Reference-satellite dependence in wide-area PPP-RTK ionospheric modeling: a controlled comparison of undifferenced and between-satellite single-differenced STEC

Introduction Wide-area slant total electron content (STEC) models provide regional ionospheric constraints for accelerating precise point positioning real-time kinematic (PPP-RTK). Between-satellite single differencing is widely used to eliminate receiver differential code bias (RDCB), but it also couples the quality and availability of all target-satellite constraints to a common reference satellite. Methods This study performs a controlled comparison of undifferenced STEC (UD-STEC) and between-satellite single-differenced STEC (SD-STEC) using 21 days of GPS and Galileo observations from a sparse European network. Both strategies are derived from the same PPP-AR-based ionospheric observations and evaluated with the same reference-network configuration, radial basis function interpolation, uncertainty-generation procedure, and user-side PPP-RTK processing. Consistent UD-STEC observations are recovered through GIM-assisted RDCB calibration. Results The two strategies show comparable modeling performance during quiet periods, whereas their differences become more evident as ionospheric variability increases. Over the full dataset, UD-STEC reduces the mean modeling RMS by 10.37% for GPS and 14.75% for Galileo relative to SD-STEC. During active periods, the P95 PPP-RTK convergence time decreases from 510 s with SD-STEC to 300 s with UD-STEC. A real-observation case and two controlled experiments show that reference-satellite errors are inherited by all associated SD-STEC pairs, while unequal satellite availability or reference-satellite loss reduces the spatial support available to the common-reference SD-STEC models. Discussion These results indicate that reference-satellite dependence is an important source of sensitivity in the SD-STEC implementation considered here, particularly when ionospheric variability or observation continuity becomes unfavorable.