scholarly journals A Filtering of Incomplete GNSS Position Time Series with Probabilistic Principal Component Analysis

2018 ◽  
pp. 247-273 ◽  
Author(s):  
Maciej Gruszczynski ◽  
Anna Klos ◽  
Janusz Bogusz
Keyword(s):  
Principal Component Analysis ◽  
Time Series ◽  
Principal Component ◽  
Component Analysis ◽  
Position Time Series ◽  
Probabilistic Principal Component Analysis ◽  
Gnss Position Time Series

scholarly journals Extracting Common Mode Errors of Regional GNSS Position Time Series in the Presence of Missing Data by Variational Bayesian Principal Component Analysis

Sensors ◽  
2020 ◽  
Vol 20 (8) ◽  
pp. 2298 ◽  
Author(s):  
Wudong Li ◽  
Weiping Jiang ◽  
Zhao Li ◽  
Hua Chen ◽  
Qusen Chen ◽  
...  
Keyword(s):  
Principal Component Analysis ◽  
Time Series ◽  
Missing Data ◽  
Principal Component ◽  
Component Analysis ◽  
Common Mode ◽  
Variational Bayesian ◽  
North East ◽  
Position Time Series ◽  
Gnss Position Time Series

Removal of the common mode error (CME) is very important for the investigation of global navigation satellite systems’ (GNSS) error and the estimation of an accurate GNSS velocity field for geodynamic applications. The commonly used spatiotemporal filtering methods normally process the evenly spaced time series without missing data. In this article, we present the variational Bayesian principal component analysis (VBPCA) to estimate and extract CME from the incomplete GNSS position time series. The VBPCA method can naturally handle missing data in the Bayesian framework and utilizes the variational expectation-maximization iterative algorithm to search each principal subspace. Moreover, it could automatically select the optimal number of principal components for data reconstruction and avoid the overfitting problem. To evaluate the performance of the VBPCA algorithm for extracting CME, 44 continuous GNSS stations located in Southern California were selected. Compared to previous approaches, VBPCA could achieve better performance with lower CME relative errors when more missing data exists. Since the first principal component (PC) extracted by VBPCA is remarkably larger than the other components, and its corresponding spatial response presents nearly uniform distribution, we only use the first PC and its eigenvector to reconstruct the CME for each station. After filtering out CME, the interstation correlation coefficients are significantly reduced from 0.43, 0.46, and 0.38 to 0.11, 0.10, and 0.08, for the north, east, and up (NEU) components, respectively. The root mean square (RMS) values of the residual time series and the colored noise amplitudes for the NEU components are also greatly suppressed, with average reductions of 27.11%, 28.15%, and 23.28% for the former, and 49.90%, 54.56%, and 49.75% for the latter. Moreover, the velocity estimates are more reliable and precise after removing CME, with average uncertainty reductions of 51.95%, 57.31%, and 49.92% for the NEU components, respectively. All these results indicate that the VBPCA method is an alternative and efficient way to extract CME from regional GNSS position time series in the presence of missing data. Further work is still required to consider the effect of formal errors on the CME extraction during the VBPCA implementation.

Extracting Common Mode Errors of Regional GNSS Position Time Series in the Presence of Missing Data by Expectation-Maximization Principal Component Analysis

2020 ◽  
Author(s):  
wudong li ◽  
weiping jiang
Keyword(s):  
Principal Component Analysis ◽  
Time Series ◽  
Missing Data ◽  
Expectation Maximization ◽  
Principal Component ◽  
Component Analysis ◽  
Computational Time ◽  
Common Mode ◽  
Position Time Series ◽  
Gnss Position Time Series

<p>Removal of the Common Mode Error (CME) is very important for the investigation of Global Navigation Satellite Systems (GNSS) technique error and the estimation of accurate GNSS velocity field for geodynamic applications. The commonly used spatiotemporal filtering methods cannot accommodate missing data, or they have high computational complexity when dealing with incomplete data. This research presents the Expectation-Maximization Principal Component Analysis (EMPCA) to estimate and extract CME from the incomplete GNSS position time series. The EMPCA method utilizes an Expectation-Maximization iterative algorithm to search each principal subspace, which allows extracting a few eigenvectors and eigenvalues without covariance matrix and eigenvalue decomposition computation. Moreover, it could straightforwardly handle the missing data by Maximum Likelihood Estimation (MLE) at each iteration. To evaluate the performance of the EMPCA algorithm for extracting CME, 44 continuous GNSS stations located in Southern California have been selected here. Compared to previous approaches, EMPCA could achieve better performance using less computational time and exhibit slightly lower CME relative errors when more missing data exists. Since the first Principal Component (PC) extracted by EMPCA is remarkably larger than the other components, and its corresponding spatial response presents nearly uniform distribution, we only use the first PC and its eigenvector to reconstruct the CME for each station. After filtering out CME, the interstation correlation coefficients are significantly reduced from 0.46, 0.49, 0.42 to 0.18, 0.17, 0.13 for the North, East, and Up (NEU) components, respectively. The Root Mean Square (RMS) values of the residual time series and the colored noise amplitudes for the NEU components are also greatly suppressed, with an average reduction of 25.9%, 27.4%, 23.3% for the former, and 49.7%, 53.9%, and 48.9% for the latter. Moreover, the velocity estimates are more reliable and precise after removing CME, with an average uncertainty reduction of 52.3%, 57.5%, and 50.8% for the NEU components, respectively. All these results indicate that the EMPCA method is an alternative and more efficient way to extract CME from regional GNSS position time series in the presence of missing data. Further work is still required to consider the effect of formal errors on the CME extraction during the EMPCA implementation.</p>

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