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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]

The emergence of multiple global navigation satellite systems (multi-GNSS), including global positioning system (GPS), global navigation satellite system (GLONASS), Beidou navigation satellite system (BDS), and Galileo, brings not only great opportunities for real-time precise point positioning (PPP), but also challenges in quality control because of inevitable data anomalies. This research aims at achieving the real-time quality control of the multi-GNSS combined PPP using additional observations with opposite weight. A robust multiple-system combined PPP estimation is developed to simultaneously process observations from all the four GNSS systems as well as single, dual, or triple systems. The experiment indicates that the proposed quality control can effectively eliminate the influence of outliers on the single GPS and the multiple-system combined PPP. The analysis on the positioning accuracy and the convergence time of the proposed robust PPP is conducted based on one week's data from 32 globally distributed stations. The positioning root mean square (RMS) error of the quad-system combined PPP is 1.2 cm, 1.0 cm, and 3.0 cm in the east, north, and upward components, respectively, with the improvements of 62.5%, 63.0%, and 55.2% compared to those of single GPS. The average convergence time of the quad-system combined PPP in the horizontal and vertical components is 12.8 min and 12.2 min, respectively, while it is 26.5 min and 23.7 min when only using single-GPS PPP. The positioning performance of the GPS, GLONASS, and BDS (GRC) combination and the GPS, GLONASS, and Galileo (GRE) combination is comparable to the GPS, GLONASS, BDS and Galileo (GRCE) combination and it is better than that of the GPS, BDS, and Galileo (GCE) combination. Compared to GPS, the improvements of the positioning accuracy of the GPS and GLONASS (GR) combination, the GPS and Galileo (GE) combination, the GPS and BDS (GC) combination in the east component are 53.1%, 43.8%, and 40.6%, respectively, while they are 55.6%, 48.1%, and 40.7% in the north component, and 47.8%, 40.3%, and 34.3% in the upward component. [ABSTRACT FROM AUTHOR]

• 1. A quality control method for estimating multi-GNSS real-time satellite clock offset is proposed. • 2. The satellite clock offset accuracy of GPS, Galileo, BDS-3 and Galileo is improved. • 3.The precise point positioning accuracy can be improved by using the clock offset. Real-time satellite clock offset plays a prominent role in the Global Navigation Satellite System (GNSS) community. However, the GNSS raw observations are impacted by outliers, resulting in the quality of observations becomes poorer, which will dramatically affect the performance of estimated multi-GNSS satellite clock offset in real-time. In this contribution, an improved Inter Quartile Range (IQR) method is proposed to improve the quality of multi-GNSS satellite clock offset estimation in real-time, in which the improvements include two aspects. Firstly, the empirical threshold C 1 is determined to adapt multi-GNSS satellite clock offset estimation, if one residual is not between (Q 1 - C 1 ∗ I Q R , Q 3 + C 1 ∗ I Q R) , the observation is deleted. More importantly, to guarantee the clock offset of each satellite can be estimated at each epoch, if one satellite corresponding to all observation of stations is deleted, the IQR is conducted again at the current epoch for these observations. Three schemes are designed: 50 stations are used to perform multi-GNSS satellite clock offset estimation in real-time, which are without quality control (S1), with the proposed quality control method in this contribution(S2), and with quality control method using 8.5 medians of residuals (S3). Compared to S1, the satellite clock offset accuracy of GPS, Galileo, BDS-3, and GLONASS for S2 can be significantly improved from 0.082 to 0.055 ns, 0.106 to 0.072 ns, 0.178 to 0.083 ns, and 0.146 to 0.100 ns, respectively. The improvement is 32.93%, 32.07%, 53.37%, and 31.51%, respectively. The clock offset performance of S2 is better than that of S3 in terms of stability and reliability for GPS, BDS-3, and GLONASS. Another 52 stations are applied to perform multi-GNSS kinematic real-time precise point positioning (RT-PPP). For the convergence time and positioning accuracy, the RT-PPP employing the satellite clock offset generated from S2 shows the best performance. The experiment shows that the proposed quality control method can obtain real-time, stable, high-precision, and reliable multi-GNSS real-time satellite clock offset. [ABSTRACT FROM AUTHOR]