Regional ionospheric TEC modeling based on a two-layer spherical harmonic approximation for real-time single-frequency PPP

The ionosphere has been considered as one of the major error sources in GNSS signal propagation, and it is still difficult to be modeled precisely, especially for real-time positioning applications. The commonly used ionospheric models are usually based on the one-layer approximation, which neglects the ionospheric variation in the vertical domain and limits the scope of improvement over one-layer models. A new ionospheric model based on the two-layer approximation and two spherical harmonic (SH) functions is proposed in this contribution, where a quasi-globe projection is designed to avoid the inherent ill-posed problem and retain the physical meaning of the SH when regional data are used. GPS and BDS data from the National Positioning Infrastructure of Australia and Crustal Movement Observation Network of China are used for validating the new model’s performance in different areas and different periods. Results show (1) the precision of ionospheric TEC estimates from the new model can be improved by about 26% and 31% in the cross-validation experiment compared to the traditional one-layer model in Australian and Chinese regions, respectively; (2) the positioning accuracy of kinematic single-frequency precise point positioning (SF-PPP) in the experimental regions using the new model reaches about 0.7 m and 0.8 m in the horizontal and vertical components, respectively, in comparison with the one-layer model’s 1.0 m (horizontal) and 1.4 m (vertical); (3) the convergence time of the SF-PPP using the new model is 5–10 min for achieving a sub-meter level of positioning accuracy in both horizontal and vertical components, whereas it needs 30–40 min in case the one-layer model is used.