Integrated ionospheric delay processing strategy for PPP-RTK: improving uncertainty estimation accuracy and mitigating delay errors

Accurately characterizing ionospheric delay uncertainties is essential but challenging for achieving reliable centimeter-level positioning in precise point positioning real-time kinematic (PPP-RTK). Unpredictable ionospheric variations often lead to discrepancies between estimated and actual corrections, especially under active ionospheric conditions. To address these limitations, this study proposes an integrated ionospheric delay processing strategy that enhances both the server and user sides. On the server side, a refined cross-validation model incorporating elevation angle variations is introduced to provide more accurate ionospheric delay uncertainty estimates. On the user side, a PPP-RTK strategy without atmospheric errors (PPP-RTK-WAE) constrains fixed ambiguities back into the PPP solution, mitigating ionospheric errors while preserving convergence speed. Experiments with dual-frequency GPS data from 335 EUREF stations over 31 days in 2023 validate the approach. When ionospheric delay errors exceed 10.0 cm, mainly from low-elevation satellites (RMS 15.0 cm), the legacy method underestimates uncertainty (4.8 cm), while the refined method provides more realistic values (11.0 cm), reducing outliers beyond three times the uncertainty from 52.2% to 0.3%. Under active ionospheric conditions, convergence time (defined as the epoch when the 68.3rd percentile positioning error first reaches 10 cm) is shortened from 10.0 to 6.0 min in the horizontal and from 12.0 to 9.0 min in the vertical component. When over-tight constraints are applied, ionospheric errors can degrade positioning. PPP-RTK-WAE addresses this, improving positioning accuracy by 13.3% horizontally and 3.4% vertically, with extreme reductions from 4.2 to 0.9 cm and from 7.7 to 1.2 cm. These results demonstrate that the integrated strategy improves uncertainty estimation and mitigates ionospheric errors, thereby enhancing the robustness of PPP-RTK applications.