{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T16:28:38Z","timestamp":1725467318866},"reference-count":34,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,3,30]],"date-time":"2018-03-30T00:00:00Z","timestamp":1522368000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41731069","41474017"],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents","award":["2017RCJJ074"]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"In the daily operation of regional GNSS (Global Navigation Satellite System) networks, the formal errors of all stations\u2019 coordinate components are calculated. However, spatiotemporal filtering based on traditional Principal Component Analysis (PCA) for regional GNSS position time series does not take these formal errors into account. This paper developed a PCA-based approach to extract Common Mode Error (CME) from the position time series of a regional GNSS station network, where formal errors were applied to construct a weight factor. Because coordinate components with larger errors have smaller weight factors in extracting CME, the performance of our proposed approach was anticipated to be better than the traditional PCA approach. The position time series of 25 stations in the Yunnan Province, China, were analyzed using our approach, as well as the traditional PCA approach. The average errors of the residual time series after removing the CMEs with our approach were 1.30 mm, 1.72 mm, and 4.62 mm for North, East and Up components, and the reductions with respect to those of the original time series were 18.23%, 15.42%, and 18.25%, respectively. If CMEs were removed from the traditional PCA approach, the corresponding average errors were 1.34 mm, 1.81 mm, and 4.84 mm, with reductions of 15.84%, 10.86%, and 14.32%, respectively. Compared to the traditional PCA approach, the average errors of our approach were reduced by about 2.39%, 4.56%, and 3.93% in the North, East and Up components, respectively. Analysis of CME indicated that it mainly contained white and flicker noise. In the synthetic position time series with 500 repeated simulations, the CME extracted by our approach was closer to the true simulated values than those extracted by the traditional PCA approach, regardless of whether local effects were considered or not. Specifically, the mean root mean square (RMS) reduction of our approach, relative to PCA, ranged from 1.35% to 3.93%. Our simulations illustrated that the RMS reductions depended not only on the magnitude, but also the variation of the formal error series, which further highlights the necessity of considering formal errors in spatiotemporal filtering.<\/jats:p>","DOI":"10.3390\/rs10040534","type":"journal-article","created":{"date-parts":[[2018,3,30]],"date-time":"2018-03-30T16:43:48Z","timestamp":1522428228000},"page":"534","source":"Crossref","is-referenced-by-count":25,"title":["The Consideration of Formal Errors in Spatiotemporal Filtering Using Principal Component Analysis for Regional GNSS Position Time Series"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"http:\/\/orcid.org\/0000-0001-9590-5125","authenticated-orcid":false,"given":"Weiwei","family":"Li","sequence":"first","affiliation":[{"name":"College of Geomatics, Shandong University of Science and Technology, Qingdao 266590, China"}]},{"given":"YunZhong","family":"Shen","sequence":"additional","affiliation":[{"name":"College of Surveying and Geo-Informatics, Tongji University, Shanghai 200092, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,3,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Dong, D., Fang, P., Bock, Y., Webb, F., Prawirodirdjo, L., Kedar, S., and Jamason, P. (2006). Spatiotemporal filtering using principal component analysis and Karhunen-Loeve expansion approaches for regional GPS network analysis. J. Geophys. Res., 111.","DOI":"10.1029\/2005JB003806"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1080","DOI":"10.1002\/2015JB012253","article-title":"Extracting the regional common-mode component of GPS station position time series from dense continuous network","volume":"121","author":"Tian","year":"2016","journal-title":"J. Geophys. Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1007\/s00190-016-0973-y","article-title":"Spatiotemporal filtering for regional GPS network in China using independent component analysis","volume":"91","author":"Ming","year":"2017","journal-title":"J. Geod."},{"key":"ref_4","unstructured":"Ji, K.H. (2011). Transient Signal Detection Using GPS Position Time Series. [Ph.D. Thesis, Massachusetts Institute of Technology]."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1038\/nature13681","article-title":"Gradual unlocking of plate boundary controlled initiation of the 2014 Iquisque earthquake","volume":"512","author":"Schurr","year":"2014","journal-title":"Nature"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"8623","DOI":"10.1002\/2015JB012503","article-title":"Hunt for slow slip along the Sumatran subduction zone in a decade of continuous GPS data","volume":"120","author":"Feng","year":"2015","journal-title":"J. Geophys. Res."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1007\/s00190-016-0886-9","article-title":"Non-negative least-squares variance component estimation with application to GPS time series","volume":"90","year":"2016","journal-title":"J. Geod."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.epsl.2015.12.038","article-title":"Vertical crustal movement around southeastern Tibetan Plateau constrained by GPS and GRACE data","volume":"437","author":"Hao","year":"2016","journal-title":"Earth Planet. Sci. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.jog.2017.01.004","article-title":"Review of current GPS methodologies for producing accurate time series and their error sources","volume":"106","author":"He","year":"2017","journal-title":"J. Geodyn."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2797","DOI":"10.1029\/1998JB900033","article-title":"Noise in GPS coordinate time series","volume":"104","author":"Mao","year":"1999","journal-title":"J. Geophys. Res."