On the Alternative Approaches to ITRF Formulation

A Theoretical Comparison
  • Athanasios DermanisEmail author
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 139)


The one-step approach for ITRF formulation is compared with the two-step technique where the ITRF parameters are first separately estimated for each space technique separately (stacking per technique) and are then combined into the final ITRF estimates (combination step). The comparison is achieved by splitting the one-step approach into two equivalent steps such that the first one is identical to the first step of the two-step approach. It is shown that the two approaches give equivalent results when the input covariance matrices in the combination step of the two-step approach are the normal equation coefficient matrices formulated in the corresponding stacking per technique first step. Furthermore it is shown that the model of the combination step can be significantly simplified by ignoring the parameters of reference system transformation from the per technique estimates to those of the final ITRF parameter estimates.


ITRF formulation Reference systems Sequential adjustment Rank deficiency Weight matrix 


  1. Altamimi, Z, Dermanis A (2009) The choice of reference system in ITRF formulation. In: IAG symposia, vol 137, pp 329–334Google Scholar
  2. Altamimi Z, Sillard P, Boucher C (2002) ITRF2000: a new release of the international terrestrial reference frame for earth science applications. J Geophys Res 107(B10):2214Google Scholar
  3. Altamimi Z, Sillard P, Boucher C (2004) ITRF2000: from theory to implementation. In: Sansò F (ed) V Hotine–Marussi symposium on mathematical geodesy. In: IAG symposia, vol 127. Springer, Berlin, pp 157–163Google Scholar
  4. Altamimi Z, Collilieux X, Legrand J, Garayt B, Boucher C (2007) ITRF2005: a new release of the International Terrestrial Reference Frame based on time series of station positions and Earth Orientation Parameters. J Geophys Res 112, B09401Google Scholar
  5. Altamimi Z, Collilieux X, Métivier L (2011) ITRF2008: an improved solution of the international terrestrial reference frame. J Geod 85:457–473CrossRefGoogle Scholar
  6. Angermann D, Drewes H, Gerstl M, Krügel M, Meisel B (2009) DGFI combination methodology for ITRF2005 computation. In: IAG symposia, vol 134, pp 11–16Google Scholar
  7. Dermanis A (2003) The rank deficiency in estimation theory and the definition of reference frames. In: IAG symposia, vol 127, pp 145–156Google Scholar
  8. Dow JM, Neilan RE, Rizos C (2009) The International GNSS Service in a changing landscape of Global Navigation Satellite Systems. J Geod 83:191–198CrossRefGoogle Scholar
  9. Gross J (2004) The general Gauss-Markov model with possibly singular dispersion matrix. J Stat Pap 45:311–336CrossRefGoogle Scholar
  10. Kelm R (2006) Rigorous variance component estimation in weekly intra-technique and inter-technique combination for global terrestrial reference frames. In: IAG symposia, vol 134, pp 39–44Google Scholar
  11. Koch K-R (1999) Parameter estimation and hypothesis testing in linear models, 2nd edn. Springer, BerlinCrossRefGoogle Scholar
  12. Pearlman MR, Degnan JJ, Bosworth JM (2002) The International Laser Ranging Service. Adv Space Res 30:135–143CrossRefGoogle Scholar
  13. Rao CR (1971) Unified theory of linear estimation. Sankhya Ser A 33:371–394; Corrigenda (1972) Sankhya Ser A 34:194, 477Google Scholar
  14. Rothacher M, Angermann D, Artz T, Bosch W, Drewes H, Gerstl M, Kelm R, König D, König R, Meisel B, Müller H, Nothnagel A, Panafidina N, Richter B, Rudenko S, Schwegmann W, Seitz M, Steigenberger P, Tesmer S, Tesmer V, Thaller D (2011) GGOS-D: homogeneous reprocessing and rigorous combination of space geodetic observations. J Geod 85:679–705CrossRefGoogle Scholar
  15. Schaffrin B (1989) An alternative approach to robust collocation. Bulletin Geodesique 63:395–404CrossRefGoogle Scholar
  16. Schlüter W, Behrend D (2007) The International VLBI Service for Geodesy and Astrometry (IVS): current capabilities and future prospects. J Geod 81:379–387CrossRefGoogle Scholar
  17. Seitz M, Angermann D, Blossfeld M, Drewes H, Gerstl M (2012) The 2008 DGFI realization of the ITRS: DTRF2008. J Geod 86(12):1097–1123. doi: 10.1007/s00190-012-0567-2 CrossRefGoogle Scholar
  18. Tanir E, Heinkelmann R, Schuh H, Kusche J, van Loon JP (2006) Assessment of the results of VLBI intra-technique combination using regularization methods. In: IAG symposia, vol 134, pp 45–51Google Scholar
  19. Willis P, Gobinddass ML, Garayt B, Fagard H (2012) Recent improvements in DORIS data processing in view of ITRF2008, the ignwd08 solution. In: IAG symposia, vol 136, pp 43–49Google Scholar
  20. Wolf H (1974) Über verallgemeinerte Kollokation. Z Vermessungswesen 99:475–478 (in German)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Geodesy and SurveyingAristotle University of ThessalonikiThessalonikiGreece

Personalised recommendations