{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T20:28:16Z","timestamp":1782160096259,"version":"3.54.5"},"reference-count":40,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2020,6,24]],"date-time":"2020-06-24T00:00:00Z","timestamp":1592956800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Global Navigation Satellite System (GNSS) coordinate time series contains obvious seasonal signals, which mainly manifest as a superposition of annual and semi-annual oscillations. Accurate extraction of seasonal signals is of great importance for understanding various geophysical phenomena. In this paper, a Weighted Nuclear Norm Minimization (WNNM) is proposed to extract the seasonal signals from the GNSS coordinate time series. WNNM assigns different weights to different singular values that enable us to estimate an approximate low rank matrix from its noisy matrix. To address this issue, the low rank characteristics of the Hankel matrix induced by GNSS coordinate time series was investigated first, and then the WNNM is applied to extract the seasonal signals in the GNSS coordinate time series. Meanwhile, the residuals have been analyzed, obtaining the estimation of the uncertainty of velocity. To demonstrate the effectiveness of the proposed algorithm, a number of tests have been carried out on both simulated and real GNSS dataset. Experimental results indicate that the proposed scheme offers preferable performances compared with many state-of-the-art methods.<\/jats:p>","DOI":"10.3390\/rs12122027","type":"journal-article","created":{"date-parts":[[2020,6,24]],"date-time":"2020-06-24T08:54:50Z","timestamp":1592988890000},"page":"2027","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Extracting Seasonal Signals in GNSS Coordinate Time Series via Weighted Nuclear Norm Minimization"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5047-9900","authenticated-orcid":false,"given":"Baozhou","family":"Chen","sequence":"first","affiliation":[{"name":"School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China"},{"name":"Hubei Subsurface Multi-Scale Imaging Key Laboratory, China University of Geosciences, Wuhan 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2017-7845","authenticated-orcid":false,"given":"Jiawen","family":"Bian","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4383-2654","authenticated-orcid":false,"given":"Kaihua","family":"Ding","sequence":"additional","affiliation":[{"name":"School of Geography and Information Engineering, China University of Geosciences, Wuhan 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3558-569X","authenticated-orcid":false,"given":"Haochen","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6809-7097","authenticated-orcid":false,"given":"Hongwei","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China"},{"name":"Hubei Subsurface Multi-Scale Imaging Key Laboratory, China University of Geosciences, Wuhan 430074, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"18035","DOI":"10.1029\/97JB01380","article-title":"Southern California Permanent GPS Geodetic Array: Error analysis of daily position estimates and site velocities","volume":"102","author":"Zhang","year":"1997","journal-title":"J. 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