GNSS time series prediction plays a significant role in monitoring crustal plate motion, landslide detection, and the maintenance of the global coordinate framework. Long short-term memory (LSTM) is a deep learning model that has been widely applied in the field of high-precision time series prediction and is often combined with Variational Mode Decomposition (VMD) to form the VMD-LSTM hybrid model. To further improve the prediction accuracy of the VMD-LSTM model, this paper proposes a dual variational modal decomposition long short-term memory (DVMD-LSTM) model to effectively handle noise in GNSS time series prediction. This model extracts fluctuation features from the residual terms obtained after VMD decomposition to reduce the prediction errors associated with residual terms in the VMD-LSTM model. Daily E, N, and U coordinate data recorded at multiple GNSS stations between 2000 and 2022 were used to validate the performance of the proposed DVMD-LSTM model. The experimental results demonstrate that, compared to the VMD-LSTM model, the DVMD-LSTM model achieves significant improvements in prediction performance across all measurement stations. The average RMSE is reduced by 9.86% and the average MAE is reduced by 9.44%; moreover, the average R2 increased by 17.97%. Furthermore, the average accuracy of the optimal noise model for the predicted results is improved by 36.50%, and the average velocity accuracy of the predicted results is enhanced by 33.02%. These findings collectively attest to the superior predictive capabilities of the DVMD-LSTM model, thereby demonstrating the reliability of the predicted results.

The global navigation satellite system (GNSS) has seen tremendous advances in measurement precision and accuracy, and it allows researchers to perform geodynamics and geophysics studies through the analysis of GNSS time series. Moreover, GNSS time series not only contain geophysical signals, but also unmodeled errors and other nuisance parameters, which affect the performance in the estimation of site coordinates and related parameters. As the number of globally distributed GNSS reference stations increases, GNSS time series analysis software should be developed with more flexible format support, better human–machine interaction, and with powerful noise reduction analysis. To meet this requirement, a new software named GNSS time series noise reduction software (GNSS-TS-NRS) was written in MATLAB and was developed. GNSS-TS-NRS allows users to perform noise reduction analysis and spatial filtering on common mode errors and to visualize GNSS position time series. The functions’ related theoretical background of GNSS-TS-NRS were introduced. Firstly, we showed the theoretical background algorithms of the noise reduction analysis (empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD)). We also developed three improved algorithms based on EMD for noise reduction, and the results of the test example showed our proposed methods with better effect. Secondly, the spatial filtering model supported five algorithms on a separate common model error: The stacking filter method, weighted stacking filter method, correlation weighted superposition filtering method, distance weighted filtering method, and principal component analysis, as well as with batch processing. Finally, the developed software also enabled other functions, including outlier detection, correlation coefficient calculation, spectrum analysis, and distribution estimation. The main goal of the manuscript is to share the software with the scientific community to introduce new users to the GNSS time series noise reduction and application.

Extreme loadings, a hostile environment and dangerous operation lead to the unsafe state of bridges under construction, especially large-span bridges. Global Navigation Satellite Systems (GNSS) tend to be the best choice for real-time deformation monitoring due to the significant advantage of automation, continuation, all-weather operation and high precision. Unfortunately, the traditional geodetic GNSS instrument with its high price and large volume is limited in its applications. Hence, we design and develop low-cost GNSS equipment by simplifying the monitoring module. The performance of the proposed solution is evaluated through an experimental dynamic scenario, proving its ability to track abrupt deformation down to 3–5 mm. We take Chongqing Guojiatuo Suspension Bridge in China as a case study. We build a real-time low-cost GNSS monitoring cloud platform. The low-cost bridge GNSS monitoring stations are located at the top of the south and north towers, midspan upstream and downstream respectively and the reference station is located in the stable zone 400 m away from the bridge management buildings. We conducted a detailed experimental assessment of low-cost GNSS on 5 April and a real-time deformation detection experiment of the towers and main cables during the dynamic cable saddle pushing process on 26 February 2022. In the static experiment, the standard deviation of the residual using the multi-GNSS solution is 2 mm in the horizontal direction and 5 mm in the vertical direction. The multi-GNSS solution significantly outperforms the BDS/GPS single system. The dynamic experiment shows that, compared with the movement measured by the robotic total station, the horizontal error of the south tower and north tower measured by low-cost GNSS is below 0.005 m and 0.008 m respectively. This study highlights the potential of low-cost GNSS solutions for Structural Health Monitoring (SHM) applications.

