Journal of Geodesy

, Volume 88, Issue 1, pp 45–63 | Cite as

Non-linear station motions in epoch and multi-year reference frames

  • Mathis BloßfeldEmail author
  • Manuela Seitz
  • Detlef Angermann
Original Article


In the conventions of the International Earth Rotation and Reference Systems Service (e.g. IERS Conventions 2010), it is recommended that the instantaneous station position, which is fixed to the Earth’s crust, is described by a regularized station position and conventional correction models. Current realizations of the International Terrestrial Reference Frame use a station position at a reference epoch and a constant velocity to describe the motion of the regularized station position in time. An advantage of this parameterization is the possibility to provide station coordinates of high accuracy over a long time span. Various publications have shown that residual non-linear station motions can reach a magnitude of a few centimeters due to not considered loading effects. Consistently estimated parameters like the Earth Orientation Parameters (EOP) may be affected if these non-linear station motions are neglected. In this paper, we investigate a new approach, which is based on a frequent (e.g. weekly) estimation of station positions and EOP from a combination of epoch normal equations of the space geodetic techniques Global Positioning System (GPS), Satellite Laser Ranging (SLR) and Very Long Baseline Interferometry (VLBI). The resulting time series of epoch reference frames are studied in detail and are compared with the conventional secular approach. It is shown that both approaches have specific advantages and disadvantages, which are discussed in the paper. A major advantage of the frequently estimated epoch reference frames is that the non-linear station motions are implicitly taken into account, which is a major limiting factor for the accuracy of the secular frames. Various test computations and comparisons between the epoch and secular approach are performed. The authors found that the consistently estimated EOP are systematically affected by the two different combination approaches. The differences between the epoch and secular frames reach magnitudes of \(23.6~\upmu \hbox {as}\) (0.73 mm) and \(39.8~\upmu \hbox {as}\) (1.23 mm) for the x-pole and y-pole, respectively, in case of the combined solutions. For the SLR-only solutions, significant differences with amplitudes of \(77.3~\upmu \hbox {as}\) (2.39 mm) can be found.


ITRF Epoch reference frame Multi-year reference frame Inter-technique combination EOP Non-linear station motions Center of Mass Center of Network 



The work described in this paper was funded by the German Research Foundation (DFG) within the research group ’Earth Rotation and Global Dynamic Processes’ (FOR 584) and contributes to the DFG research group ’Space-time reference systems for monitoring global change and for precise navigation’ (FOR1503). The authors thank P. Steigenberger at the Technische Universität München and S. Böckmann at the Universität Bonn for computing the GPS and VLBI input data. Furthermore, the authors want to thank the associate editor J. Freymueller and the three anonymous reviewers who helped to improve the quality of the paper a lot. Finally, the authors want to thank H. Drewes for discussions about essential definitions made in the paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Mathis Bloßfeld
    • 1
  • Manuela Seitz
    • 1
  • Detlef Angermann
    • 1
  1. 1.Deutsches Geodätisches Forschungsinstitut (DGFI)MunichGermany

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