Improved PPP-RTK by Considering the Non-Homogeneous Uncertainty of the ionosphere with a Spatial Three-Direction Model

Abstract

The ultimate goal of PPP-RTK is to achieve rapid ambiguity resolution, which is influenced by the prior precision of the external ionospheric information. This study proposes a method for determining the precision of ionospheric corrections for each satellite. In this method, an 8 min piece-wise function linearly related to the spatial three-direction distance components (SDC) within the geocentric coordinate system is constructed. By exploiting the SDC model, the user can calculate the precision of the ionospheric corrections satellite by satellite. Using the German and French stations, we validate this method experimentally and compare it to a method with an 8 min piece-wise function constructed by the baseline length (BLL). The SDC model provides an accuracy better than 10 mm in modeling ionospheric correction precision for each GPS satellite, with an average improvement of 43% compared to the BLL model. In addition, the SDC model offers an accuracy of approximately 5 mm in the reference network with an inter-station distance of less than 100 km, which is about 15% better than that of the BLL model during the active ionospheric period. The SDC model exhibits advantages over ionospheric correction precision modeling, with an average improvement of 73.5% for a reference network with station spacing of 125–155 km. By adopting the adaptive ionospheric precision derived from the SDC model, the GPS/GPS + Galileo PPP-RTK achieves a horizontal error of 50 mm and a vertical error of 100 mm within an average of three to four epochs. Notably, the convergence time is significantly enhanced by 30% in reference networks with inter-station distances of 125–155 km, compared to that of the PPP-RTK solution generated with dynamic ionospheric correction precision from the BLL model for all observed satellites.