp., 1967.

  2. Baarda, W., A testing procedure for use in geodetic networks, Netherlands Geodetic Commission, Publications on Geodesy, New Series, vol. 2, no. 5, 97 pp., 1968.

  3. Euler, H. J. and C. Goad, On optimal filtering of GPS dual-frequency observations without using orbit information, Bulletin Géodésique, 65, pp. 130–143, 1991.

    Article  Google Scholar 

  4. de Jong, C.D., Real-time integrity monitoringofdual-frequency GPS observations for a single receiver, Acta Geodaetica et Geophysica Hungarica, 31, pp. 37–46, 1996.

    Google Scholar 

  5. de Jong, C. D., Principles and Applications of Permanent GPS Arrays, 105 pp., Delft University Press, Delft, 1997.

    Google Scholar 

  6. de Jong, C. D., Aunified approachtoreal-timeintegrity monitoring of single-and dual frequency GPS and Glonass observations, Acta Geodaetica et Geophysica Hungarica, 33, pp. 247–257, 1998.

    Google Scholar 

  7. de Jong, C. D., Reliability of GPS observations using a weighted ionosphere, 1999 (in preparation).

  8. Jonkman, N. F., Integer GPS Ambiguity Resolution without the Receiver-satellite Geometry, LGR-series, no. 18, 95pp., Delft Geodetic Computing Centre, Delft, 1998.

    Google Scholar 

  9. Schaffrin, B. and Y. Bock, A unified scheme for processing GPS dual-band phase observations, Bulletine Géodésique, 62, pp. 142–160, 1988.

    Article  Google Scholar 

  10. Teunissen, P. J. G., Quality control in geodetic networks, in Optimization and Design of Geodetic Networks, edited by E. W. Grafarend and F. Sanso, pp. 526–547, Springer, Berlin Heidelberg New York, 1985.

    Chapter  Google Scholar 

  11. Teunissen, P. J. G., An analytical study of ambiguity decorrelation using dual-frequency code and carrier phase, J. Geod., 70, pp. 515–528, 1996.

    Article  Google Scholar 

  12. Teunissen, P. J. G., Minimal Detectable Biases of GPS data, J. Geod., 72, pp. 236–244, 1998.

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to K. de Jong.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

de Jong, K., Teunissen, P.J.G. Minimal Detectable Biases of GPS observations for a weighted ionosphere. Earth Planet Sp 52, 857–862 (2000).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Baseline Model
  • Ionospheric Disturbance
  • Geodetic Network
  • Carrier Outlier
  • Ionospheric Variance