Skip to main content
SpringerLink
Log in

Datum Definition and Minimal Constraints

  • Living reference work entry
  • First Online:
Encyclopedia of Geodesy

Part of the book series: Encyclopedia of Earth Sciences Series ((EESS))

Definitions

Datum definition:

An operational procedure to fix the coordinate system with respect to which the station positions in a geodetic network will be estimated by least-squares adjustment techniques.

Minimal constraints:

A set of algebraic conditions involving the coordinates for some or all stations in a geodetic network. Their purpose is to define, in a unique and implicit way, the fundamental components (origin, orientation, scale) of the coordinate system for the network adjustment without interfering with the estimable elements of the available observations.

Introduction

Terrestrial reference frames (TRFs) are indispensable tools for mapping and monitoring the Earth system at various spatio-temporal scales. They provide the fundamental apparatus to realize an Earth-fixed reference system in terms of ground control networks with accurately known station positions in that system (Kovalevsky et al., 1989). Their determination relies on the analysis of geodetic measurements...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

References and Reading

  • Altamimi, Z., 2003. Discussion on how to express a regional GPS solution in the ITRF. EUREF Publication No. 12, Frankfurt am Main: Verlag des Bundesamtes für Kartographie und Geodäsie, pp. 162–167.

    Google Scholar 

  • Altamimi, Z., and Dermanis, A., 2012. The choice of reference system in ITRF formulation. In IAG Symposia Series. Berlin/Heidelberg: Springer-Verlag, Vol. 137, pp. 329–334.

    Google Scholar 

  • Altamimi, Z., Boucher, C., and Sillard, P., 2002. New trends for the realization of the international terrestrial reference system. Advances in Space Research, 30(2), 175–184.

    Article  Google Scholar 

  • Altamimi, Z., Collilieux, X., and Mtivier, L., 2011. ITRF2008: an improved solution of the international terrestrial reference frame. Journal of Geodesy, 85(8), 457–473.

    Article  Google Scholar 

  • Angermann, D., Drewes, H., Krugel, M., Meisel, B., Gerstl, M., Kelm, R., Muller, H., Seemuller, W., and Tesmer, V., 2004. ITRS Combination Center at DGFI: A Terrestrial Reference Frame Realization 2003. Deutsche Geodätische Kommission, Reihe B, Heft Nr. 313.

    Google Scholar 

  • Baarda, W., 1973. S-transformations and Criterion Matrices. Netherlands Geodetic Commission, Publications on Geodesy (new series), Vol. 5, no. 1.

    Google Scholar 

  • Bevis, M., Brown, A., and Kendrick, E., 2013. Devising stable geometric reference frames for use in geodetic studies of vertical crustal motion. Journal of Geodesy, 87(4), 311–321.

    Article  Google Scholar 

  • Blaha, G., 1971. Inner Adjustment Constraints with Emphasis on Range Observations. Report no. 148. Columbus, OH: Department of Geodetic Science, The Ohio State University.

    Google Scholar 

  • Blewitt, G., 2003. Self-consistency in reference frames, geocenter definition, and surface loading of the solid Earth. Journal of Geophysical Research, 108(B2). https://doi.org/10.1029/2002JB002082.

  • Davies, P., and Blewitt, G., 2000. Methodology for global geodetic time series estimation: a new tool for geodynamics. Journal of Geophysical Research, 105(B5), 11083–11100.

    Article  Google Scholar 

  • Delikaraoglou, D., 1985. Estimability analyses of the free networks of differential range observations to GPS satellites. In Grafarend and Sansò (eds.), Optimization and Design of Geodetic Networks. Berlin Heidelberg: Springer-Verlag, pp. 196–220.

    Chapter  Google Scholar 

  • Dermanis, A., 1994. The photogrammetric inner constraints. ISPRS Journal of Photogrammetry and Remote Sensing, 49(1), 25–39.

    Article  Google Scholar 

  • Dermanis, A., 2004. The rank deficiency in estimation theory and the definition of reference frames. In IAG Symposia Series. Berlin/Heidelberg: Springer-Verlag, Vol. 127, pp. 145–156.

    Google Scholar 

  • Dermanis, A., 2016. Global reference systems: theory and open problems. In IAG Symposia Series. Berlin/Heidelberg: Springer-Verlag, Vol. 142, pp. 9–17.

    Google Scholar 

  • Glaser, S., Fritsche, M., Sosnica, K., Rodriguez-Solano, C. J., Wang, K., Dach, R., Hugentobler, U., Rothacher, M., and Dietrich, R., 2015. A consistent combination of GNSS and SLR with minimum constraints. Journal of Geodesy, 89(12), 1165–1180.

    Article  Google Scholar 

  • Grafarend, E. W., and Heinz, K., 1978. Rank defect analysis of satellite geodetic networks II – dynamic mode. Manuscripta Geodaetica, 3, 135–158.

