# Phase Center Corrections for BDS IGSO and MEO Satellites in IGb14 and IGSR3 Frame
## 1 Introduction
To keep the consistency between upcoming GNSS constellations and the established ones, the PCOs and PCVs were estimated for Galileo in IGS14 frame [7], and for BDS in IGS08 frame [11; 12; 13; 14] by modeling the receiver antenna PCCs with that of GPS L1 and L2, as no ground calibrations were available for the new GNSS satellites at that time. In 2017, the European GNSS Agency (ESA) released the pre-launch calibrated PCOs and PCVs for Galileo satellites [15]. Moreover, the new receiver antenna models covering all GNSS frequencies, based on robot calibrations, were available when IGS prepared for the third reprocess. Hence, it provides an essential chance to evaluate whether GNSS global network solutions qualify to contribute to the scale determination of terrestrial networks [16]. Additionally, it is well known that the fundamental issue concerning the determination of the terrestrial scale with GNSS is that there is a high correlation between the terrestrial scale, the satellite PCOs in Z component (Z-PCOs), the zenith wet delays, and the station as well as satellite clock offsets. Since pre-launch antenna calibrations are not available for the established GPS and GLONASS satellites, this high correlation prevents a reliable estimation of the terrestrial scale by using GNSS. By fixing the PCOs of the Galileo satellite transmitter antenna to the ground calibrated values, the entire terrestrial scale issue could be solved. Based on global data of the years 2017 to 2019, the Galileo-only coordinates were derived, and it showed the scale discrepancy was up to about +1.16 ppb (part per billion) with respect to IGb14 [17]. With the gravitational constraint on low earth orbiters (LEOs) in the integrated process of GPS and three SWARM satellites, the GPS Z-PCOs were recalibrated, and it shifted about \(-\)221 mm (equivalent +1.72 ppb) with respect to that in igs14_WWWW.atx file [18]. Considering the good consistency of the scales derived with the above two approaches, the independent GNSS scale based on Galileo officially released PCCs were used by the third IGS reprocess (repro3). The scale discrepancy was about \(-\)1.24 ppb when the frame of repro3 (IGSR3) was transformed to IGb14. Correspondingly, the Z-PCOs of GPS and GLONASS were biased by about +160.0 mm to keep the consistency with Galileo-released PCCs in IGS repro3. Besides Galileo, the ground calibrated PCO values for BDS and QZSS were also released by the China Satellite Navigation Office (CSNO) as well as the Japanese Cabinet Office. However, their contribution to the terrestrial scale and the consistency with Galileo antenna models have not been investigated. Previous PCO estimations of regional BDS (BDS-2) satellites in IGS08 frame show significant differences in the Z-offset, especially for IGSO satellites, possibly caused by data processing methods and software [13; 14]. For the global BDS constellation (BDS-3), although the ground calibrated PCO values have already been provided by the CSNO [19], the preliminary estimations of satellite antenna PCCs in IGb14 were carried out by [PERSON] et al. [13], [PERSON] et al. [20], and [PERSON] et al. [21]. The results demonstrate that the discrepancy between estimated and released PCOs is within the level of a decimeter, and the estimated ones was impacted by the receiver antenna models as well as solar radiation pressure (SRP) model. For the first two estimates, the ground receiver antenna corrections for BDS B1I and B3I signals were replaced by that of GPS L1 and L2. For the last one, although the ground antenna PCCs were modeled, only PCOs were calibrated within IGb14, and the PCVs were completely omitted. Furthermore, the above estimates were aligned to IGS08 or IGb14 frame; however, the Galileo derived scale is used by IGS repro3, and will be adopted by IGS legacy products shortly. Hence, the PCO estimates in IGS repro3 frame (called IGSR3 hereafter) for BDS will facilitate inclusion of BDS in IGS repro3 and the legacy analysis.