Journal of Geodesy

, Volume 87, Issue 6, pp 539–553 | Cite as

Ambiguity resolution for triple-frequency geometry-free and ionosphere-free combination tested with real data

  • K. Wang
  • M. Rothacher
Original Article


The recent GPS Block IIF satellites SVN62 and SVN63 and the Galileo satellites GIOVE-A, GIOVE-B, PFM and FM2 already send signals on more than two frequencies, and more GNSS satellites will provide tracking data on at least three frequencies in the near future. In this paper, a simplified general method for ambiguity resolution minimizing the noise level for the triple-frequency geometry-free (GF) and ionosphere-free (IF) linear combinations is presented, where differently scaled code noise on the three frequencies was introduced. For the third of three required linear combinations, the most demanding one in triple-frequency ambiguity resolution, we developed a general method using the ambiguity-corrected phase observations without any constraints to search for the optimal GF and IF linear combination. We analytically demonstrate that the noise level of this third linear combination only depends on the three frequencies. The investigation concerning this frequency-dependent noise factor was performed for GPS, Galileo and Compass frequency triplets. We verified the theoretical derivations with real triple-frequency GPS and Galileo data from the Multi-GNSS Experiment (M–GEX) of the International GNSS Service (IGS). The data of about 30 M–GEX stations around the world over 11 days from 29 April 2012 to 9 May 2012 were used for the test. For the third linear combinaton using Galileo E1, E5b and E5a, which is expected to have the worst performance among all the GNSS frequency triplets in our investigation, the formal errors of the estimated ambiguities are in most cases below 0.2 cycles after 400 observation epochs. If more GPS satellites sending signals on three frequencies or more stations tracking Galileo E6 signal are available in the future, an improvement by a factor of two to three can be expected.


Triple-frequency ambiguity resolution Geometry-free and ionosphere-free Linear combination GNSS 



This work was funded by ESA as part of the project (Satellite and Station Clock Modeling for GNSS, Reference: AO/1-6231/09/D/SR). We would like to thank M. Müller from the Institute of Geodesy and Photogrammetry, Eidgenössische Technische Hochschule Zürich (ETHZ) for processing the Galileo Two Line Element Set (TLE) (TLE 2012) and T.S. Kelso from CelesTrack for providing TLE of the four Galileo satellites (GIOVE–A, GIOVE–B, GALILEO–PFM and GALILEO–FM2) for the time interval April 29, 2012 to May 9, 2012. We also want to thank IGS for providing triple-frequency M–GEX data on its archive (


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institute of Geodesy and Photogrammetry, ETH ZurichZurichSwitzerland

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