The existence of the common mode error (CME) in the continuous global navigation satellite system (GNSS) coordinate time series affects geophysical studies that use GNSS observations. To understand the potential contributors of CME in GNSS networks in Taiwan and their effect on velocity estimations, we used the principal component analysis (PCA) and independent component analysis (ICA) to filter the vertical coordinate time series from 44 high-quality GNSS stations in Taiwan island in China, with a span of 10 years. The filtering effects have been evaluated and the potential causes of the CME are analyzed. The root-mean-square values decreased by approximately 14% and 17% after spatio-temporal filtering using PCA and ICA, respectively. We then discuss the relationship between the CME sources obtained by ICA and the environmental loads. The results reveal that the independent displacements extracted by ICA correlate with the atmospheric mass loading (ATML) and land water storage mass loading (LWS) of Taiwan in terms of both its amplitude and phase. We then use the white noise plus power law noise model to quantitatively estimate the noise characteristics of the pre- and post-filtered coordinate time series based on the maximum likelihood estimation criterion. The results indicate that spatio-temporal filtering reduces the amplitude of the PL and the periodic terms in the GPS time series.

We explored the driving factors of nonlinear signals in vertical coordinate sequences of stations in a Taiwan global navigation satellite system (GNSS) network, including atmospheric loading (ATML), hydrological loading (HYDL), and non-tidal ocean loading (NTOL) effects. At the same time, we used the finite element analysis software MIDAS to quantify the vertical displacements of different types of monuments due to the thermal expansion effect, including deep drilled braced (DDB) and short drilled braced (SDB). By quantitatively comparing the correction results of GNSS time series with different single mass loading models, we found that there was little difference in the correction of different environmental loading products. We compared different combinations of each loading product to correct the GNSS time series, and finally selected the best combination suitable for Taiwan GNSS network, that is, ATML (GFZ_ECMWF IB) + HYDL (IMLS_MERRA2) + NTOL (IMLS_MPIOM06). We found that the spatial and temporal models of ATML and NTOL are very similar, with non-tidal atmospheric loading and non-tidal ocean loading working together, a pattern that may be related to tropical cyclones. Both models also showed good correction effect on GNSS stations in the western plain of Taiwan, but with limited correction effect in the eastern part of Taiwan. This may be due to the influence of the subtropical monsoon climate in Taiwan and the barrier of the central mountain range, resulting in obvious differences between eastern and western Taiwan. The hydrological loading was found to act in the opposite way to the thermal expansion effect in the temporal domain, indicating that some displacements in hydrological loading may cancel out displacements caused by the thermal expansion effect. This aspect of displacement is not included in the hydrological loading model but should be considered when accurately estimating the temporal and spatial variation of water storage capacity in Taiwan using GNSS observed displacements.

Long-term settlement monitoring of infrastructure built in soft clay areas is of great importance. When using InSAR technology for soft clay settlement monitoring, deformation modeling is a key process. In most InSAR deformation modeling, each component of the total deformation is expressed directly with a fixed functional model in phase functions and assumed to occupy an equal weight. This causes equal weight assumption uncertainty and ignores the actual certain contribution of each phase component related to certain deformational factors. Moreover, the commonly used mathematical empirical models in traditional InSAR are not suitable for describing the nonlinear characteristics of the temporal settlement evolution for soft clay. To address these limitations, we propose an SAR interferometry algorithm, namely, FIPR (FastICA Poisson-curve reciprocal accumulation method), which separates the original InSAR signal based on FastICA to extract each deformation component, and then the models can each extract deformation components and estimate the unknown parameters based on a reciprocal accumulation method. Each independent component and the obtained deformation parameters are used to generate the final deformation time series. Both simulated and real data experiments were designed. The simulated experimental results indicated that the sICA (spatial independent component analysis) separated results were much closer to the original signals than those of the tICA (temporal independent component analysis), with their RMSE lower than 2 mm, and the sICA is thus more highly recommended. Beijing Capital International Airport in China was selected as the study area in the real data experiment. Using 24 high-resolution TerraSAR-X radar satellite images from January 2012 to February 2015, the time-series deformation was obtained, with the maximum cumulative subsidence of 126 mm. The modeling accuracy for the proposed model was estimated as ±2.6 mm, with an improvement of 36.6% compared to the EWA-LM (linear model with equal weight accumulation) algorithm and 16.1% compared to the EWA-PC (Poisson curve with equal weight accumulation) algorithm. The RMSE with external leveling measurements was estimated as ±1.0 mm, with 69.7% improvement compared to EWA-LM and 50% to EWA-PC. This indicated that FIPR can reduce the uncertainty of artificial assumptions in deformation modeling and improve the accuracy of deformation analysis for highways in soft clay areas, providing a reference for road maintenance and management.