On vectorial integer bootstrapping implementations in the estimation of satellite orbits and clocks based on small global networks

Lotfi Massarweh*, Sebastian Strasser, Torsten Mayer-Gürr

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The estimation of satellite orbits and clocks plays a central role in different Global Navigation Satellite System (GNSS) domains, e.g. precise positioning or time transfer. Such products can be computed in the process of Orbit Determination and Time Synchronization (ODTS), which relies on a network of ground-based stations, well distributed around the globe. The mm-level precision of carrier-phase measurements is exploited in this network estimation following a correct resolution of their ambiguities. For several stations, satellites and/or signals, thousands of ambiguities have to be processed, which means having to deal with high-dimensional ambiguity resolution (HDAR) problems. In this research work, we firstly account for the impact of ambiguity resolution in a varying network size, based on GPS-only, Galileo-only and GPS+Galileo configurations. Using 25 or more stations, the accuracy (1D RMS orbital errors) of fixed solutions reaches a plateau at 1–2 cm. Hence, we focus on a small global network of 14 stations, where the model strength decreases, so does the reliability of the ambiguity fixing process and advantages over a float solution might become less evident. In order to allow reliable HDAR, two implementations of the Vectorial Integer Bootstrapping estimator are presented and evaluated with respect to their scalar counterpart. Finally, it is shown how the proposed fixing processes are more robust, still very efficient, and on certain days they provide a large improvement to satellite products. The orbital results are ultimately validated by considering the satellite midnight discontinuity errors over a 3-month period in 2019.

Original languageEnglish
Pages (from-to)4303-4320
Number of pages18
JournalAdvances in Space Research
Issue number11
Publication statusPublished - 1 Dec 2021


  • Ambiguity Resolution (AR)
  • Global Navigation Satellite System (GNSS)
  • Orbit Determination and Time Synchronization (ODTS)
  • Vectorial Integer Bootstrapping (VIB)

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Aerospace Engineering
  • Geophysics
  • Earth and Planetary Sciences(all)
  • Space and Planetary Science
  • Atmospheric Science


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