Utilizing real-time precise point positioning (PPP) technology is an effective approach for obtaining high-precision zenith tropospheric delay (ZTD). Without relying on the terrestrial internet, Galileo high accuracy service (HAS) can provide precise orbit and precise clock products for the world. A thorough assessment of the ZTD accuracy of real-time PPP calculations based on Galileo HAS products in global regions is necessary to promote its application in the field of global navigation satellite system (GNSS) meteorology. The observation data of HAS from 1 to 7 September 2023 were selected for the experiment. Firstly, the accuracy of satellite orbit and clock products of the HAS GPS and HAS Galileo system are evaluated. Then, real-time PPP positioning accuracy within and outside the HAS service area is analyzed. Finally, 104 IGS stations in the world are selected to analyze the ZTD accuracy of real-time PPP calculations based on Galileo HAS products. The experimental results show that during the test period, the RMSE values of the satellite orbit products of the HAS GPS in the radial, along, and cross directions were 4.57 cm, 10.62 cm, and 7.56 cm, respectively. The HAS Galileo RMSE values were 2.81 cm, 8.02 cm, and 7.47 cm, respectively. The RMSE values of the clock products were 0.38 ns and 0.15 ns, respectively. At the selected stations, the real-time PPP positioning accuracies outside the HAS service area and within the service area were similar, and the correlation coefficient between HAS ZTD and IGS ZTD was above 0.90. In the global region, the average bias and RMSE values of the real-time PPP ZTD of the HAS GPS were −0.31 mm and 16.78 mm. Those of the HAS Galileo were 2.30 mm and 15.89 mm, and those of the HAS GPS/Galileo were −0.25 mm and 16.11 mm, respectively. Moreover, each system showed that the accuracy of the HAS ZTD inside the service area was better than that outside the service area. Compared with the single system, the real-time PPP ZTD continuity and stability of the dual system were better.

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.

The Galileo navigation system offers a free High Accuracy Service (HAS) to global users via the E6 signal and the Internet, enabling the broad application of real-time precise point positioning (PPP) time transfer. However, tropospheric delay is not only a major error source in real-time PPP time transfer but also correlates with clock offset parameters, thereby limiting the achievable accuracy. We employed our proprietary ray-tracing software (NRT-2D) to compute high-precision tropospheric delays and proposed a real-time PPP time-transfer model with Zenith Tropospheric Delay (ZTD) constraints based on Galileo HAS. The experimental results showed that the root mean square error of NRT-2D ZTD and VIE-2D (a ray tracing software developed by the Vienna University of Technology) ZTD are 10.05 mm and 12.11 mm, respectively, which verifies that NRT-2D has higher accuracy in ZTD calculation. The tropospheric slant delay exhibits anisotropy that increases with decreasing elevation angle and is significantly stronger in summer and autumn than in spring and winter. Compared to conventional PPP time transfer models, the proposed model achieves accuracy improvements of up to 28.20% and 21.08% in GPS and Galileo-based PPP time transfer, respectively. Short-term frequency stability (1920 s) improvement rates reached as high as 40.27% and 52.99%. Additionally, during the PPP re-convergence stage caused by the interruption of observation data, the model can effectively suppress the volatility of time transfer results. The research demonstrated that the ZTD constrained real-time PPP time transfer based on Galileo HAS can significantly improve the accuracy and stability of the time transfer results, thereby offering robust support for high-precision time transfer applications.

Universal Time (UT1) is a core component of the Earth orientation parameters (EOP). High-precision UT1 predictions are essential for satellite navigation, deep-space exploration, and the maintenance of national standard time. Although effective angular momentum (EAM) information can improve UT1 predictions, the impacts of different angular momentum combinations on prediction performance have not yet been systematically investigated. To improve the prediction accuracy of the National Time Service Center (NTSC) UT1 products, we constructed four prediction schemes: Case 1 uses only atmospheric angular momentum (AAM) data; Case 2 uses AAM + oceanic angular momentum (OAM) data; Case 3 uses AAM + OAM + hydrological angular momentum (HAM) data; and Case 4 uses the full EAM datasets combining AAM, OAM, HAM, and sea-level angular momentum (SLAM) data. The input UT1 series is from the NTSC EOP products, and the 10-day angular momentum forecasts are provided by the German Research Centre for Geosciences (GFZ). The rolling forecast evaluation was conducted from June 2024 to September 2025. The results show that Case 2 performs best for short-term UT1 predictions over 1–12 days, improving the mean prediction accuracy by 10.7%, 10.0%, and 52.0% relative to the predictions using Case 4, IERS finals.daily, and the original NTSC predictions, respectively. For medium- and long-term UT1 predictions over 13–90 days, Case 1 performs best, with corresponding mean improvements of 9.8%, 50.7%, and 61.3%, respectively. These results indicate that incorporating more angular momentum components does not necessarily lead to better UT1 predictions, i.e., Case 2 is preferable for short-term UT1 predictions, whereas Case 1 is more suitable for medium- and long-term UT1 predictions. These findings provide empirical evidence and practical guidance for optimizing UT1 prediction models.

It is important for a geostationary Earth orbit (GEO) satellite to rapidly recover its orbit after a maneuver with short-arc precise orbit determination (POD). Based on orbit determination by transfer tracking (ODTT), the POD accuracy of a GEO satellite is less than 10 m over a short arc. ODTT can achieve high accuracy in the radial direction but is weak in the transverse direction. Considering that very long baseline interferometry (VLBI) can reduce the value of position dilution of precision (PDOP), especially in the transverse direction, a joint POD method using both VLBI and ODTT is proposed herein to improve POD accuracy and rapidly recover the orbit. An ODTT system and the first VLBI 2010 Global Observation System (VGOS) in China was used to track the ZX 12# GEO satellite. The results showed that the ODTT POD accuracy was 3.016 and 2.707 m for 2 and 4 h arcs, respectively. When using both VLBI and ODTT, the POD accuracy was 2.658 m for the 2 h arc, an improvement of 11.87% compared to the POD using ODTT alone. Therefore, VLBI and ODTT can be used together to increase the short-arc POD accuracy while also reducing the arc length necessary to recover the orbit.