GPS Solutions

, Volume 21, Issue 3, pp 949–961 | Cite as

Particle filter-based estimation of inter-system phase bias for real-time integer ambiguity resolution

  • Yumiao Tian
  • Maorong Ge
  • Frank Neitzel
  • Jianjun Zhu
Original Article


Although double-differenced (DD) observations between satellites from different systems can be used in multi-GNSS relative positioning, the inter-system DD ambiguities cannot be fixed to integer because of the existence of the inter-system bias (ISB). Obviously, they can also be fixed as integer along with intra-system DD ambiguities if the associated ISBs are well known. It is critical to fix such inter-system DD ambiguities especially when only a few satellites of each system are observed. In most of the existing approaches, the ISB is derived from the fractional part of the inter-system ambiguities after the intra-system DD ambiguities are successfully fixed. In this case, it usually needs observations over long times depending on the number of observed satellites from each system. We present a new method by means of particle filter to estimate ISBs in real time without any a priori information based on the fact that the accuracy of a given ISB value can be qualified by the related fixing RATIO. In this particle filter-based method, the ISB parameter is represented by a set of samples, i.e., particles, and the weight of each sample is determined by the designed likelihood function related to the corresponding RATIO, so that the true bias value can be estimated successfully. Experimental validations with the IGS multi-GNSS experiment data show that this method can be carried out epoch by epoch to provide precise ISB in real time. Although there are only one, two, or at most three Galileo satellites observed, the successfully fixing rate increases from 75.5% for GPS only to 81.2%. In the experiment with five GPS satellites and one Galileo satellites, the first successfully fixing time is reduced to half of that without fixing the inter-system DD ambiguities.


Ambiguity fixing Multi-GNSS integration Phase inter-system bias Particle filter 



The first author is financially supported by the China Scholarship Council (CSC) for his study at the Technische Universität Berlin and the German Research Centre for Geosciences (GFZ). This research is also partly supported by the Collaborative Innovation Center of Geospatial Technology of China.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Yumiao Tian
    • 1
  • Maorong Ge
    • 2
  • Frank Neitzel
    • 1
  • Jianjun Zhu
    • 3
  1. 1.Technische Universität BerlinBerlinGermany
  2. 2.German Research Centre for GeosciencesPotsdamGermany
  3. 3.Central South UniversityChangshaChina

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