Noise Filtering Augmentation of the Helmert Transformation for the Mapping of GNSS-Derived Position Time Series to a Target Frame

  • Miltiadis Chatzinikos
  • Christopher Kotsakis
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 147)


The generation of position time series in geodetic networks is often based on the successive forward implementation of the Helmert transformation (HT) to daily/weekly solutions using the transformation parameters obtained from a separate least-squares adjustment over a selected set of reference stations. An overlooked problem with this approach is that the noise of the daily/weekly solutions is fully absorbed into the transformed station positions, or even amplified if we consider the additional uncertainty of the estimated Helmert parameters. Its filtering is therefore a desirable task which could enhance the geophysical content of geodetic time series to be analyzed in a global secular frame. To accommodate the need for such filtering, we present in this paper an epoch-wise stacking approach for the HT-based alignment of a series of daily/weekly frames to a common secular frame via an integrated estimation process. The resulting transformation formulae differ from the classic HT solution in terms of Kalman-like corrections, and they lead to an improved solution in the sense of minimizing the error variances of the transformed positions in the target frame.


Daily/weekly solutions Frame alignment GNSS networks Helmert transformation Noise filtering Position time series 


  1. Altamimi Z, Collilieux X, Métivier L (2011) ITRF2008: an improved solution of the international terrestrial reference frame. J Geod 85:457–473CrossRefGoogle Scholar
  2. Bastos L, Bos M, Fernandes RM (2010) Contribution of GPS measurements to plate tectonics–overview and recent developments. In: Xu G (ed) Sciences of geodesy-I: advances and future directions. Springer, Berlin, pp 155–184CrossRefGoogle Scholar
  3. Biagi L, Sansò F (2012) Some pitfalls to be avoided in combining simultaneous GNSS networks. IAG symposia, vol. 137. Springer, Berlin, pp 335–340Google Scholar
  4. Chatzinikos M (2013) Study of the earth’s crust displacements in the area of Greece analyzing GNSS data. PhD Thesis, School of Rural and Surveying Engineering, Aristotle University of Thessaloniki, GreeceGoogle Scholar
  5. Collilieux X, Altamimi Z, Coulot D, van Dam T, Ray J (2010) Impact of loading effects on determination of the International Terrestrial Reference Frame. Adv Space Res 45:144–154CrossRefGoogle Scholar
  6. Collilieux X, van Dam T, Ray J, Coulot D, Metivier L, Altamimi Z (2012) Strategies to mitigate aliasing of loading signals while estimating GPS frame parameters. J Geod 86(1):1–14CrossRefGoogle Scholar
  7. Dach R, Hugentobler U, Fridez P, Meindl M (2007) Bernese GPS software version 5.0. Astronomical Institute, University of Bern, SwitzerlandGoogle Scholar
  8. Kotsakis C, Vatalis A, Sanso F (2014) On the importance of intra-frame and inter-frame covariances in frame transformation theory. J Geod 88(12):1187–1201CrossRefGoogle Scholar
  9. Kotsakis C, Vatalis A, Sanso F (2015) The Helmert transformation approach in network densification revisited. IAG Symposia Series, Springer, Heidelberg, vol. 146. Proceedings of the IAG International Symposium on Reference Frames for Applications in Geosciences, Kirchberg, Luxemburg, 13–17 Oct 2014Google Scholar
  10. Tregoning P, van Dam T (2005) Effects of atmospheric pressure loading and seven parameter transformations on estimates of geocenter motion and station heights from space geodetic observations. J Geoph Res 110:B03408. doi: 10.1029/2004JB003334 CrossRefGoogle Scholar
  11. van Dam T, Collilieux X, Wuite J, Altamimi Z, Ray J (2012) Nontidal ocean loading: amplitudes and potential effects in GPS height time series. J Geod 86(11):1043–1057CrossRefGoogle Scholar

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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Geodesy and SurveyingAristotle University of ThessalonikiThessalonikiGreece
  2. 2.Royal Observatory of BelgiumBrusselsBelgium

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