The extraction of landslide deformation using terrestrial laser scanning (TLS) has many important applications. The landslide deformation can be extracted based on a digital terrain model (DTM). However, such methods usually suffer from the ill-posed problem of a multiplicative error model as illustrated in previous studies. Moreover, the edge drift of commonly used spherical targets for point cloud registration (PCR) is ignored in the existing method, which will result in the unstable precision of the PCR. In response to these problems, we propose a method for extracting landslide deformations from TLS data. To archive the PCR of different period point clouds, a new triangular pyramid target is designed to eliminate the edge drift. If a fixed target is inconvenient, we also propose a PCR method based on total station orientation. Then, the use of the Tikhonov regularization method to derive the weighted least squares regularization solution is presented. Finally, the landslide deformation is extracted by DTM deference. The experiments are conducted on two datasets with more than 1.5 billion points. The first dataset takes Lashagou NO. 3 landslide in Gansu Province, China, as the research object; the point cloud data were collected on 26 February 2021 and 3 May 2021. The registration accuracy was 0.003 m based on the permanent triangular pyramid target and 0.005 m based on the total station orientation. The landslide deforms within 3 cm due to the ablation of the frozen soil. The second dataset is TLS data from the Lihua landslide in Chongqing, China, collected on 20 April 2021 and 1 May 2021. The overall deformation of the Lihua landslide is small, with a maximum value of 0.011 m. The result shows that the proposed method achieves a better performance than previous sphere-based registration and that the weighted least square regularization iterative solution can effectively reduce the ill-condition of the model.

GNSS time series prediction plays a significant role in monitoring crustal plate motion, landslide detection, and maintenance of the global coordinate framework. Long Short-Term Memory (LSTM), a deep learning model has been widely applied in the field of high-precision time series prediction especially when combined with Variational Mode Decomposition (VMD) to form the VMD-LSTM hybrid model. To further improve the prediction accuracy of the VMD-LSTM model, this paper proposes a dual variational modal decomposition long short-term memory (DVMD-LSTM) model to effectively handle the noise in GNSS time series prediction. This model extracts fluctuation features from the residual terms obtained after VMD decomposition to reduce the prediction errors associated with residual terms in the VMD-LSTM model. Daily E, N, and U coordinate data recorded at multiple GNSS stations between 2000 and 2022 are used to validate the performance of the proposed DVMD-LSTM model. The experimental results demonstrate that compared to the VMD-LSTM model, the DVMD-LSTM model achieves significant improvements in prediction performance across all measurement stations. The average RMSE is reduced by 9.86%, and the average MAE is reduced by 9.44%. Furthermore, the average accuracy of the optimal noise model for the predicted results is improved by 36.50%, and the average speed accuracy of the predicted results is enhanced by 33.02%. These findings collectively attest to the superior predictive capabilities of the DVMD-LSTM model, thereby enhancing the reliability of the predicted results.

Accurate noise model identification for GNSS time series is crucial for obtaining a reliable GNSS velocity field and its uncertainty for various studies in geodynamics and geodesy. Here, by comprehensively considering time span and missing data effect on the noise model of GNSS time series, we used four combined noise models to analyze the duration of the time series (ranging from 2 to 24 years) and the data gap (between 2% and 30%) effects on noise model selection and velocity estimation at 72 GNSS stations spanning from 1992 to 2022 in global region together with simulated data. Our results show that the selected noise model have better convergence when GNSS time series is getting longer. With longer time series, the GNSS velocity uncertainty estimation with different data gaps is more homogenous to a certain order of magnitude. When the GNSS time series length is less than 8 years, it shows that the flicker noise and random walk noise and white noise (FNRWWN), flicker noise and white noise (FNWN), and power law noise and white noise (PLWN) models are wrongly estimated as a Gauss–Markov and white noise (GGMWN) model, which can affect the accuracy of GNSS velocity estimated from GNSS time series. When the GNSS time series length is more than 12 years, the RW noise components are most likely to be detected. As the duration increases, the impact of RW on velocity uncertainty decreases. Finally, we show that the selection of the stochastic noise model and velocity estimation are reliable for a time series with a minimum duration of 12 years.