The carrier-phase (CP) technique based on the Global Navigation Satellite System (GNSS) has proved to be a useful spatial tool for remote and precise time transfer. In order to improve the robustness and stability of the time transfer solution for a time link, a new CP approach based on a combination of GPS, BeiDou (BDS), and Galileo satellite systems is proposed in this study. The mathematical model for the obtained unique time transfer solution is discussed. Three GNSS stations that can track GPS, BeiDou, and Galileo satellites were used, and two time links are established to assess the performance of the approach. Multi-GNSS time transfer outperforms single GNSS by increasing the number of available satellites and improving the time dilution of precision. For the long time link, with a geodetic distance of 7537.5 km, the RMS value of the combined multi-system solution improves by 18.8%, 59.4%, and 35.0% compared to GPS-only, BDS-only, and Galileo-only, respectively. The average frequency stability improves by 12.9%, 62.3%, and 36.0%, respectively. For the short time link, with a geodetic distance of 4.7 m, the improvement after combining the three GNSSs is 6.7% for GPS-only, 52.6% for BDS-only, and 38.2% for Galileo-only.

The Global Navigation Satellite System (GNSS) is currently one of the important tools for landslide monitoring and early warning. However, the majority of GNSS devices are installed in mountainous areas and a variety of vegetation. These harsh environments lead to defective signals at high elevation angles, rendering real-time successive and reliable positioning results for monitoring difficult. In this study, an environmental model derived from signal-to-noise ratio (SNR) is proposed to enhance the precision and convergence time of positioning in harsh environments. A series of experiments are conducted on weighting and ambiguity-fixed models to evaluate performance. The results indicate that the proposed SNR-dependent environment model could lead to a significant improvement in precision and convergence time; with an obtained root mean squared result on the millimeter level, a convergence time of a few seconds, and utilization which could reach 100%, for continuous and reliable positioning results. These results indicate that the proposed SNR-dependent environment model enhances the performance of GNSS monitoring and early warning to provide continuous and reliable positioning results in real-time.

Inter-system bias (ISB) is important for the fusion of multiple global navigation satellite system data. They should be estimated or corrected for precise position, navigation, and timing solutions. In this study, ISB estimation models are developed for the global positioning system, GLONASS, BeiDou Navigation Satellite System, and Galileo systems. Six stations, with three different types of receivers, are used to analyze the ISB characteristics of different systems. A pair of time-link stations, which have a short baseline and are connected to a common external time frequency from the laboratory, are used to analyze the performance of three different estimation strategies (epoch-wise variable, 30 min piece-wise constant, and daily constant). These stations are also used to evaluate the influence of ISB constrains on the precise estimation of time transfer, coordinates, and the troposphere. The results illustrate: (a) ISBs variation exists between different systems, and the same types of receivers also exhibit large differences between the different stations due to the receiver hardware delay; (b) the precision of the different measurements and their related errors, the estimated ISBs that exhibit large differences between pseudorange and carrier phase observations, and the different ISB estimation strategies can also cause differences in the final fusion results; and (c) using the estimated ISB as constraints can improve the precise estimation of time transfer, coordinates, and the troposphere in the real-time solution mode.

The combination of multiple Global Navigation Satellite Systems (GNSSs) may improve the performance of time and frequency transfers by increasing the number of available satellites and improving the time dilution of precision. However, the receiver clock estimation is easily affected by the inappropriate weight of multi-GNSSs due to the different characteristics of individual GNSS signals as well as the outliers from observations. Thus, we utilised a robust Helmert variance component estimation (RVCE) approach to determine the appropriate weights of different GNSS observations, and to control for the influence of outliers in these observation in multi-GNSS time and frequency transfer. In order to validate the effectiveness of this approach, four time links were employed. Compared to traditional solutions, the mean improvement of smoothed residuals is 3.43% using the RVCE approach. With respect to the frequency stability of the time links, the RVCE solution outperforms the traditional solution, particularly in the short-term, and the mean improvement is markedly high at 14.89%.

The satellite-induced code bias variation of geostationary satellite orbit satellites and medium earth orbit satellites of the second-generation BeiDou Navigation Satellite System (BDS-2) exceeds 1 m, which severely affects the accuracy and stability of the ambiguity resolution and high-precision positioning. With the development of the third-generation BDS (BDS-3) with a new system design and new technology, analysis of the satellite-induced code variation characteristics of BDS-3 has become increasingly important. At present, many scholars have explored the satellite-induced code bias of BDS-3, but most of them focus on BDS-3 experimental satellites via normal geodetic antenna. Compared to normal geodetic antenna, the 40-m dish antenna from the National Time Service Center can accurately detect satellite-induced code variations with low noise and high gain. Thus, observational data from fifteen BDS-3 medium earth orbit satellites are collected with the B1I/B2b/B3I/B1C/B2a frequency bands on the day of year (DOY) 199–206 in 2019, the PRN numbers of which are C19/C20/C21/C22/C23/C24/C25/C26/C27/C28/C30/C32/C33 /C35/C37, via the 40 m dish antenna to analyze the code bias variation characteristics. The results show that the obvious satellite-induced elevation‑dependent code bias variations exist in the B1I/B2b/B3I/B1C/B2a frequency bands of C28, compared with other satellites. Similarly, the multipath (MP) combination of B3I has an obvious elevation‑dependent variation within a range of 0.1 m for C21/C24/C27/C28/C37 and elevation‑dependent variation of the B2a and B2b frequency bands also exists in most satellites with a range of 0.1 m. However, the MP combination values of some satellites are asymmetric with respect to elevation, which is different from BDS-2 satellites and especially obvious for BDS-3 satellites B1I and BIC frequency bands with elevation‑dependent variations of 0.2 m, indicating that the code bias variation is not uniquely related to elevation, especially for the B1I/BIC frequency bands. What’s more, the satellite-induced code bias variation of the BDS-3 satellites is greatly reduced compared with that of the BDS-2 satellites. In addition, the similar code bias variation appears at the Xia1 station with a normal geodetic antenna of B1I/B1C/B3I/B2a/B2b of C21, B3I/B2a/B2b of C24 and B2b of C28 among B1I/B1C/B3I/B2a/B2b of C21/C24/C27/C28/C37. The influence of the BDS-3 satellite-induced elevation‑dependent code bias on precision positioning and ambiguity fixing is worth further study using different antennas or receivers.

Several global navigation satellite systems (GNSS) broadcast overlapping frequencies to enhance interoperability, allowing tight integration with only one reference satellite for every system with the same frequency. The key to realizing tight integration is estimating and utilizing differential intersystem biases, which allows the integer characteristic of the differenced ambiguity of two satellites from different systems to be retrieved. In this study, a detailed algorithm flow of a tight integration kinematic uncalibrated phase delay (UPD)-based PPP ambiguity resolution (PPP-AR) method, which includes multiple parts, is introduced. Subsequently, PPP-AR numerical experiments were conducted in a high-shade observation environment to determine the performance. In comparison with traditional methods, our results indicate that the average success fix rate improves from 83% to 100% after using the tight integration method in an environment where only three satellites are observed for each system. Moreover, for fewer than nine satellites, the tight integration method can still consistently maintain a fixed state. However, for comparison, the traditional loose integration method could no longer be implemented.