Journal of Geodesy

, Volume 93, Issue 7, pp 1073–1087 | Cite as

Multi-dimensional particle filter-based estimation of inter-system phase biases for multi-GNSS real-time integer ambiguity resolution

  • Yumiao Tian
  • Zhizhao LiuEmail author
  • Maorong Ge
  • Frank Neitzel
Original Article


In multi-GNSS integration, fixing inter-system double-difference ambiguities to integers is still a challenge due to the existence of inter-system biases (ISB) when mixed types of GNSS receivers are used. It has been shown that when ISB is known, the inter-system ambiguities can be fixed and the reliability of ambiguity fixing can be improved significantly, especially under poor conditions when the number of observed satellites is small. In traditional methods, the intra-system ambiguity is fixed first; then, the ISB is estimated to ultimately fix the inter-system ambiguity. In our work, we use the particle filter-based method to estimate the ISB parameter and fix the inter-system ambiguities to integers at the same time. This method shows higher reliability and higher ambiguity fixing rate. Nevertheless, the existing particle filter approach for ISB parameter estimation is a one-dimensional algorithm. When satellites from three or more systems are observed, there are two or more ISB parameters. We extend the current one-dimensional particle filter approach to multi-dimensional case and estimate multi-ISB parameters in this study. We first present a multi-dimensional particle filter approach that can estimate multi-ISB parameters simultaneously. We also show that the RATIO values can be employed to judge the quality of multi-dimensional ISB values. Afterward, a two-dimensional particle filter approach is taken as an example to validate this approach. For example, in the experiment of GPS L5, Galileo E5a and QZSS L5 integration with 6 satellites using the IGS baseline SIN0-SIN1, only three ambiguities are resolved to integer when the ISBs are unknown. The integer ambiguity fixing rate is 41.0% with 53% of the ambiguity-fixed solutions having positioning errors larger than 3 cm. However, when our approach is adopted, the number of integer ambiguity parameters increases to five. The integer ambiguity fixing rate increases to 99.7% with 100% of ambiguity-fixed solutions having positioning errors smaller than 3 cm.


Multi-dimensional particle filter approach Multi-GNSS integration Ambiguity resolution Inter-system bias estimation 



Zhizhao Liu thanks the support of Hong Kong Research Grants Council (RGC) Project (PolyU 5203/13E, B-Q37X) and Hong Kong Polytechnic University (Projects 152103/14E, 152168/15E and 1-BBYH) and the grant supports from the Key Program of the National Natural Science Foundation of China (Project No.: 41730109). Yumiao Tian is supported by the Young Scientists Fund of the National Natural Science Foundation of China (Project No.: 41804022) and the Fundamental Research Funds for the Central Universities (2682018CX33).


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Copyright information

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

Authors and Affiliations

  1. 1.Faculty of Geosciences and Environmental EngineeringSouthwest Jiaotong UniversityChengduChina
  2. 2.Department of Land Surveying and Geo-Informatics (LSGI)The Hong Kong Polytechnic University (PolyU)KowloonChina
  3. 3.German Research Centre for GeosciencesPotsdamGermany
  4. 4.Institute of Geodesy and Geoinformation ScienceTechnische Universität BerlinBerlinGermany
  5. 5.State-Province Joint Engineering Laboratory of Spatial Information Technology for High-Speed Railway SafetyChengduChina

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