Beyond three frequencies: an extendable model for single-epoch decimeter-level point positioning by exploiting Galileo and BeiDou-3 signals


GNSS is indispensable to self-driving vehicles by delivering decimeter-level or better absolute positioning solutions. Such a high precision normally requires a convergence time spanning seconds to minutes, which is, however, unrealistic in extremely difficult driving conditions where GNSS signals are obstructed frequently. Such convergences, no matter how short, will greatly risk and discredit autonomous driving in satisfying stringent life safety standards. In this study, we therefore developed an extendable GNSS precise point positioning (PPP) model to exploit the advanced Galileo/BeiDou-3 more-than-three-frequency signals with the goal of achieving instant or single-epoch 10–30 cm positioning accuracy and over 99% availability for the horizontal components over wide areas. In particular, uncombined Galileo/BeiDou-3 signals on all available frequencies were injected simultaneously into PPP to perform single-epoch wide-lane ambiguity resolution (PPP-WAR) after phase bias calibrations on raw observations. Experimenting on the Galileo five-frequency data from 36 stations in Australia, we found that instant PPP-WAR was accomplished at more than 99.5% of all epochs; we achieved an instant positioning accuracy of 0.10 and 0.11 m (1σ) for the east and north components, respectively, using Galileo E1/E5a/E5/E5b/E6 signals from less than 10 satellites, while 0.16 and 0.23 m using BeiDou-3 B1C/B1I/B2a/B2b/B3I signals from only 5–6 satellites per epoch observed by 10 stations within China. Moreover, we carried out vehicle-borne experiments collecting multi-frequency Galileo/BeiDou-3 signals in the case of overpass and tunnel adversities. With 7 Galileo/BeiDou-3 satellites per epoch on average, instant PPP-WAR reached a mean positioning accuracy of 0.23 and 0.24 m for the horizontal components, which can be further improved to 0.14 and 0.12 m when multi-epoch filtering is preferably enabled. More encouragingly, though this positioning accuracy can also be ensured with triple-frequency data, the data redundancy favored by even more frequencies can reduce the high-precision recovery time from up to 4 s to 2 s in the case of total signal blockages. With the rapidly ongoing deployment of Galileo, BeiDou-3 and other GNSS constellations, we can envision an instant global positioning service characterized by around 20 cm horizontal accuracy and over 99% availability for self-driving vehicles.

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Data availability

The raw GNSS data from ARGN are publicly available at, while the IGS products can be accessed at All data from IGMAS and the vehicle-borne experiments in the study are available from the authors upon request.


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This study is funded by the National Science Foundation of China (41674033) and National Key Research and Development Program of China (2018YFC1504002). We thank IGS (International GNSS Service), ARGN (Australian Regional GNSS Network) and IGMAS for the multi-GNSS data and the high-quality satellite products. The computation work was accomplished on the high-performance computing facility of Wuhan University.

Author information

JHG devised the project and the main conceptual ideas. JHG and JG worked out almost all of the technical details and performed the numerical calculations for the suggested experiments; JG analyzed the data; JHG and JG wrote the paper. All authors provided critical feedback and helped to shape the research, analysis and manuscript.

Correspondence to Jianghui Geng.

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Geng, J., Guo, J. Beyond three frequencies: an extendable model for single-epoch decimeter-level point positioning by exploiting Galileo and BeiDou-3 signals. J Geod 94, 14 (2020).

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  • Instant decimeter-level point positioning
  • Five-frequency
  • BeiDou-3
  • Galileo E6
  • Precise point positioning
  • Ambiguity resolution