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Zhang et al. Satell Navig (2021) 2:11 Page 9 of 10

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course of interest. To account for this, the PPP functional of Sciences, Wuhan, China. University of Chinese Academy of Sciences,
3
model was modifed by assuming that the receiver code Beijing, China. National School of Surveying, University of Otago, Dunedin,
biases can vary freely in time. By means of re-parameter- New Zealand.
ization the rank defciencies were overcome, resulting in Received: 5 November 2020 Accepted: 9 February 2021
a full-rank functional model in which the variations of
receiver code biases on both frequencies between epochs
are directly estimated, and thus have no impact on the
performance. References
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Funding Håkansson, M., Jensen, A. B., Horemuz, M., & Hedling, G. (2017). Review of code
This work was partially funded by the National Natural Science Foundation and phase biases in multi-GNSS positioning. GPS Solutions, 21, 849–860.
of China (Grant No. 41774042) and the Scientifc Instrument Developing Hernández-Pajares, M., Roma-Dollase, D., Krankowski, A., García-Rigo, A., &
Project of the Chinese Academy of Sciences (Grant No. YJKYYQ20190063). The Orús-Pérez, R. (2017). Methodology and consistency of slant and vertical
frst author is supported by the Chinese Academy of Sciences (CAS) Pioneer assessments for ionospheric electron content models. Journal of Geodesy,
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The authors declare that they have no competing interests. Liu, T., Zhang, B., Yuan, Y., & Li, M. (2018). Real-time precise point positioning
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1 State Key Laboratory of Geodesy and Earth’s Dynamics, Innovation Academy Martínez-Belda, M. C., Defraigne, P., Baire, Q., & Aerts, W. (2011). Single-
for Precision Measurement Science and Technology, Chinese Academy frequency time and frequency transfer with Galileo E5. In 2011 Joint