GPS z-PCO and GNSS-based scale determined by integrated processing with LEOs and Galileo

The Global Positioning System (GPS) satellite transmitter antenna phase center offsets (PCOs) in z-direction and the scale of the terrestrial reference frame are highly correlated when neither of them is constrained to an a priori value in a least-squares adjustment. The commonly used PCO values offered by the International GNSS Service (IGS) are estimated in a global adjustment by constraining the ground station coordinates to the current International Terrestrial Reference Frame (ITRF). As the scale of the ITRF is determined by other techniques, the estimated GPS z-PCOs are not independent. Consequently, the z-PCOs transfer the scale to any subsequent GNSS solution. To get a GNSS-based scale that can contribute to a future ITRF realization, two methods are proposed to determine scale-independent GPS z-PCOs. One method is based on the gravitational constraint on Low Earth Orbiters (LEOs) in an integrated processing of the GPS satellites and LEOs. The correlation coefficient between the GPS PCO-z and the scale is reduced from 0.85 to 0.3 by supplementing a 54-ground-station network with seven LEOs. The impact of individual LEOs on the estimation is discussed by including different subsets of the LEOs. The accuracy of the z-PCOs of the LEOs is very important for the accuracy of the solution. In another method, the GPS z-PCOs and the scale are determined in a GPS+Galileo processing where the PCOs of Galileo are fixed to the values calibrated on ground from the released metadata. The correlation between the GPS PCO-z and the scale is reduced to 0.13 by including the current constellation of Galileo with 24 satellites. We use the whole constellation of Galileo and the three LEOs of the Swarm mission to perform a direct comparison and cross-check of the two methods. The two methods provide mean GPS z-PCO corrections of -186±25 mm and -221±37 mm with respect to the IGS values, and +1.55±0.22 ppb (part per billion) and +1.72±0.31 ppb in the terrestrial scale with respect to the IGS14 reference frame. The results of both methods agree with each other with only small differences. Due to the larger number of Galileo observations, the Galileo-PCO-fixed method leads to more precise and stable results. In the joint processing of GPS+Galileo+Swarm in which both methods are applied, the constraint on Galileo dominates the results. We also discuss how fixing either the Galileo transmitter antenna z-PCO or the Swarm receiver antenna z-PCOs in the GPS+Galileo+Swarm processing propagates to the respective freely estimated z-PCOs of Swarm or Galileo.