LEO-based solution of GPS PCOs and impact on terrestrial scale

The deviations of phase center offsets (PCOs) of GPS satellites were and still are significant bias sources for GPS-based terrestrial reference frames (TRF). Because of the strong correlation between the scale of the TRF and the satellite PCOs in the z-direction (z-PCOs), a no-net-scale (NNT) condition relative to, for instance, the International Terrestrial Reference Frame (ITRF) is commonly applied. Based on the released Galileo metadata, the GPS z-PCOs have been calibrated without introducing a scale determined by other techniques in the third re-processing of the International GNSS Service (IGS). Another approach purely based on GNSS is by integrating low Earth orbiters (LEOs) into the estimation of the GPS z-PCOs and the realization of the scale. Within this study, we estimated the GPS z-PCOs based on zero-difference ionosphere-free observations from six low LEOs and ground networks with different numbers of stations in 2019 and 2020. Besides the study based on six LEOs in two years, a twelve-year-based estimation of GPS z-PCOs and scale realization is done by using the two satellites of the GRACE mission.

We jointly estimate orbits (GPS and LEOs), station coordinates, z-PCOs of GPS satellites, and some other parameters in an integrated processing. The NNT condition on the ground network is not applied in the processing. By adding six LEOs, the correlation coefficients between the GPS z-PCOs and the scale is reduced significantly (from about 0.85 to 0.30). It means that the GPS z-PCOs and the scale have been decorrelated efficiently, and consequently the precision of the estimation is improved. For GPS satellites operated in 2019 and 2020, excluding GPS III, their estimated z-PCOs have an average difference of -231 mm compared to the values in igs14_2134.atx and the corresponding scale to the IGS14 reference frame is +1.89 part per billion. These results agree well with the solutions based on the metadata of Galileo. The improvement due to different numbers of LEOs and the impact of LEO z-PCO errors on the estimation is studied, where more LEOs decorrelate the GPS z-PCOs and the scale more efficiently. The accuracy of the LEO z-PCOs is critical to the solution. A one-millimeter accuracy of the z-PCOs of the LEOs is required to achieve a one-millimeter scale on the surface of the Earth. Thanks to the long-term available data of LEO missions in the last decade and even longer, the LEO-based method has an advantage on the real-data-based estimation of PCOs of former GPS satellites over the Galileo-based method. The z-PCOs of satellites of GPS blocks IIA, IIR, IIRM, and IIF are estimated by integrating the two GRACE satellites from 2004 to 2015. A twelve-year scale relative to the ITRF is realized simultaneously. The performance of the LEO-based method is shown by the long-time series.