GPS Solutions

, 23:49 | Cite as

An optimal linear combination model to accelerate PPP convergence using multi-frequency multi-GNSS measurements

  • Viet DuongEmail author
  • Ken Harima
  • Suelynn Choy
  • Denis Laurichesse
  • Chris Rizos
Original Article


We propose an optimal ionospheric-free linear combination (LC) model for dual- and triple-frequency PPP which can accelerate carrier phase ambiguity and decrease the position solution convergence time. To reduce computational complexity, a near-optimal LC model for triple-frequency PPP is also proposed. The uncombined observation (UC) model estimating ionospheric delay gives the best performance, because all information contained within the observations are kept. The proposed optimal and near-optimal LC models are compared with the UC model, using both simulated and real data from five GNSS stations in Australia over 30 consecutive days in 2017. We determine a necessary and sufficient condition for a combination operator matrix which can eliminate the first-order ionospheric component to obtain the optimal LC model for dual- and triple-frequency PPP. Numerical results show that the proposed LC model is identical to the UC model. In addition, the proposed near-optimal LC model even outperforms the current LC models. Ambiguity resolution (AR) is faster and positioning accuracy is improved using the optimal triple-frequency LC model compared to using the optimal dual-frequency LC model. An average time-to-first-fix of 10 min with a fixing success rate of 95% can be achieved with triple-frequency AR.


Precise point positioning (PPP) Optimal linear combination Convergence time Triple frequency Multi-GNSS 



Geoscience Australia, CNES and the IGS are acknowledged for providing the GNSS data from the Australian Regional GNSS Network as well as the satellite orbits, clocks and biases. Raijin-NCI National Computational Infrastructure Australia is acknowledged for providing high-performance research computing resources for GNSS data processing. The authors thank the Editor and the two anonymous reviewers for their constructive comments which have improved the paper significantly. The first author is supported by the Australia Award Scholarship Scheme to pursue a Ph.D. at RMIT University, Melbourne, Australia.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of ScienceRMIT UniversityMelbourneAustralia
  2. 2.Centre National d’Etudes SpatialesToulouseFrance
  3. 3.School of Civil and Environmental EngineeringUNSWSydneyAustralia

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