Refined real-time PPP-based timing via data fusion of meteorological models and Galileo HAS

Abstract Galileo high accuracy service (HAS) via Galileo navigation signals has provided state space representation for GPS and Galileo since January 2023. Tropospheric delay remains a dominant error source in HAS-based real-time precise point positioning (PPP) for global positioning and timing applications. To mitigate this effect, we propose a refined NWP-constrained real-time PPP model (NWP-CR-PPP), which incorporates high-precision zenith tropospheric delay (ZTD) estimates derived from numerical weather prediction (NWP) systems into the standard PPP framework (S-PPP), thereby enhancing HAS real-time PPP timing services globally. The primary research components comprise: (1) optimal weight determination for NWP ZTD through error characteristic analysis, (2) systematic investigation of the NWP-CR-PPP model’s positioning and timing performance under static and kinematic scenarios. Experimental results demonstrated that the NWP ZTD achieves mean absolute error and root mean square error values of 9.87 mm and 12.07 mm, respectively, when validated against IGS ZTD, confirming its reliability as a high-precision constraint. In the static scenario, the NWP-CR-PPP model demonstrates significant improvements in both positioning accuracy and timing precision compared to the S-PPP model, regardless of single-system or dual-system configurations. Quantitatively, the positioning accuracy mean Gain is 2.82 cm for single-GPS, 2.31 cm for single-Galileo, and 2.13 cm for the combined GPS/Galileo system, while the corresponding timing precision mean Gain are 0.07 ns, 0.06 ns, and 0.06 ns, respectively. The long-term timing stabilities (61 440 s) at MBAR and OUS2 stations fluctuate within ranges of 1.99–2.29 × 10 −13 and 1.29–1.53 × 10 −13 , respectively. In the kinematic scenario, the NWP-CR-PPP model also demonstrates a significant improvement, and the improvement margin is greater than that in the static scenario. Quantitatively, the mean Gain values of positioning accuracy for each system are 3.00 cm, 2.79 cm, and 2.39 cm, while the mean Gain values of timing accuracy are 0.16 ns, 0.13 ns, and 0.08 ns. The long-term (61 440 s) stabilities of the timing results for each system at the two stations are within the ranges of 1.94–2.39 × 10 −12 and 1.28–1.34 × 10 −12 , respectively. Overall, by assimilating high-precision ZTD constraints from NWP, the NWP-CR-PPP model significantly enhances positioning accuracy and timing performance in both static and kinematic scenarios.