Low Earth Orbit (LEO) satellites can augment the traditional GNSS-based positioning, navigation and timing services, which require real-time high-precision LEO satellite clock products. As the complicated systematic effects contained in the LEO satellite clock estimates limit their high-precision mid- to long-term prediction, high-frequency LEO satellite clocks need to be estimated within a Kalman filter, resulting in a short prediction time for real-time applications. Compared to the clock estimation using Batch Least-Squares (BLS) adjustment, filter-based clock estimation experiences a lower precision. Increasing the model strength by introducing external orbital information, thus, de-correlating the orbital and clock parameters, will benefit real-time clock precision. In this contribution, reduced-dynamic LEO satellite orbits are first estimated using BLS adjustment in near real-time and predicted in the short term. The predicted orbits are then constrained during the Kalman-filter-based clock estimation process. The variance–covariance matrix of the introduced orbital errors is tested for different sets of values in the radial, along-track and cross-track directions when constraining orbits of different prediction times. One week of GPS data from the Sentinel-3B satellite in 2018 was used for validation of the proposed method. When weakly constraining high-accuracy predicted orbits within a prediction time of 20 min, i.e., with a standard deviation of the constraint set to 2–3 dm in the radial and cross-track directions, and 4–6 dm in the along-track direction, the estimated clock accuracy can be improved from about 0.27 to 0.23 ns, with a 13.4% improvement. Depending on the prediction period of the introduced orbits, the Signal-In-Space Range Error (SISRE) of the LEO satellite to Earth can also be improved, from about 9.59 cm without constraints, to 7.38–8.07 cm after constraining the predicted orbits, with an improvement of 16–23%. The improvements in the SISRE also indicate a better consistency between the real-time clock and orbital estimates.

Ambiguity resolution (AR) is a core technology that helps to speed up convergence time and increase positioning accuracy for precise point positioning (PPP), and the performance of PPP-AR is based on the quality of ambiguity resolution products. Real-time PPP-AR becomes a reality as users can now obtain publicly accessible real-time observable-specific signal bias (OSB) products from the Centre National d’Etudes Spatiales (CNES). Therefore, an analysis of the quality of OSB products and an evaluation of the performance of PPP-AR are required to promote the application of real-time positioning. For a total of 31 days between day of year (DOY) 121 and 151 in 2021, observation data were collected from 90 stations, and the OSB products were used to assess the experiments. As for the quality of the OSB products, the data availability (DA) of the GPS and Galileo satellites was greater than 97%, whereas that of BDS was less than 60%; the maximum fluctuation value (MAX) and standard deviation (STD) of the GPS, Galileo, and BDS satellites were 0.045 and 0.012; 0.081 and 0.028; and 0.292 and 0.085 cycles, respectively. In terms of ambiguity residuals using the OSB products, the wide-lane (WL) residual percentages within ±0.25 cycles for the GPS, Galileo, BDS-2, and BDS-3 systems were more than 92%, and the narrow-lane (NL) residual percentages within ±0.25 cycles for the four systems were 92%, 89%, 79%, and 60%, respectively. With regard to the performance of PPP-AR, the GPS+Galileo solution showed the best performance in the kinematic positioning mode, in which the mean root mean square (RMS) of positioning accuracy was 1.06, 1.27, and 2.85 cm for the east (E), north (N), and up (U) components, respectively, and the mean convergence time reached 9.6 min. In the static positioning mode, the mean convergence times of the GPS-only and GPS+Galileo solutions were 11.4 min and 8.0 min, respectively, and both of their mean RMS for positioning accuracy reached 0.79, 0.95, and 1.48 cm for the E, N, and U components, respectively. However, the addition of BDS did not further enhance the performance of multi-GNSS PPP-AR in either the kinematic or static positioning mode due to the poor quality of the real-time BDS products. More importantly, a prediction method was proposed to avoid re-convergence and to enhance the reliability of PPP-AR in the event of short-time missing real-time OSB products and to improve the positioning accuracy and the ambiguity fixed rate.

In the Global Navigation Satellite System (GNSS) community, the Quasi-Zenith Satellite System (QZSS) is an augmentation system for users in the Asia-Pacific region. However, the characteristics and performance of four QZSS satellite clocks in a long-term scale are unknown at present. However, it is crucial to the positioning, navigation and timing (PNT) services of users, especially in Asia-Pacific region. In this study, the characteristics and performance variation of four QZSS satellite clocks, which including the phase, frequency, frequency drift, fitting residuals, frequency accuracy, periodic terms, frequency stability and short-term clock prediction, are revealed in detail for the first time based on the precise satellite clock offset products of nearly 1000 days. The important contributions are as follows: (1) It is detected that the times of phase and frequency jump are 2.25 and 1.5 for every QZSS satellite clock in one year. The magnitude of the frequency drift is about 10⁻¹⁸. The periodic oscillation of frequency drift of J01 and J02 satellite clocks is found. The clock offset model precision of QZSS is 0.33 ns. (2) The two main periods of QZSS satellite clock are 24 and 12 hours, which is the influence of the satellite orbit; (3) The frequency stability of 100, 1000 and 10,000 s are 1.98 × 10⁻¹³, 6.59 × 10⁻¹⁴ and 5.39 × 10⁻¹⁴ for QZSS satellite clock, respectively. The visible “bump” is found at about 400 s for J02 and J03 satellite clocks. The short-term clock prediction accuracy of is 0.12 ns. This study provides a reference for the state monitoring and performance variation of the QZSS satellite clock.