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.

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.

Common Mode Error (CME) presents a kind of spatially correlated error that is widespread in regional Global Navigation Satellite System (GNSS) networks and should be eliminated during postprocessing of a GNSS position time series. Several spatiotemporal filtering methods have been developed to mitigate the effects of CME. However, such methodologies become inappropriate when missing and noisy data exists. In this research, we introduce a novel spatial filtering algorithm called Weighted Expectation Maximization Principal Component Analysis (WEMPCA) for detecting and removing CME from noisy GNSS position time series with missing values, among which formal errors of daily GNSS solutions are utilized to weight the input data. Compared with traditional PCA and the special case of EMPCA, simulation experiments demonstrate that the new WEMPCA algorithm always has outstanding performance over others. The WEMPCA algorithm was then successfully used to extract the CME from real noisy and missing GNSS position time series in Xinjiang province. Our results show that only the first principal component exhibits significant spatial response, with average values of 70.11%, 66.53%, and 52.45% for North, East, and Up (NEU) components, respectively, indicating that it represents the CME of this region. After removing CME, the canonical correlation coefficients and root mean square error of GNSS residual time series, as well as the amplitudes of power-law noises (PLN), are obviously decreased in all three directions. However, the white noise (WN) amplitudes are found to diminish exclusively in the North and East component, not in the Up components. Moreover, the average velocity differences before and after filtering CME are 0.19 mm/year, 0.03 mm/year, and −0.56 mm/year for the NEU components, respectively, indicating that CME has an influence on the GNSS station velocity estimation. The velocity uncertainty is also reduced by 43.51%, 38.64%, and 40.39% on average for the NEU components, respectively, implying that the velocity estimates are more reliable and accurate after removing CME. Therefore, we conclude that the new WEMPCA approach provides an efficient solution to detect and mitigate CME from the noisy and missing GNSS position time series.

Smartphones, due to their ubiquity, portability, and low cost, have become the primary devices for navigation and location services, while access to the GNSS and MEMS-IMU observations has further stimulated research into seamless road-level positioning using smartphones. However, in urban environments, GNSS observations are susceptible to non-line-of-sight (NLOS) signals, leading to numerous outliers and substantial errors in GNSS/MEMS-IMU integrated positioning. This study proposes a fisheye camera-assisted GNSS/MEMS-IMU sliding window factor graph fusion positioning method. The scheme employs an external fish-eye camera attached to the smartphone for NLOS detection, re-weights line-of-sight (LOS) and NLOS observations using our comprehensive weighting model, and utilizes sliding window marginalization to optimize the GNSS and MEMS-IMU data. The experimental results show that the proposed method enhances 3D positioning accuracy by 46.7%, 50.7%, and 58.4% in the light urban, middle urban, and dense urban kinematic environments, respectively, compared with the conventional factor graph optimization method. Additionally, with respect to the conventional batch optimization method, the proposed method also reduces the total computation time by more than 60%. This work presents a novel approach for enhancing road-level real-time positioning to lane-level real-time positioning, based on low-cost smartphones, thus would be of extensive application potential in the field of smartphone urban seamless positioning.

The site displacement due to ocean tidal loading is regarded as one of the largest uncertainties in precise geodetic positioning measurements, among which the effect of minor ocean tides (MOT), except for the 11 main tidal constituents, are sometimes neglected in routine precise global positioning system (GPS) data processing. We find that MOT can cause large vertical loading displacements with peak-to-peak variations reaching more than 8 mm at coastal/island stations. The impact of MOT on the 24-hour GPS solution is slightly larger than the magnitude of MOT loading itself, with peak-to-peak displacement variation at about 10 mm for the horizontal and 30 mm for the vertical components. We also find that the vertical velocity of all the selected stations in the Southwest Pacific was reduced by more than 10% after considering the MOT effect, while stations with weighted root mean square reduced data account for 62%, 59%, and 36% for the up, east, and north components respectively, in particular for most coastal/island stations. Furthermore, MOT correction could significantly reduce the annual signal of the global stacked east component, the near fortnightly and the long-term periodic signals in the up component. The power of some anomalous harmonics of 1.04 cycle per year is also decreased to some extent. These results further proved the benefits of MOT correction in precise GPS data processing.

Utilizing global positioning system (GPS) to determine the precise kinematic orbits for the twin satellites of the Gravity Recovery and Climate Experiment (GRACE) plays a very important role in the earth’s gravitational and other scientific fields. However, the orbit quality is highly depended on the geometry of observed GPS satellites. In this study, we propose a kinematic orbit determination method for improving the GRACE orbit quality especially when the geometry of observed GPS satellites is weak, where an appropriate random walk clock constraint between adjacent epochs is recommended according to the stability of on-board GPS receiver clocks. GRACE data over one month were adopted in the experimental validation. Results show that the proposed method could improve the root mean square (RMS) by 20–40% in radial component and 5–20% in along and cross components. For those epochs with position dilution of precision (PDOP) larger than 4, the orbits were improved by 50–70% in radial component and 17–50% in along and cross components. Meanwhile, the Allan deviation of clock estimates in the proposed method was much closer to the reported Allan deviation of GRACE on-board oscillator. All the results confirmed the improvement of the proposed method.