Abstract
Precise point positioning with ambiguity resolution (PPP AR) is a valuable tool for high-precision geodetic observations, while phase observable-specific signal bias (OSB) is critical to implementing PPP AR. We present a reliable approach to effectively estimate the multi-frequency phase OSB based on the triple-frequency phase geometry-free and ionospheric-free (GF–IF) combination. First, when the first- and second-frequency phase OSB (e.g., L1/L2 for GPS) and their undifferenced ambiguity have been resolved, we introduced them as known quantity into the phase GF–IF combination. Then, the third-frequency phase OSB is estimated as completely independent between epochs in the phase GF–IF combination. Finally, both the time-invariable and time-variable hardware biases will be absorbed into the third-frequency phase OSB. We used a global network of multi-frequency GPS/Galileo data over a month (January 2022) to verify this approach. The results demonstrated that such multi-frequency phase OSB is able to recover integer ambiguities with eligible frequency choices and observable combinations. In addition, after multi-frequency phase OSB corrections on the raw observation, the impact of large time-variable hardware biases of GPS IIF L5 could be mitigated at user. Regarding multi-frequency GPS/Galileo kinematic PPP AR with phase OSB, the positioning root mean square (RMS) of 1.0, 1.3 and 3.0 cm could be achieved in the east, north and up components with the 3-h observation session, respectively, while the corresponding positioning RMS without phase OSB was 2.9, 2.1 and 4.4 cm. Furthermore, when the multi-frequency phase OSB was applied, the horizontal positioning RMS of ambiguity-fixed solutions could achieve below the level of 10 cm within 4 min. Our multi-frequency phase OSB approach proves to be convenient and efficient in the multi-frequency PPP AR and can be flexibly generalized to five- or even more frequency phase OSB estimation.
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The rapid orbit products are provided freely by GFZ (ftp://ftp.gfz-potsdam.de/pub/GNSS/products/mgnss). GNSS data, IGS weekly solutions files and igs14_2196.atx files are provided freely by IGS and MGEX (https://cddis.nasa.gov/archive/gps/data/daily). The multi-frequency code OSB is provided by CAS (ftp://ftp.gipp.org.cn/product/dcb/). The availability of real-time and post-process multi-frequency phase OSB is provided freely by CNES/NAV (www.ppp-wizard.net/products). The dual-frequency phase OSB is provided by CNES/CLS, GFZ, CODE and WUM (https://cddis.nasa.gov/archive/gps/products/mgex/). The experimental satellite clocks and multi-frequency GPS/Galileo phase OSB in this manuscript can be requested from the second author (viper_tjliu@whu.edu.cn).
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Acknowledgements
We are indebted to Simon Banville (Natural Resources Canada) and Denis Laurichesse (Centre National d’Etudes Spatiales Navigation Team) for providing research assistance on the multi-frequency phase OSB estimation. The authors thank Jianghui Geng (Wuhan university) and Shengfeng Gu (Wuhan university) for valuable discussions and improving the theoretical part. This study is supported by the Program for Hubei Provincial Science and Technology Innovation Talents (No. 2022EJD010), the Special Fund of Huber Luojia Laboratory (No. 220100020), the Natural Science Innovation Group Foundation of China (No. 41721003), and National Natural Science Foundation of China (Grant No. 42004017).
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W.J. and T.L. worked out all technical details and wrote the paper. C.S. provided the software. H.C., Q.C and T. G. provided research advice and reviewed the paper.
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Jiang, W., Liu, T., Chen, H. et al. Multi-frequency phase observable-specific signal bias estimation and its application in the precise point positioning with ambiguity resolution. GPS Solut 27, 4 (2023). https://doi.org/10.1007/s10291-022-01325-0
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DOI: https://doi.org/10.1007/s10291-022-01325-0