Consistency and analysis of ionospheric observables obtained from three precise point positioning models

Ionospheric observables based on Global Navigation Satellite System can be obtained by a variety of approaches. The most widely used one is the geometry-free combination of carrier-phase smoothed code measurements. This method, however, introduces leveling errors that substantially degrade the performance of ionospheric modeling and bias estimation. To reduce leveling errors, precise point positioning (PPP) model is preferred for obtaining the ionospheric observables. We aim to investigate whether the ionospheric observables obtained from three different PPP models are consistent and how the PPP-based ionospheric observables relates to the smoothed code method. The paper begins by formulating the ionospheric observables. We then explain the statistical evaluation methods used for analyzing the bias terms derived from these methods and assessing the leveling errors from the carrier-phase smoothed code method. Numerical analysis is then conducted to compare the bias terms in the ionospheric observables and evaluate the leveling errors. The ionospheric observables based on the three PPP models show strong consistency. Compared to leveling errors in the carrier-phase smoothed code method, the leveling errors using the uncombined PPP model are significantly reduced up to five times.