GPS Solutions

, 23:81 | Cite as

Multi-GNSS inter-system biases: estimability analysis and impact on RTK positioning

  • Xiaolong Mi
  • Baocheng ZhangEmail author
  • Yunbin Yuan
Original Article


Inter-system biases (ISB) are of great relevance for the combined processing of the code and phase data of multiple global navigation satellite systems (GNSSs). Calibrating the ISB makes it possible to enhance the interoperability among different GNSS constellations and thus benefits multi-GNSS-based positioning, navigation and timing applications. Initial investigations of the characteristics of ISB have been carried out, usually making use of overlapping frequencies and adopting the double-differenced (DD) model. However, this approach seems inapplicable when dealing with ISB for non-overlapping frequencies. We identify the estimability of the ISB by using the ionospheric-float, ionospheric-fixed and ionospheric-weighted models formulated on the basis of between-receiver single-differenced (SD) multi-GNSS observation equations, resulting in the so-called SD method, which is capable of estimating the ISB in case of both overlapping and non-overlapping frequencies. Using dual-frequency data for short and medium baselines, we analyze 30-s epoch-by-epoch estimates of the GPS–Galileo and GPS–BDS ISB. The quantitative results indicate that the same conclusion is reached using either the SD method or the customary method based on DD observations (called the DD method); that is, the code and phase ISB time series are both approximately constant on a time scale of a few days from a statistical perspective. However, the SD method has the advantage that it can be used to flexibly estimate ISB for both overlapping and non-overlapping frequencies and thus can be better applied for real-time kinematic positioning than the DD method. Furthermore, the multi-GNSS positioning accuracy using inter-system differencing can be improved by 20–35%, as compared to the SD classical differencing in which S-basis is selected per constellation, thanks to the reasonable calibration of the ISB.


Global navigation satellite systems (GNSSs) Inter-system biases (ISB) Ionospheric-fixed model Ionospheric-weighted model Ionospheric-float model Real-time kinematic (RTK) 



Many thanks are due to Curtin University and Hong Kong SatRef for providing GNSS data. This work was funded by the National Natural Science Foundation of China (Nos. 41604031, 41774042, and 41621091) and the National Key Research Program of China Collaborative Precision Positioning Project (No. 2016YFB0501900). The second author is supported by the CAS Pioneer Hundred Talents Program. The third author acknowledges the LU JIAXI International team program supported by the K.C. Wong Education Foundation and CAS.


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Copyright information

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

Authors and Affiliations

  1. 1.State Key Laboratory of Geodesy and Earth’s DynamicsInstitute of Geodesy and GeophysicsWuhanChina
  2. 2.University of Chinese Academy of SciencesBeijingChina

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