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A modified phase clock/bias model to improve PPP ambiguity resolution at Wuhan University

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Precise point positioning ambiguity resolution (PPP-AR) is a valuable tool for high-precision geodetic observations, while phase bias products are critical to implementing GNSS PPP-AR. Based on the conventional integer clock and uncalibrated phase delay (UPD) models, we proposed a modified phase clock/bias model to enable undifferenced ambiguity fixing where it is the phase clocks, rather than the International GNSS Service (IGS) legacy clocks, which are estimated in a network solution by first correcting carrier-phase data for both pre-resolved integer ambiguities and predetermined phase biases. Such phase clock/bias product is compatible with IGS legacy clock and code bias products as opposed to the integer clock model, while ensuring more accurate daily positions in contrast to the UPD model. We carried out precise point positioning (PPP) ambiguity fixing using 1 year of GPS data from about 500 stations and took the IGS weekly solutions as benchmarks: The phase clock/bias model reproduced the positioning achievement of the integer clock model without biasing pseudorange processing, whereas improving markedly the east component of daily positions by 20% compared to the UPD model; interestingly, negligible differences exist between the UPD-based hourly positions and those based on the phase clock/bias model, corroborating that the UPD model is a good approximation to the phase clock/bias model in case of short observation periods. Finally, since phase biases are linearly dependent on clocks, we suggest to compute daily phase bias products, instead of the usual 15-min UPDs, by driving all their temporal variations to the phase clocks, which will greatly facilitate ambiguity-fixed PPP (

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Data availability statement

All original data in this article are publicly available. The raw GNSS data and the IGS products can be accessed at while the phase clock/bias products can be found at


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This work is funded by National Key Research and Development Program of China (Nos. 2018YFC1503601, 2016YFB0501802) and National Science Foundation of China (No. 41674033). We are grateful to IGS for the high-quality GPS data and satellite products. This work is taken as a contribution from Wuhan University Analysis Center to the new IGS Working Group “PPP-AR”. We thank the high-performance computing facility at Wuhan University where all computational work of this study were accomplished.

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

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Correspondence to Jianghui Geng.

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Geng, J., Chen, X., Pan, Y. et al. A modified phase clock/bias model to improve PPP ambiguity resolution at Wuhan University. J Geod 93, 2053–2067 (2019).

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