GPS Solutions

, 22:82 | Cite as

Estimating satellite phase fractional cycle biases based on Kalman filter

  • Guorui XiaoEmail author
  • Lifen Sui
  • Bernhard Heck
  • Tian Zeng
  • Yuan Tian
Original Article


Phase fractional cycle biases (FCBs) originating from satellites and receivers destroy the integer nature of PPP carrier phase ambiguities. To achieve integer ambiguity resolution of PPP, FCBs of satellites are required. In former work, least squares methods are commonly adopted to isolate FCBs from a network of reference stations. However, it can be extremely time consuming concerning the large number of observations from hundreds of stations and thousands of epochs. In addition, iterations are required to deal with the one-cycle inconsistency among FCB measurements. We propose to estimate the FCB based on a Kalman filter. The large number of observations are handled epoch by epoch, which significantly reduces the dimension of the involved matrix and accelerates the computation. In addition, it is also suitable for real-time applications. As for the one-cycle inconsistency, a pre-elimination method is developed to avoid iterations and posterior adjustments. A globally distributed network consisting of about 200 IGS stations is selected to determine the GPS satellite FCBs. Observations recorded from DoY 52 to 61 in 2016 are processed to verify the proposed approach. The RMS of wide lane (WL) posterior residuals is 0.09 cycles while that of the narrow lane (NL) is about 0.05 cycles, which indicates a good internal accuracy. The estimated WL FCBs also have a good consistency with existing WL FCB products (e.g., CNES-GRG, WHU-SGG). The RMS of differences with respect to GRG and SGG products are 0.03 and 0.05 cycles. For satellite NL FCB estimates, 97.9% of the differences with respect to SGG products are within ± 0.1 cycles. The RMS of the difference is 0.05 cycles. These results prove the efficiency of the proposed approach.


Precise point positioning Integer ambiguity resolution Fractional cycle bias Kalman filter 



We thank the IGS, GFZ and CNES for providing GNSS data and products. Thanks also goes to Prof. ZHANG Xiaohong and Dr. LI Pan from WHU-SGG for FCB products and valuable discussions. Guorui XIAO is supported by the China Scholarship Council. This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 41674016 and 41274016).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Geodetic InstituteKarlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.Zhengzhou Institute of Surveying and MappingZhengzhouChina

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