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Real-time satellite clock offset is a crucial element for real-time precise point positioning (RT-PPP). However, the elapsed time for undifferenced (UD) multi-global navigation satellite system (GNSS) real-time satellite clock offset estimation at each epoch is increased with the growth of stations, which may fall short of real-time application requirements. Therefore, a rapid estimation method for UD multi-GNSS real-time satellite clock offset is proposed to improve the computation efficiency, in which both the dimension of the normal equation (NEQ) and the number of redundant observations are calculated before adjustment; if these two values are larger than the predefined thresholds, the elevation mask is gradually increased until they are less than the predefined thresholds. Then, the clock offset estimation is conducted; this method is called clock offset estimation using partial observations. Totals of 50, 60, 70 and 80 stations are applied to perform experiments. Compared to clock offset estimation using all observations, the elapsed times of clock offset estimation using partial observations can be reduced from 6.80 to 3.10 s, 7.93 to 2.97 s, 12.04 to 3.14 s for 60, 70 and 80 stations, respectively. By using the proposed method, the elapsed time of the clock offset estimation at each epoch is less than 5 s. The estimated clock offset accuracy for GPS, BDS-3, Galileo and GLONASS satellites are better than 0.04, 0.05, 0.03 and 0.16 ns when using the partial observations to estimate clock offset with 50, 60, 70 and 80 stations, respectively. For the multi-GNSS kinematic PPP using the estimated clock offset from 50, 60, 70 and 80 stations with partial observations, the positioning accuracy at 95% confidence level in the east, north and up direction are better than 2.70, 2.20 and 5.60 cm, respectively. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]