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Williams, S. (2004). Error analysis of continuous GPS position time series. J. Geophys. Res., 109.","DOI":"10.1029\/2003JB002741"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Amiri-Simkooei, A.R., Tiberius, C.C.J.M., and Teunissen, P.J.G. (2007). Assessment of noise in GPS coordinate time series: Methodology and results. J. Geophys. Res., 112.","DOI":"10.1029\/2006JB004913"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Shen, Y., and Li, W. (2014). Spatiotemporal signal and noise analysis of GPS position time series of the permanent stations in China. Earth on the Edge: Science for a Sustainable Planet, International Association of Geodesy Symposia Springer.","DOI":"10.1007\/978-3-642-37222-3_30"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"6003","DOI":"10.1002\/2013JB010102","article-title":"Vertical GPS ground motion rates in the Euro-Mediterranean region: New evidence of velocity gradients at different spatial scales along the Nubia-Eurasia plate","volume":"118","author":"Serpelloni","year":"2013","journal-title":"J. Geophys. Res."},{"key":"ref_15","first-page":"149","article-title":"Velocity estimation of GPS base stations considering the coloured noises","volume":"6","author":"Li","year":"2012","journal-title":"J. Appl. Geod."},{"key":"ref_16","first-page":"291","article-title":"Orthogonal transformation in extracting of common mode error from continuous GPS network","volume":"13","author":"Gruszczynski","year":"2016","journal-title":"Acta Geodyn. Geomater."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"18057","DOI":"10.1029\/97JB01378","article-title":"Southern California permanent GPS geodetic array: Spatial filtering of daily positions for estimating coseismic and postseismic displacements induced by the 1992 Landers earthquake","volume":"102","author":"Wdowinski","year":"1997","journal-title":"J. Geophys. Res."},{"key":"ref_18","unstructured":"Nikolaidis, R. (2002). Observation of Geodetic and Seismic Deformation with the Global Positioning System. [Ph.D. Thesis, University of California]."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1515\/geo-2015-0021","article-title":"Spatio-temporal filtering for determination of common mode error in regional GNSS networks","volume":"7","author":"Bogusz","year":"2015","journal-title":"Open Geosci."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"M\u00e1rquez-Az\u00faa, B., and DeMets, C. (2003). Crustal velocity field of Mexico from continuous GPS measurements, 1993 to June 2001: Implications for the neotectonics of Mexico. J. Geophys. Res., 108.","DOI":"10.1029\/2002JB002241"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1316","DOI":"10.1016\/j.asr.2014.12.016","article-title":"Accuracy enhancement of GPS time series using principal component analysis and block spatial filtering","volume":"55","author":"He","year":"2015","journal-title":"Adv. Space Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1175\/1520-0442(2001)014<0853:AOICDE>2.0.CO;2","article-title":"Analysis of incomplete climate: Estimation of mean values and covariance matrices and imputation of missing values","volume":"14","author":"Schneider","year":"2001","journal-title":"J. Clim."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Liu, N., Dai, W., Santerre, R., and Kuang, C. (2018). A MATLAB-based Kriged Kalman filter software for interpolating missing data in GNSS coordinate time series. GPS Solut., 22.","DOI":"10.1007\/s10291-017-0689-3"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00190-013-0663-y","article-title":"Spatiotemporal filtering of regional GNSS network\u2019s position time series with missing data using principal component analysis","volume":"88","author":"Shen","year":"2014","journal-title":"J. Geod."},{"key":"ref_25","unstructured":"Jolliffe, I.T. (2002). Principal Component Analysis, Springer. [2nd ed.]."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1007\/s40328-015-0100-1","article-title":"Weighted spatiotemporal filtering using principal component analysis for analyzing regional GNSS position time series","volume":"50","author":"Li","year":"2015","journal-title":"Acta Geod. Geophys."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Langbein, J., and Bock, Y. (2004). High-rate real-time GPS network at Parkfield: Utility for detecting fault slip and seismic displacements. Geophys. Res. Lett., 31.","DOI":"10.1029\/2003GL019408"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1093\/gji\/ggv190","article-title":"Geodetic secular velocity errors due to interannual surface loading deformation","volume":"202","year":"2015","journal-title":"Geophys. J. Int."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1007\/s10291-015-0478-9","article-title":"On the significance of periodic signal in noise analysis of GPS station coordinate time series","volume":"20","author":"Bogusz","year":"2016","journal-title":"GPS Solut."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.geog.2017.01.004","article-title":"Study of the effects on GPS coordinate time series caused by higher-order ionospheric corrections calculated using the DIPOLE model","volume":"8","author":"Deng","year":"2017","journal-title":"Geod. Geodyn."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Klos, A., Bogusz, J., Figurski, M., and Gruszczynski, M. (2015). Error analysis for European IGS stations. Stud. Geophys. Geod., 60.","DOI":"10.1007\/s11200-015-0828-7"},{"key":"ref_32","unstructured":"Bos, M.S., and Fernandes, R.M.S. (2016). Hector User Manual 1.6, University of Beira Interior."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/s00190-012-0605-0","article-title":"Fast error analysis of continuous GNSS observations with missing data","volume":"87","author":"Bos","year":"2013","journal-title":"J. Geod."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1002\/2013EO450001","article-title":"Generic mapping tools: Improved version released","volume":"94","author":"Wessel","year":"2013","journal-title":"EOS Trans. AGU"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/4\/534\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,10]],"date-time":"2024-06-10T08:17:06Z","timestamp":1718007426000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/10\/4\/534"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,30]]},"references-count":34,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,4]]}},"alternative-id":["rs10040534"],"URL":"https:\/\/doi.org\/10.3390\/rs10040534","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,30]]}}}