GNSS time-series prediction plays an important role in the monitoring of crustal plate movement, and dam or bridge deformation, and the maintenance of global or regional coordinate frames. Deep learning is a state-of-the-art approach for extracting high-level abstract features from big data without any prior knowledge. Moreover, long short-term memory (LSTM) networks are a form of recurrent neural networks that have significant potential for processing time series. In this study, a novel prediction framework was proposed by combining a multi-scale sliding window (MSSW) with LSTM. Specifically, MSSW was applied for data preprocessing to effectively extract the feature relationship at different scales and simultaneously mine the deep characteristics of the dataset. Then, multiple LSTM neural networks were used to predict and obtain the final result by weighting. To verify the performance of MSSW-LSTM, 1000 daily solutions of the XJSS station in the Up component were selected for prediction experiments. Compared with the traditional LSTM method, our results of three groups of controlled experiments showed that the RMSE value was reduced by 2.1%, 23.7%, and 20.1%, and MAE was decreased by 1.6%, 21.1%, and 22.2%, respectively. Our results showed that the MSSW-LSTM algorithm can achieve higher prediction accuracy and smaller error, and can be applied to GNSS time-series prediction.

The Global Positioning System (GPS) records monsoonal precipitable water vapor (PWV) and vertical crustal displacement (VCD) due to hydrological loading, and can thus be applied jointly to diagnose meteorological and hydrological droughts. We have analyzed the PWV and VCD observations during 2007.0–2015.0 at 26 continuous GPS stations located in Yunnan province, China. We also obtained equivalent water height (EWH) derived from the Gravity Recovery And Climate Experiment (GRACE) and precipitation at these stations with the same period. Then, we quantified the annual variations of PWV, precipitation, EWH and VCD and provided empirical relationships between them. We found that GPS-derived PWV and VCD (positive means downward movement) are in phase with precipitation and GRACE-derived EWH, respectively. The annual signals of VCD and PWV show linearly correlated amplitudes and a two-month phase lag. Furthermore, the results indicate that PWV and VCD anomalies can also be used to explore drought, such as the heavy drought during winter/spring 2010. Our analysis results verify the capability of GPS to monitor monsoon variations and drought in Yunnan and show that a more comprehensive understanding of the characteristics of regional monsoon and drought can be achieved by integrating GPS-derived PWV and VCD with precipitation and GRACE-derived EWH.

Global navigation satellite system (GNSS) site coordinate time series provides essential data for geodynamic and geophysical studies, realisation of a regional or global geodetic reference frames, and crustal deformation research. The coordinate time series has been conventionally modelled by least squares (LS) fitting with harmonic functions, alongside many other analysis methods. As a key limitation, the traditional modelling approaches simply use the functions of time variable, despite good knowledge of various underlying physical mechanisms responsible for the site displacements. This paper examines the use of machine learning (ML) models to reflect the effects or residential effects of physical variables related to Sun and the Moon ephemerides, polar motion, temperature, atmospheric pressure, and hydrology on the site displacements. To form the ML problem, these variables are constructed as the input vector of each ML training sample, while the vertical displacement of a GNSS site is regarded as the output value. In the evaluation experiments, three ML approaches, namely the gradient boosting decision tree (GBDT) approach, long short-term memory (LSTM) approach, and support vector machine (SVM) approach, are introduced and evaluated with the time series datasets collected from 9 GNSS sites over the period of 13 years. The results indicate that all three approaches achieve similar fitting precision in the range of 3–5 mm in the vertical displacement component, which is an improvement in over 30% with respect to the traditional LS fitting precision in the range of 4–7 mm. The prediction of the vertical time series with the three ML approaches shows the precision in the range of 4–7 mm over the future 24- month period. The results also indicate the relative importance of different physical features causing the displacements of each site. Overall, ML approaches demonstrate better performance and effectiveness in modelling and prediction of GNSS time series, thus impacting maintenance of geodetic reference frames, geodynamics, geophysics, and crustal deformation analysis.