Abstract
Independent component analysis (ICA) is one of the most effective approaches in extracting independent signals from a global navigation satellite system (GNSS) regional station network. However, ICA requires the involved time series to be complete, thereby the missing data of incomplete time series should be interpolated beforehand. In this contribution, a modified ICA is proposed, by which the missing data are first recovered based on the reversible property between the original time series and decomposed principal components, then the complete time series are further processed with FastICA. To evaluate the performance of the modified ICA for extracting independent components, 24 regional GNSS network stations located in North China from 2011 to 2019 were selected. After the trend, annual and semiannual terms were removed from the GNSS time series, the first two independent components captured 17.42, 18.44 and 17.38% of the total energy for the North, East and Up coordinate components, more than those derived by the iterative ICA that accounted for 16.21%, 17.72% and 16.93%, respectively. Therefore, modified ICA can extract more independent signals than iterative ICA. Subsequently, selecting the 7 stations with less missing data from the network, we repeatedly process the time series after randomly deleting parts of the data and compute the root mean square error (RMSE) from the differences of reconstructed signals before and after deleting data. All RMSEs of modified ICA are smaller than those of iterative ICA, indicating that modified ICA can extract more exact signals than iterative ICA.
Highlights
principal component analysis (PCA) is one of the data-driven multivariate approaches based on second-order statistics and isolates the underlying sources without any prior knowledge [7], which implicitly assumes that a global navigation satellite system (GNSS) time series is polluted only by multivariate Gaussian noise
Since PCA decomposition is based on the maximization of the variance of decomposed components, PCA works efficiently if only a single source exists in the GNSS time series
We rearrange all independent components in descending order according to their contribution ratios, the most significant signals of the time series can be represented by the first several distinctive independent components, which are expressed as: d
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The other spatiotemporal signals are more effectively extracted and analyzed with some classic signal analysis methods, such as wavelet analysis (WA) [8,9,10], Kalman filter (KF) [11,12], empirical orthogonal function (EOF) [13], singular spectrum analysis (SSA) [14,15], and principal component analysis (PCA) [16,17,18,19] Among these methods, PCA is one of the data-driven multivariate approaches based on second-order statistics (variance and covariance) and isolates the underlying sources without any prior knowledge [7], which implicitly assumes that a GNSS time series is polluted only by multivariate Gaussian noise.
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