GPS Solutions

, 23:33 | Cite as

Regional BDS satellite clock estimation with triple-frequency ambiguity resolution based on undifferenced observation

  • Xinhao Yang
  • Shengfeng GuEmail author
  • Xiaopeng Gong
  • Weiwei Song
  • Yidong Lou
  • Jingnan Liu
Original Article


Real-time precise satellite clock estimation is fundamental for real-time precise point positioning. To take full advantage of the triple-frequency (TF) signal of the BeiDou Navigation Satellite System (BDS), we used undifferenced observations directly in the TF data processing. In addition, TF ambiguity resolution (AR) was performed in a sequential manner, in which the wide-lane (WL) and extra wide-lane (EWL) ambiguities were fixed based on the Hatch–Melbourne–Wübbena (HMW) combination of B1/B2 and B1/B3, and then we followed with narrow-lane (NL) ambiguity fixing. By applying the ambiguity integer constraints, an ambiguity-fixed BDS satellite clock was obtained. To evaluate the contribution of TF AR in a satellite clock solution when a regional station network is involved, experiments were carried out based on the observations collected by 11 stations from the crustal movement observation network of China (CMONOC) during day of year (DOY) 153–188, 2016. First, the temporal behavior of the BDS EWL and WL uncalibrated phase delays (UPDs) were analyzed. The results suggested that they were quite stable over several days with standard deviations (STDs) of 0.004 cycles and 0.015 cycles for EWL and WL, respectively. Then, the ambiguity-fixed solution of the satellite clock was obtained with average success rates of about 99%, 90%, and 63% for EWL, WL, and NL AR, respectively. Attributed to the efficient AR, not only was the initialization time shortened but also the precision was improved. The overall averaged improvements of STD for geostationary orbits (GEO), inclined geostationary orbits (IGSO), and medium-altitude Earth orbit (MEO) satellites were 48.7%, 40.8%, and 34.4%, respectively, for the EWL and WL ambiguity-fixed solution and 72.6%, 71.0%, and 62.8%, respectively, for the NL ambiguity-fixed solution. As a comparison, a dual-frequency (DF) ambiguity-fixed satellite clock was also generated. Although the precision of the NL ambiguity-fixed clock was roughly the same, a larger root mean square (RMS) by a factor of 52% suggested that the DF ambiguity-fixed solution may have been biased with incorrect integer ambiguity fixing, whereas the TF ambiguity-fixed solution was more reliable because of the third frequency observation. In addition, precise point positioning (PPP) was carried out to assess the performance of these clock products. Compared with the PPP based on the ambiguity-float clock solution, improvements of 32.0% and 42.9% for horizontal and vertical, respectively, were obtained with the TF NL ambiguity-fixed clock solution.


BDS Triple-frequency Ambiguity resolution Satellite clock estimation 



This study was sponsored by the National Natural Science Foundation of China (41231174, 41504028), the National Key Research and Development Plan (2016YFB0501802). The authors thank the anonymous reviewers for their valuable comments. Thanks also go to IGS and CMONOC for providing data. Finally, the authors really appreciate the patience of the chief editor and the reviewers.


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Copyright information

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

Authors and Affiliations

  1. 1.GNSS Research CenterWuhan UniversityWuhanChina

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