Wen Lai

GNSS Precise Point Positioning (PPP) technology has been applied to the time transfer for a long time, enabling time synchronization between two arbitrary stations on a global scale. Over the past decade, Low Earth Orbit (LEO) satellite constellations have been developed to enhance GNSS, offering rapid geometry configuration variations that can accelerate PPP convergence and enhance the time link performance. In this contribution, LEO observations are integrated into GNSS to enhance the real-time PPP time transfer. Simulated LEO constellations with varying numbers of satellites are used to assess their impact on real-time PPP time transfer performance. One week of observation data from 11 globally distributed stations is used to generate 10 time links, and five experimental schemes are designed: (1) GPS/BDS-3/Galileo solution (GCE), (2) GCE with 120 LEO satellites (GCE+120L), (3) GCE with 180 LEO satellites (GCE+180L), (4) GCE with 240 LEO satellites (GCE+240L), and (5) GCE with 300 LEO satellites (GCE+300L). Results showed that compared to the GCE solution, integrating 120, 180, 240, and 300 LEO satellites increases the average number of observed satellites from 23.4 to 30.6, 34.1, 37.7, and 41.3, respectively, while reducing Time Dilution of Precision (TDOP) values from 0.547 to 0.424, 0.391, 0.363, and 0.342, respectively. Using 30 s observations, the average convergence time to STD of time link errors better than 0.1 ns is reduced from 7.95 to 5.94, 4.83, 4.46, and 4.45 min in static mode, with improvements of 25.3%, 39.2%, 43.9%, and 44.0%, respectively, and from 8.75 to 6.18, 5.17, 4.89, and 4.72 min in kinematic mode, with improvements of 29.3%, 40.8%, 44.1%, and 46.0%, respectively. Using 1 s observations, Scenarios GCE+120L, GCE+180L, GCE+240L, and GCE+300L can achieve 1 ns convergence within 1 min. The time link precision was also found to be significantly improved, i.e., from 0.337 to 0.243 ns in static mode with improvements of 27.9%, and from 0.377 to 0.253 ns in kinematic mode with improvements of 32.9%. The time link stability is significantly enhanced for averaging times between 60 and 20,000 s in both static and kinematic modes, with a maximum improvement of nearly 50%. These results have demonstrated that integrating LEO satellites can significantly enhance real-time PPP time transfer performance.

BDS-3 faces challenges in achieving precision orbit determination (POD) due to the difficulty of establishing a globally uniform distribution of independently operated ground tracking stations. The use of onboard BDS-3 observations collected by low Earth orbit (LEO) satellites can partially mitigate this limitation. However, these observations introduce additional parameters, such as receiver clock offsets and carrier-phase ambiguities, which substantially increase the computational burden. Therefore, the capability of achieving real-time (RT) joint POD for BDS-3 and LEO satellites, relying solely on independently operated tracking stations, is greatly constrained. Currently, the inter-satellite links (ISLs) of BDS-3 have been successfully demonstrated to be effective for POD of BDS-3 satellites. In the future, ISLs of LEO satellites will also be incorporated as a measurement technique. Compared to traditional BDS-3 onboard observations, POD using ISLs involves almost no additional parameters other than the orbital states. Therefore, this paper proposes a method that combines onboard BDS-3 receivers on a subset of LEO satellites with LEO ISL observations to achieve rapid high-precision joint POD for BDS-3 and the full LEO constellation. To validate the proposed approach, measured BDS-3 data from regional ground stations in China are employed, together with simulated onboard BDS-3 data and simulated LEO ISL observations. All datasets were obtained over a three-day period, corresponding to days 131–133 of the year 2025. Firstly, it is demonstrated that, when relying solely on regional ground stations, the 24 MEO and 3 IGSO satellites of BDS-3 cannot achieve high-precision POD, with 1D RMS orbit accuracies of only 11.6 cm and 26.9 cm, respectively. Incorporating onboard BDS-3 data from LEO satellites significantly improves orbit determination accuracy, with 1D RMS accuracies reaching 4.9 cm for MEO and 6.4 cm for IGSO satellites, while LEO satellites themselves achieve orbit accuracy better than 5 cm. Subsequently, the computational burden introduced by onboard BDS-3 data from LEO satellites in joint POD is further assessed. On average, incorporating onboard BDS-3 data from 10 LEO satellites adds approximately 6780 parameters to be estimated, substantially increasing computation time. When onboard BDS-3 data from 20 LEO satellites are included, the achieved BDS-3 orbit accuracy shows negligible degradation compared to using data from all LEO satellites, with 1D RMS accuracies of 4.9 cm and 6.7 cm for MEO and IGSO, respectively. Meanwhile, the processing time for a single batch least squares (BLSQ) solution decreases dramatically from 27.0 min to 5.7 min. Increasing the number of LEO satellites to 30 further improves BDS-3 orbit accuracy, mainly due to the enhanced orbit precision of the LEO satellites. After incorporating LEO ISLs, LEO satellites achieve orbit accuracy in the 1D direction of approximately 1 cm, regardless of whether their onboard BDS-3 data are used. In summary, the proposed approach significantly reduces computational burden while ensuring orbit determination accuracy for both BDS-3 and LEO satellites. This approach is more likely to realize real-time joint POD of BDS-3 and LEO satellites based on large-scale LEO constellations.

High-precision clock offset products directly affect the performance and reliability of precise point positioning (PPP) applications. Currently, real-time clock offset products offered by institutions such as the Centre national d’études spatiales (CNES) rely on ultra-rapid predicted orbits. However, these orbits have limited accuracy and exhibit jumps during updates, constraining the accuracy of real-time clock estimation. To address this issue, we propose an undifferenced ambiguity resolution (UD AR) technique for clock offset estimation based on epoch-wise updated orbits. Clock estimation experiments were performed using both predicted and epoch-wise updated orbits, with square root information filtering (SRIF) applied in three schemes: double-differenced (DD), UD, and float solutions. Compared with predicted orbits, epoch-wise updated orbits provided smoother sequences with higher accuracy, significantly improving clock offset estimation accuracy in all schemes. Moreover, the UD AR solution significantly enhanced clock offset estimation accuracy, and the high-precision epoch-wise updated orbit products increased the narrow-lane fixing rate of the UD solutions. The clock accuracies of BDS-3, Galileo, and GPS reached 0.032 ns, 0.023 ns, and 0.026 ns, respectively, representing improvements of 36%, 34%, and 41% compared with the float solutions and 41%, 30%, 26% compared with the UD solution based on 1 h predicted orbits. Finally, the positioning performance of the proposed method was validated via PPP using 25 stations, showing improvements of 50%, 48%, and 41% in the north, east, and up directions compared with CNES products. Therefore, by combining epoch-wise updated orbit products with the UD AR to improve clock accuracy, this method provides a new approach to generating high-precision clock products, significantly contributing to enhancing PPP services.