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Wang et al. Satell Navig (2021) 2:9 Satellite Navigation
https://doi.org/10.1186/s43020-021-00039-x
https://satellite-navigation.springeropen.com/
ORIGINAL ARTICLE Open Access
Estimation of fractional cycle bias for GPS/
BDS-2/Galileo based on international
GNSS monitoring and assessment system
observations using the uncombined PPP model
*
Jin Wang, Qin Zhang and Guanwen Huang
Abstract
The Fractional Cycle Bias (FCB) product is crucial for the Ambiguity Resolution (AR) in Precise Point Positioning (PPP).
Diferent from the traditional method using the ionospheric-free ambiguity which is formed by the Wide Lane (WL)
and Narrow Lane (NL) combinations, the uncombined PPP model is fexible and efective to generate the FCB prod-
ucts. This study presents the FCB estimation method based on the multi-Global Navigation Satellite System (GNSS)
precise satellite orbit and clock corrections from the international GNSS Monitoring and Assessment System (iGMAS)
observations using the uncombined PPP model. The dual-frequency raw ambiguities are combined by the integer
coefcients (4,− 3) and (1,− 1) to directly estimate the FCBs. The details of FCB estimation are described with the
Global Positioning System (GPS), BeiDou-2 Navigation Satellite System (BDS-2) and Galileo Navigation Satellite System
(Galileo). For the estimated FCBs, the Root Mean Squares (RMSs) of the posterior residuals are smaller than 0.1 cycles,
which indicates a high consistency for the foat ambiguities. The stability of the WL FCBs series is better than 0.02
cycles for the three GNSS systems, while the STandard Deviation (STD) of the NL FCBs for BDS-2 is larger than 0.139
cycles. The combined FCBs have better stability than the raw series. With the multi-GNSS FCB products, the PPP AR for
GPS/BDS-2/Galileo is demonstrated using the raw observations. For hourly static positioning results, the performance
of the PPP AR with the three-system observations is improved by 42.6%, but only 13.1% for kinematic positioning
results. The results indicate that precise and reliable positioning can be achieved with the PPP AR of GPS/BDS-2/Gali-
leo, supported by multi-GNSS satellite orbit, clock, and FCB products based on iGMAS.
Keywords: PPP AR, Fractional cycle bias, Satellite orbit and clock products, iGMAS
Introduction (Gabor and Nerem 1999). Currently, it is assumed that
Precise Point Positioning (PPP) Ambiguity Resolution FCBs contain the biases from satellite and receiver hard-
(AR) is important to obtain the positioning accuracy at ware delays. Unlike the relative positioning model, where
centimeter-level in a short time at a station (Bisnath FCBs are eliminated in double-diferenced Global Navi-
and Gao 2008; Wang et al. 2019). Due to the Fractional gation Satellite System (GNSS) observations (Ge et al.
Cycle Biases (FCBs) in phase measurements which are 2008; Geng et al. 2012), the PPP processing needs the
assimilated into the undiferenced ambiguities in PPP, the FCB products to correct the foat ambiguities for recov-
integer properties of the estimated ambiguities are lost ering their integer properties.
Te method of ambiguity resolution based on the
satellite-satellite single diferences was frst proposed in
*Correspondence: zhangqinle@263.net.cn PPP (Gabor and Nerem 1999), many methods have then
College of Geology Engineering and Geomatics, Chang’an University, been developed with diferent products to obtain the
Xi’an 710054, China
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