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.

Global Navigation Satellite Systems (GNSS)-based technologies have become an indispensable part of current structural health monitoring (SHM) systems because of the unique capability of the GNSS technologies to provide accurate real-time displacement information. GNSS equipment with a data sampling rate of up to about 20 Hz has been widely used for this purpose. High-rate GNSS systems (typically up to about 100 Hz) offer additional advantages in structural health monitoring as some highly dynamic civil structures, such as some bridges, require high-rate monitoring data to capture the dynamic behaviors. However, the performance of high-rate GNSS positioning in the context of structural health monitoring is not entirely known, as studies on structural monitoring with high-rate GNSS positioning are very limited, especially considering that some of the satellite systems just reached their full constellations very recently. We carried out a series of experiments with the help of a shaking table to assess the SHM performance of a set of 100 Hz GNSS equipment and three commonly used GNSS positioning techniques, PPP (precise point positioning), PPP-AR (precise point positioning with ambiguity resolution), and RTK (real-time kinematic). We found that the standard deviations of the 100 Hz GNSS displacement solutions derived from PPP, PPP-AR, and RTK techniques were 5.5 mm, 3.6 mm, and 0.8 mm, respectively, when the antenna was in quasi-static motion, and about 9.2 mm, 6.2 mm, and 3.5 mm, respectively, when the antenna was in vibration (up to about 0.7 Hz), under typical urban observational conditions in Hong Kong. We also found that the higher a sampling rate is, the lower the accuracy of a measured displacement series is. On average, the 10 Hz and 100 Hz results are 5.5% and 10.3%, respectively, noisier than the 1 Hz results.

Code Differential Global Positioning System (DGPS) is widely used in satellite navigation and positioning because of its simple algorithm and preferable precision. Multi-Global Navigation Satellite System (GNSS) is expected to enhance the accuracy, reliability and availability of Differential GNSS (DGNSS) positioning. Traditional DGNSS models should set separate clock parameters due to the clock differences between the different systems. Awareness of the Inter-System Bias (ISB) could help to maximise the redundancy of the positioning model, thus improving the performance of multi-GNSS positioning. This paper aims to examine the inter-system bias of GPS/GLONASS/BeiDou (BDS)/Galileo and their benefits in DGNSS positioning. Results show that Differential ISB (DISB) characteristics vary with different receiver types and systems. The size of DISB could reach metre-level and the precision of estimated DISBs can reach approximately several centimetres within tens of epochs. Therefore, a new real-time DGNSS model that accounts for ISB is proposed. After differential ISBs are initialised, positioning with four satellites from arbitrarily the same or different systems can be realised. Moreover, compared with the traditional DGNSS model, the precision of the positioning results with the new model are obviously improved, especially in harsh environments.

For GPS medium-long baseline real-time kinematic (RTK) positioning, the troposphere parameter is introduced along with coordinates, and the model is ill-conditioned due to its strong correlation with the height parameter. For BeiDou Navigation Satellite System (BDS), additional difficulties occur due to its special satellite constellation. In fact, relative zenith troposphere delay (RZTD) derived from high-precision empirical zenith troposphere models can be introduced. Thus, the model strength can be improved, which is also called the RZTD-constrained RTK model. In this contribution, we first analyze the factors affecting the precision of BDS medium-long baseline RTK; thereafter, 15 baselines ranging from 38 km to 167 km in different troposphere conditions are processed to assess the performance of RZTD-constrained RTK. Results show that the troposphere parameter is difficult to distinguish from the height component, even with long time filtering for BDS-only RTK. Due to the lack of variation in geometry for the BDS geostationary Earth orbit satellite, the long convergence time of ambiguity parameters may reduce the height precision of GPS/BDS-combined RTK in the initial period. When the RZTD-constrained model was used in BDS and GPS/BDS-combined situations compared with the traditional RTK, the standard deviation of the height component for the fixed solution was reduced by 52.4% and 34.0%, respectively.

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.