The rapid movement of low Earth orbit (LEO) satellite can improve geometric diversity, which contributes to the rapid convergence of Global Navigation Satellite System (GNSS) precise point positioning (PPP). However, the LEO onboard receiver clock cannot be used directly by PPP users as the LEO satellite clock because the LEO onboard receiver clock and LEO satellite clock absorb different code delays when receiving and transmitting signals. In this study, a real-time estimation approach for the LEO satellite clock based on ground tracking stations was proposed for the first time. The feasibility for the rapid convergence of the LEO satellite clock was analyzed using the satellite time dilution of precision (TDOP) that one satellite is relative to multiple ground tracking stations. The LEO constellation of 168 satellites and observations for 15 ground tracking stations were simulated to verify the proposed method. The experiment results showed that the average convergence time was 31.21 min for the Global Positioning System (GPS) satellite clock, whereas the value for the LEO satellite clock was only 2.86 min. The average root mean square (RMS) and standard deviation (STD) values after convergence were 0.71 and 0.39 ns for the LEO satellite clock, whereas the values were 0.31 and 0.13 ns for the GPS satellite clock. The average weekly satellite TDOP for the LEO satellite was much smaller than that for the GPS satellite. The average satellite TDOPs for all LEO and GPS satellites were 19.13 and 1294.70, respectively. However, the average delta TDOPs caused by satellite motion for all LEO and GPS satellites were both 0.10. Therefore, the rapid convergence of the LEO satellite clock resulted from the better geometric distribution of the LEO satellite relative to ground stations. Despite errors and the convergence time of the LEO satellite clock, the convergence time and positioning accuracy for LEO-augmented GPS and BeiDou Navigation Satellite System (BDS) PPP with the real-time estimated LEO satellite clock can still reach 10.63 min, 1.94 cm, 1.44 cm, and 4.18 cm in the east, north, and up components, respectively. The improvements caused by LEO satellite for GPS/BDS PPP were 59%, 30%, 31%, and 33%, respectively.

The BeiDou navigation satellite system (BDS-3) has been deployed and provides positioning, navigation, and timing (PNT) services for users all over the world. On the basis of BDS-2 system signals, BDS-3 adds B1C, B2a, B2b, and other signals to realize compatibility and interoperability with other global navigation satellite systems (GNSS). Network real-time kinematic (RTK) technology is an important real-time regional high-precision GNSS positioning technology. Combined with the network RTK high-precision service platform software developed by the author’s research group and the measured data of a provincial continuously operating reference station (CORS) in Hubei, this paper preliminarily evaluates the network RTK service performance under the new signal system of BDS-3. The results show that single BDS-3 adopts the new signal combination (B1C+B2a) and transition signal combination (B1I+B3I) when providing virtual reference station (VRS) services, the RTK fixation rate of the terminal is above 95%, and the horizontal and elevation accuracies are within 1cm and 2 cm, respectively, which meets the requirements of providing high-precision network RTK services by a single BDS-3 system. In addition, the positioning accuracy of BDS-2 is relatively poor, while the accuracy of BDS-3 is better than global positioning systems (GPS) and BDS-2. The combined processing effect of the B1I+B3I transition signal of BDS-2/3 is optimal, the accuracy of E and N directions is better than 0.5 cm, and the accuracy of U direction is better than 1.5 cm. It can be seen from the atmosphere correction accuracy, regional error modeling accuracy, and network RTK terminal positioning accuracy that the service effect of the B1C+B2a combination is slightly better than that of the B1I+B3I combination. When a single BDS-3 constellation provides network RTK services, it is recommended to use the B1C+B2a combination as the main frequency solution, and when the BDS-2/3 constellation provides service, it is recommended to use the B1I+B3I combination as the main frequency solution.

For short baseline real-time kinematic (RTK) positioning, the atmosphere and broadcast ephemeris errors can be usually eliminated in double-differenced (DD) processing for synchronous observations. However, in the case of possible communication latency time, these errors may not be eliminated in DD treatments due to their variations during latency time. In addition, the time variation of these errors may present different characteristics among GPS, GLONASS, BDS, and GALILEO due to different satellite orbit and clock types. In this contribution, the formulas for studying the broadcast orbit and clock offset errors and atmosphere error in asynchronous RTK (ARTK) model is proposed, and comprehensive experimental analysis is performed to numerically show time variations of these errors and their impacts on RTK results from short-baselines among four systems. Compared with synchronous RTK, the degradation of position precision for ARTK can reach a few centimeters, but the accuracy degradation to a different degree by different systems. BDS and Galileo usually outperform GPS and GLONASS in ARTK due to the smaller variation of broadcast ephemeris error. The variation of broadcast orbit error is generally negligible compared with the variation of broadcast clock offset error for GPS, BDS, and Galileo. Specifically, for a month of data, the root mean square (RMS) values for the variation of broadcast ephemeris error over 15 seconds are 11.2, 16.9, 7.3, and 3.0 mm for GPS, GLONASS, BDS, and Galileo, respectively. The variation of ionosphere error for some satellites over 15 seconds can reach a few centimeters during active sessions under a normal ionosphere day. In addition, compared with other systems, BDS ARTK shows an advantage under high ionosphere activity, and such advantage may be attributed to five GEO satellites in the BDS constellation.

The frequency division multiple access (FDMA) strategy used in GLONASS causes inter-frequency phase bias (IFPB) and inter-frequency code bias (IFCB) between receivers from different manufacturers. The existence of IFPB and IFCB significantly increases the difficulties of fixing GLONASS ambiguity and limits the accuracy and reliability of GLONASS positioning. Moreover, the initial value of IFPB and IFCB may be unavailable or unreliable with the increasing number of receivers from different manufacturers in recent years. In this study, a real-time and reliable calibration algorithm of IFPB and IFCB based on multi-GNSS assistance is proposed by providing a fixed solution. Real-time IFPB rate and IFCB can be obtained using this algorithm without the initial IFPB and IFCB. The IFPB rate for all GLONASS satellites and IFCB for each GLONASS satellite are estimated due to different characteristics of IFPB and IFCB. IFPB calibration can be divided into constant and real-time IFPB calibrations to meet the different positioning requirements. Results show that constant IFPB rate has only 2 mm difference from the mean value of real-time IFPB rate. The IFPB rate and IFCB estimated by this algorithm have excellent stability, and the change in reference satellite cannot affect the results of IFPB rate and the stability of IFCB. The centimetre-level positioning results can be obtained using two calibration methods, and the positioning results with real-time calibration method are 10%–20% better than those with the constant calibration method. Under satellite-deprived environments, the improvements of multi-GNSS positioning accuracy with constant inter-frequency bias calibration gradually increase as the satellite cut-off elevation angle increases compared with GPS/BDS, which can reach up to 0·9 cm in the vertical direction.