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.

Precise Point Positioning (PPP) has become a very hot topic in GNSS research and applications. However, it usually takes about several tens of minutes in order to obtain positions with better than 10 cm accuracy. This prevents PPP from being widely used in real-time kinematic positioning services, therefore, a large effort has been made to tackle the convergence problem. One of the recent approaches is the ionospheric delay constrained precise point positioning (IC-PPP) that uses the spatial and temporal characteristics of ionospheric delays and also delays from an a priori model. In this paper, the impact of the quality of ionospheric models on the convergence of IC-PPP is evaluated using the IGS global ionospheric map (GIM) updated every two hours and a regional satellite-specific correction model. Furthermore, the effect of the receiver differential code bias (DCB) is investigated by comparing the convergence time for IC-PPP with and without estimation of the DCB parameter. From the result of processing a large amount of data, on the one hand, the quality of the a priori ionosphere delays plays a very important role in IC-PPP convergence. Generally, regional dense GNSS networks can provide more precise ionosphere delays than GIM and can consequently reduce the convergence time. On the other hand, ignoring the receiver DCB may considerably extend its convergence, and the larger the DCB, the longer the convergence time. Estimating receiver DCB in IC-PPP is a proper way to overcome this problem. Therefore, current IC-PPP should be enhanced by estimating receiver DCB and employing regional satellite-specific ionospheric correction models in order to speed up its convergence for more practical applications.

The Low Earth Orbit (LEO) satellites can be used to effectively speed up Precise Point Positioning (PPP) convergence. In this study, 180 LEO satellites with a global distribution are simulated to evaluate their contribution to the PPP convergence. LEO satellites can give more redundant observations and improve satellite geometric distributions, particularly for a single Global Navigation Satellite System (GNSS). The convergence speed of the PPP float solution using the Global Positioning System (GPS, G) or BeiDou Navigation Satellite System (BDS, C) single system as well as the G/C/Galileo navigation satellite system (Galileo, E)/GLObal NAvigation Satellite System (GLONASS, R) combined system with LEO satellites added is improved by 90.0%, 91.0%, and 90.7%, respectively, with respect to the system without LEO satellites added. We introduced LEO observations to assist GNSS in PPP-AR (Ambiguity Resolution) and PPP-RTK (Real Time Kinematic). The success fix rate of a single system is significantly improved, and the Time-To-First-Fix (TTFF) of G and G/C/E is reduced by 86.4% and 82.8%, respectively, for the PPP-AR solution. We analyzed the positioning performance of LEO satellite assisted G/C/E PPP-RTK in the reference networks of different scales, namely different atmospheric delay interpolation accuracies. The success fix rate of the G/C/E combined system is improved from 86.8 to 94.9%, and the TTFF is reduced by 36.8%, with the addition of LEO satellites in the 57 km reference network. In the 110 km reference network, the success fix rate of the G/C/E combined system is improved from 64.0 to 88.6%, and the TTFF is reduced by 32.1%. GNSS PPP-RTK with adding the LEO satellites in the reference networks of different scales shows obvious improvement because the atmospheric correlation decreases with increasing distance from the reference networks.

The volatility of the cumulative displacement of landslides is related to the influence of external factors. To improve the prediction of nonlinear changes in landslide displacement caused by external influences, a new combined forecasting model of landslide displacement has been proposed. Variational modal decomposition (VMD) was used to obtain the trend and fluctuation sequences of the original sequence of landslide displacement. First, we established a stacked long short time memory (LSTM) network model and introduced rainfall and reservoir water levels as influencing factors to predict the fluctuation sequence; next, we used a threshold autoregressive (TAR) model to predict the trend sequence, following which the trend and fluctuation prediction sequence were superimposed to obtain the cumulative predicted displacement of the landslide. Finally, the VMD-stacked LSTM-TAR combination model based on the variational modal decomposition, stacked long short time memory network, and a threshold autoregressive model was built. Taking the landslide of Baishuihe in the Three Gorges Reservoir area as an example, through comparison with the prediction results of the VMD-recurrent neural network-TAR, VMD-back propagation neural network-TAR, and VMD-LSTM-TAR, the proposed combined prediction model was noted to have high accuracy, and it provided a novel approach for the prediction of volatile landslide displacement.