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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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