On the relation of GNSS phase center offsets and the terrestrial reference frame scale: a semi-analytical analysis

Abstract

Phase center offsets (PCOs) of Global Navigation Satellites Systems (GNSS) transmit antennas along the boresight axis introduce line-of-sight dependent range changes in the modeling of GNSS observations that are strongly correlated with the estimated station heights. As a consequence, changes in the adopted PCOs impact the scale of GNSS-based realizations of the terrestrial reference frame (TRF). Vice versa, changes in the adopted TRF scale require corrections to the GNSS transmit antenna PCOs for consistent observation modeling. Early studies have determined an approximate value of alpha=-0.050 for the ratio of station height changes and satellite PCO changes in GPS orbit determination and phase center adjustment. However, this is mainly an empirical value and limited information is available on the actual PCO-scale relation and how it is influenced by other factors. In view of the recurring need to adjust the IGS antenna models to new ITRF scales, a semi-analytical model is developed to determine values of \alpha for the four current GNSSs from first principles without a need for actual network data processing. Given the close coupling of satellite boresight angle and station zenith angle, satellite PCO changes are essentially compensated by a combination of station height, zenith troposphere delay, and receiver clock offset. As such, the value of alpha depends not only on the orbital altitude of the considered GNSS but also on the elevation-dependent distribution of GNSS observations and their weighting, as well as the elevation mask angle and the tropospheric mapping function. Based on the model, representative values of alpha_GPS=-0.051, alpha_GLO=-0.055, alpha_GAL=-0.041, and alpha_BDS-3=-0.046 are derived for GPS, GLONASS, Galileo, and BeiDou-3 at a 10° elevation cut-off angle. These values may vary by dalpha~0.003 depending on the specific model assumptions and data processing parameters in a precise orbit determination or precise point positioning. Likewise changes of about +/-0.003 can be observed when varying the cut-off angle between 5° and 15°.