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Interpolation of the GNSS position time series is necessary because missing data will produce inaccurate conclusions made from the studies. The spatio-temporal correlations between GNSS reference stations cannot be considered when using traditional interpolation methods. This paper examines the use of machine learning models to reflect the spatio-temporal correlation among GNSS reference stations. To form the machine learning problem, the time series to be interpolated are treated as output values, and the time series from the remaining GNSS reference stations are used as input data. Specifically, three machine learning algorithms (i.e., the gradient boosting decision tree (GBDT), eXtreme gradient boosting (XGBoost), and random forest (RF)) are utilized to perform interpolation with the time series data from five GNSS reference stations in North China. The results of the interpolation of discrete points indicate that the three machine learning models achieve similar interpolation precision in the Up component, which is 45% better than the traditional cubic spline interpolation precision. The results of the interpolation of continuous missing data indicate that seasonal oscillations caused by thermal expansion effects in summer significantly affect the interpolation precision. Meanwhile, we improved the interpolation precision of the three models by adding data from five stations which have high correlation with the initial five GNSS reference stations. The interpolated time series for the North, East, and Up (NEU) are examined by principal component analysis (PCA), and the results show that the GBDT and RF models perform interpolation better than the XGBoost model.<\/jats:p>","DOI":"10.3390\/rs15184374","type":"journal-article","created":{"date-parts":[[2023,9,6]],"date-time":"2023-09-06T10:23:42Z","timestamp":1693995822000},"page":"4374","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Interpolation of GNSS Position Time Series Using GBDT, XGBoost, and RF Machine Learning Algorithms and Models Error Analysis"],"prefix":"10.3390","volume":"15","author":[{"given":"Zhen","family":"Li","sequence":"first","affiliation":[{"name":"School of Surveying and Geoinformation Engineering, East China University of Technology, Nanchang 330013, China"}]},{"given":"Tieding","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Surveying and Geoinformation Engineering, East China University of Technology, Nanchang 330013, China"},{"name":"Key Laboratory of Mine Environmental Monitoring and Improving around Poyang Lake of Ministry of Natural Resources, East China University of Technology, Nanchang 330013, China"}]},{"given":"Kegen","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Environmental Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-4634-3981","authenticated-orcid":false,"given":"Jie","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Civil and Surveying & Mapping Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"e2021JB022579","DOI":"10.1029\/2021JB022579","article-title":"Integrated Sentinel-1 InSAR and GNSS Time-Series along the San Andreas Fault System","volume":"126","author":"Xu","year":"2021","journal-title":"JGR Solid Earth"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1116","DOI":"10.1016\/j.asr.2021.10.036","article-title":"Secular crustal deformation characteristics prior to the 2011 Tohoku-Oki earthquake detected from GNSS array, 2003\u20132011","volume":"69","author":"Xu","year":"2022","journal-title":"Adv. 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