# Phase Center Corrections for BDS IGSO and MEO Satellites in IGb14 and IGSR3 Frame
## 1 Introduction  
With the launch of the last satellite on 23 June 2020, Chinese BeiDou navigation satellite system (BDS) completed its construction and was officially announced to provide global position, navigation, and timing (PNT) services. Until 2 December 2020, there have been 49 satellites distributed in geosynchronous orbit (GEO), inclined geostationary orbit (IGSO), and medium earth orbit (MEO) [1]. To analyze all available Global Navigation Satellite System (GNSS) signals by preparing the International GNSS Service (IGS) for multi-GNSS data processing, the pilot project named as the multi-GNSS experiment (MGEX) wasinitiated in 2012 [2]. As a backbone of the MGEX project, a new network of multi-GNSS monitoring stations has been deployed around the globe. With the observations collected by MGEX and other tracking networks, several analysis centers (ACs), e.g., the Center for Orbit Determination in Europe (CODE, Bern, Switzerland), German Research Center for Geosciences (GFZ, Potsdam, German), and Wuhan University (WHU, Wuhan, China), have provided the precise ephemeris, clock, and biases products for BDS satellites. The experimental combination indicates that the BDS orbit consistency between the contributingACs has reached a level of more than several decimeters to meters for GEO and IGSO, and several centimeters for MEO satellites [3]. Besides the dynamic model, the consistent measurement models, particularly phase center corrections (PCCs), used in data processing are essential for more consistency of GPS and GLONASS orbits as shown by [PERSON] et al. [4] and [PERSON] et al. [5]. GNSS observations measure the geometric distance between the antenna phase center locations of the navigation satellite at signal emission time and the receiving antenna at signal reception time. The phase center locations are usually different from the mechanical antenna reference points (ARP) which are used for GNSS observation modeling. Because of this difference, high-precision GNSS applications require a set of PCCs to tie the GNSS measurements consistently to the ARP of the satellite and receiver antenna. Normally, the set of PCCs for the antenna phase center consists of the phase center offset (PCO) and phase center variation (PCV). PCO of satellite antenna is a vector which defines the position of the \"mean antenna phase center\" with respect to the center of mass (CoM), which is the ARP of the satellite [6]. PCV is a consistent function which models the locations of actual antenna phase centers with respect to the \"mean antenna phase center\" depending on the observation direction. For signal transmitting antennas, although its PCC could be estimated from global GNSS tracking data, due to high mathematical correlations between the station heights, tropospheric delays, and PCC of receiver antenna, it is not possible to obtain reasonable solutions without making two fundamental assumptions [7; 8; 9]: (1) absolute antenna PCCs for the receiving antennas have to be introduced as known, and (2) the scale of the terrestrial network has to be fixed with respect to a particular terrestrial reference frame. For the first assumption, prior to 6 November 2006, the relative PCCs were used for receiver antenna. However, using relative calibrations in global networks yields systematic effects. Hence, the absolute antenna calibration approaches have been developed for the estimation of the PCO and PCV of receiving antenna [10]. With the reprocess of GNSS data, IGS has provided an official absolute antenna model with PCOs and PCVs for both GPS and GLONASS satellites in ATX file, e.g., jigs14_WWWW.atv (WWWW represents the GPS week hereafter) consistent with IGb14 frame. For upcoming GNSS systems, e.g., Galileo and BDS, the PCOs and PCVs from officially released metadata are recommended by IGS currently without investigating the consistency with GPS and GLONASS antenna offsets as well as the terrestrial scale.