PMID- 32316478
OWN - NLM
STAT- PubMed-not-MEDLINE
LR  - 20200523
IS  - 1424-8220 (Electronic)
IS  - 1424-8220 (Linking)
VI  - 20
IP  - 8
DP  - 2020 Apr 17
TI  - Extracting Common Mode Errors of Regional GNSS Position Time Series in the 
      Presence of Missing Data by Variational Bayesian Principal Component Analysis.
LID - 10.3390/s20082298 [doi]
LID - 2298
AB  - 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.
FAU - Li, Wudong
AU  - Li W
AD  - School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, 
      China.
FAU - Jiang, Weiping
AU  - Jiang W
AD  - School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, 
      China.
AD  - GNSS Research Center, Wuhan University, Wuhan 430079, China.
FAU - Li, Zhao
AU  - Li Z
AD  - Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic 
      University, 181 Chatham Road South, Hung Hom, Kowloon 999077, Hong Kong, China.
FAU - Chen, Hua
AU  - Chen H
AD  - School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, 
      China.
FAU - Chen, Qusen
AU  - Chen Q
AD  - GNSS Research Center, Wuhan University, Wuhan 430079, China.
FAU - Wang, Jian
AU  - Wang J
AD  - School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, 
      China.
FAU - Zhu, Guangbin
AU  - Zhu G
AD  - Key Laboratory of Earth Observation and Geospatial Information Science, Beijing 
      100039, China.
AD  - Land Satellite Remote Sensing Application Center, Beijing 100048, China.
LA  - eng
GR  - 41525014/the National Science Foundation for Distinguished Young Scholars of 
      China/
GR  - 41721003/the Natural Science Innovation Group Foundation of China/
GR  - 2018YFC1503600/the National Key Research and Development Program of China/
GR  - 2018AAA066/the Major Technology Innovation Project of Hubei Province of China/
GR  - 201907/Key Laboratory of Surveying and Mapping Science and Geospatial Information 
      Technology of Ministry of Natural Resources/
PT  - Journal Article
DEP - 20200417
PL  - Switzerland
TA  - Sensors (Basel)
JT  - Sensors (Basel, Switzerland)
JID - 101204366
SB  - IM
PMC - PMC7219079
OTO - NOTNLM
OT  - GNSS position time series
OT  - common mode error
OT  - missing data
OT  - variational Bayesian principal component analysis
COIS- The authors declare no conflicts of interest.
EDAT- 2020/04/23 06:00
MHDA- 2020/04/23 06:01
PMCR- 2020/04/01
CRDT- 2020/04/23 06:00
PHST- 2020/02/25 00:00 [received]
PHST- 2020/04/08 00:00 [revised]
PHST- 2020/04/08 00:00 [accepted]
PHST- 2020/04/23 06:00 [entrez]
PHST- 2020/04/23 06:00 [pubmed]
PHST- 2020/04/23 06:01 [medline]
PHST- 2020/04/01 00:00 [pmc-release]
AID - s20082298 [pii]
AID - sensors-20-02298 [pii]
AID - 10.3390/s20082298 [doi]
PST - epublish
SO  - Sensors (Basel). 2020 Apr 17;20(8):2298. doi: 10.3390/s20082298.