GPS Solutions

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Inter-system and inter-frequency code biases: simultaneous estimation, daily stability and applications in multi-GNSS single-frequency precise point positioning

  • Nan Zang
  • Bofeng LiEmail author
  • Liangwei Nie
  • Yunzhong Shen
Original Article


Both inter-system and inter-frequency code biases (ISCB and IFCB) embodied in the multi-GNSS single-frequency precise point positioning (MSFPPP) exhibit mainly as systematic errors. Comprehensive analysis of the ISCB and IFCB characteristics and proper assimilation of their impact on MSFPPP are very important. We study the simultaneous estimation of all ISCBs for GLONASS, BDS and Galileo relative to GPS and the IFCBs of GLONASS by using our newly formulated estimable ionospheric-weighted MSFPPP model. Then, the daily stability of the ISCBs and IFCBs is examined, on which the application strategy is advised to improve the MSFPPP performance. One-month multi-GNSS single-frequency observation at 60 stations with eight types of receivers is carried out. The results indicate that the ISCBs of Galileo are most stable, followed by GLONASS and BDS, and all ISCBs and IFCBs are sufficiently stable on a daily scale. Imposing this stable information on the MSFPPP model can significantly enhance the model strength and improve the positioning performance.


Single-frequency precise point positioning (SFPPP) Multi-GNSS SFPPP (MSFPPP) Ionospheric-weighted (IW) model Inter-system code bias (ISCB) Inter-frequency code bias (IFCB) Allan variance 



This study is sponsored by National Natural Science Foundation of China (41874030, 41622401, 41574023 and 41730102), The Scientific and Technological Innovation Plan from Shanghai Science and Technology Committee (18511101801), The National Key Research and Development Program of China (2016YFB0501802, 2017YFA0603102) and The Fundamental Research Funds for the Central Universities. We are sincerely grateful to the efforts of the IGS MGEX campaign for providing multi-GNSS data and products.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Surveying and GeoInformaticsTongji UniversityShanghaiChina
  2. 2.Institute of Geodesy and Geoinformation TechnologyTechinical University BerlinBerlinGermany

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