Abstract
The short-term variability in receiver code biases (RCBs) has been identified as a prominent source of error leading to the degradation of precise point positioning (PPP) performance and ionospheric total electron content (TEC) estimation accuracy. To minimize the adverse impact of RCB variability, this study extends the modified PPP (MPPP) method from the GPS only dual-frequency (DF) model to multifrequency (MF) and multiconstellation cases. In the MF MPPP method, multi-GNSS (GPS, BDS and Galileo) dual-, triple- or even arbitrary-frequency observations can be jointly processed in a flexible and reliable way by taking the time-varying RCBs of all available signals into account. Benefiting from this, the between-epoch fluctuations experienced by RCBs for all constellations and frequencies can be detected and their adverse impacts on the ionospheric observables and ambiguity parameters are mitigated. Compared to the traditional MF PPP method, the retrieval accuracy of the multi-GNSS-based ionospheric observables using our proposed method can be improved by more than 74% in the presence of significant intraday RCB variations. The variation trends are not always consistent for RCBs in different frequency bands for different satellite systems. The dependence of multi-GNSS and MF RCB variations on the ambient temperature is also verified. The percentages of the stations analyzed with the absolute Pearson correlation coefficient (PCC) values above 0.8 for BDS are higher than those of GPS and Galileo, and the temperature dependence of RCB on the second frequency band is higher than those of the first frequency band for all the three constellations.
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Data availability
The multi-GNSS observation data and meteorological data from the IGS MGEX networks are available at ftp://cddis.gsfc.nasa.gov/pub/gps/data/daily/. The multi-GNSS observation data and meteorological data from the AUSCORS are available at ftp://ftp.ga.gov.au/geodesy-outgoing/gnss/data/daily/. The multi-GNSS precise ephemeris and satellite clock products from WUM are available at ftp://igs.gnsswhu.cn/pub/gps/products/. The GIM products from IGS can be obtained at ftp://cddis.gsfc.nasa.gov/pub/gps/products/ionex/. CODE’s monthly mean intra-DCB products can be found at ftp.aiub.unibe.ch//CODE/.
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Acknowledgements
Many thanks are due to the IGS for providing access to the Multi-GNSS Experiment (MGEX) data, the ionospheric GIM products, and the differential code bias (DCB) products. We also would like to acknowledge the Geosciences Australia for providing access to their data. This work was partially supported by the China Natural Science Funds (No. 42004027), the Hubei International Science and technology cooperation program (No. 2023004), the Open Fund of Hubei Luojia Laboratory (No. 220100061), the State Key Laboratory of Geodesy and Earth’s Dynamics (No.S22L620103). All of this support is gratefully acknowledged.
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ML and JZ initiated the idea and designed the research; ML performed the research and wrote the paper; ML and JZ analyzed the data; XZ also contributed to the data analysis; YY, TL and CZ gave helpful discussions on additional analyses and result interpretation.
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Li, M., Zha, J., Yuan, Y. et al. A unified model of multi-GNSS and multi‑frequency precise point positioning for the joint estimation of ionospheric TEC and time-varying receiver code bias. J Geod 98, 12 (2024). https://doi.org/10.1007/s00190-023-01808-z
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DOI: https://doi.org/10.1007/s00190-023-01808-z