Abstract
The accuracy of the tropospheric mapping functions is greatly influenced by the mapping function modeling methods. In the past decades, the ‘fast’ method rather than the rigorous least-squares methods was dominantly used for the development of mapping functions, such as Vienna Mapping Functions 1 (VMF1), considering the convergence issue and computation efficiency. In this study, we reconsider the suitability of the rigorous least-squares methods in operational mapping function development and present a new mapping function modeling method where the number of to-be-estimated coefficients in the mapping function continued fraction is adaptively determined according to the convergence in the least-squares fitting. The modeling accuracy of the new method is evaluated during 40 days spanning four seasons in 2020 at globally distributed 905 Global Navigation Satellite Systems (GNSS) stations. Significant improvement of the new method to the ‘fast’ method is found, with hydrostatic and wet mapping function modeling mean absolute errors (MAEs) of 1.6 and 1.3 mm for the new method and of 3.6 and 3.0 mm for the ‘fast’ method, respectively. Multi-GNSS Precise Point Positioning (PPP) of the new method is conducted at 107 International GNSS Service (IGS) Multi-GNSS Experiment (MGEX) stations. Effectiveness of the new method is also found for the PPP station height and zenith total delay estimation.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (41774036; 41804023; 41961144015) and the Fundamental Research Funds for the Central Universities (2042020kf0020). Authors would like to thank Copernicus Climate Data Store, IGS CDDIS and GFZ for providing the research datasets and products and acknowledge Technische Universität Wien for developing the ray-tracing package RADIATE and releasing APL products. The numerical calculations in this paper have been done on the supercomputing system in the Supercomputing Center of Wuhan University.
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YDL and WXZ initiated the study. YZZ, WXZ and YDL proposed the conceptual ideas and designed and performed the experiments with the help and support from JNB and ZYZ. YZZ, WXZ and YDL were involved in the manuscript writing. All authors read and approved the final manuscript.
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ERA5 was downloaded from Copernicus Climate Data Store (https://cds.climate.copernicus.eu/). IGS MGEX RINEX data and GFZ GBM satellite orbit product are available through IGS CDDIS FTP (ftp://gdc.cddis.eosdis.nasa.gov/) and GFZ FTP (ftp://ftp.gfz-potsdam.de/). APL products were downloaded from Technische Universität Wien (http://vmf.geo.tuwien.ac.at/).
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Zhou, Y., Lou, Y., Zhang, W. et al. An improved tropospheric mapping function modeling method for space geodetic techniques. J Geod 95, 98 (2021). https://doi.org/10.1007/s00190-021-01556-y
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DOI: https://doi.org/10.1007/s00190-021-01556-y