Uncertainties of Interpolating Satellite-Specific Slant Ionospheric Delays and Impacts on PPP-RTK

Precise point positioning-real-time kinematic (PPP-RTK) achieves fast convergence in global navigation satellite system (GNSS) positioning and navigation. Correcting slant ionospheric delays is crucial for this purpose. One way to obtain the slant ionospheric corrections is by interpolating from nearby reference stations. However, the interpolation performance depends on many factors, such as time, elevation, and distance. This article aims to study the performance of three interpolation algorithms, i.e., inverse-distance weighting (IDW), radial basis function (RBF), and Kriging, under different ionospheric conditions. For inhomogeneously distributed ionospheric density, the performance of IDW is unsatisfying compared with the other two methods. In addition, we represent uncertainties on a 2-D map and find that the uncertainties increase on average linearly with distance. Elevation also plays an important role in interpolation uncertainty. Comprehensively, we build a mathematical model between the uncertainties of different interpolation methods as a function of time, elevation, and distance. They all degrade significantly with a large rate of change in the total electron content index (ROTI). Finally, we validate the proposed uncertainties by applying them to PPP-RTK processing. A convergence time within 2 min and positioning accuracy within 3.5 cm in horizontal and 6 cm in vertical directions are achieved.