    Google Scholar 

  • Grafarend, E. W., and Livieratos, E., 1978. Rank defect analysis of satellite geodetic networks I – geometric and semi-dynamic mode. Manuscripta Geodaetica, 3, 107–134.

    Google Scholar 

  • Grafarend, E. W., and Sansò, F., (eds.), 1985. Optimization and Design of Geodetic Networks. Berlin/Heidelberg: Springer-Verlag.

    Google Scholar 

  • Kelm, R., 2003. Rank defect analysis and variance component estimation for inter-technique combination. In Richter, B., Schwegmann, W., and Dick, W. R., (eds.), Proceedings of the IERS Workshop on Combination Research and Global Geophysical Fluids, IERS Technical Note No. 30, Frankfurt am Main: Verlag des Bundesamts fur Kartographie und Geodäsie, pp. 112–114.

    Google Scholar 

  • Kotsakis, C., 2012. Reference frame stability and nonlinear distortion in minimum-constrained network adjustment. Journal of Geodesy, 86(9), 755–774.

    Article  Google Scholar 

  • Kotsakis, C., 2013. Generalized inner constraints for geodetic network densification problems. Journal of Geodesy, 87(7), 661–673.

    Article  Google Scholar 

  • Kotsakis, C., 2016. Reference station weighting and frame optimality in minimally constrained networks. In IAG Symposia Series. Berlin/Heidelberg: Springer-Verlag, Vol. 142, pp. 221–226.

    Google Scholar 

  • Kotsakis, C., and Chatzinikos, M., 2017. Rank defect analysis and the realization of proper singularity in normal equations of geodetic networks. Journal of Geodesy, 91(6), 627–652.

    Article  Google Scholar 

  • Kovalevsky, J., Mueller, I., and Kolaczek, B., (eds.), 1989. Reference Frames in Astronomy and Geophysics. Astrophysics and Space Science Library. Dortrecht/Boston/London: Kluwer Academic Publishers.

    Google Scholar 

  • Meissl, P., 1965. Ãœber die innere Genauigkeit dreidimensionaler Punkthaufens. Zeitschrift für Vermessungswesen, 90(4), 109–118.

    Google Scholar 

  • Meissl, P., 1969. Zusammengfassung und Ausbau der inneren Fehlertheorie eines Punkthaufens. Deutsche Geodätische Kommission, Reihe A, 61, 8–21.

    Google Scholar 

  • Petit, G., and Luzum, B., (eds.), 2010. IERS Conventions 2010. International Earth Rotation and Reference Systems Service Technical Note, Report No. 36. Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am Main.

    Google Scholar 

  • Pope, A. J., 1971. Transformation of covariance matrices due to changes in minimal control. Presented at the AGU Fall Meeting, San Francisco, December 9, 1971. National Ocean Survey Geodetic Research and Development Laboratory.

    Google Scholar 

  • Rebischung, P., 2014. Can GNSS Contribute to Improving the ITRF Definition? PhD Thesis, Paris, Institut National de l’Information Géographique et Forestière (IGN/LAREG).

    Google Scholar 

  • Rebischung, P., Altamimi, Z., Ray, J., and Garayt, B., 2016. The IGS contribution to the ITRF2014. Journal of Geodesy, 90(7), 611–630.

    Article  Google Scholar 

  • Schaffrin, B., 1985. Aspects of network design. In Grafarend and Sansò (eds.), Optimization and Design of Geodetic Networks. Berlin/Heidelberg: Springer-Verlag, pp. 549–597.

    Chapter  Google Scholar 

  • Sillard, P., and Boucher, C., 2001. A review of algebraic constraints in terrestrial reference frame datum definition. Journal of Geodesy, 75(2–3), 63–73.

    Article  Google Scholar 

  • Torge, W., 2001. Geodesy, 3rd edn. Berlin: de Gruyter.

    Google Scholar 

  • van Gelder, B. H. W., 1973. Estimability and Simple Dynamical Analyses of Range (Range-Rate and Range-Difference) Observations to Artificial Satellites. Report no. 284. Columbus: Department of Geodetic Science, The Ohio State University.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Geodesy and Surveying, School of Rural and Surveying Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece

    Christopher Kotsakis

Authors
  1. Christopher Kotsakis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christopher Kotsakis .

Editor information

Editors and Affiliations

  1. Geodetic Institute, University of Stuttgart, Stuttgart, Germany

    Erik Grafarend

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Kotsakis, C. (2018). Datum Definition and Minimal Constraints. In: Grafarend, E. (eds) Encyclopedia of Geodesy. Encyclopedia of Earth Sciences Series. Springer, Cham. https://doi.org/10.1007/978-3-319-02370-0_157-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-02370-0_157-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02370-0

  • Online ISBN: 978-3-319-02370-0

  • eBook Packages: Springer Reference Earth and Environm. ScienceReference Module Physical and Materials ScienceReference Module Earth and Environmental Sciences

Publish with us

Policies and ethics

Search

Navigation