{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T12:35:37Z","timestamp":1780317337104,"version":"3.54.1"},"reference-count":37,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,3,26]],"date-time":"2023-03-26T00:00:00Z","timestamp":1679788800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["41731066"],"award-info":[{"award-number":["41731066"]}]},{"name":"National Natural Science Foundation of China","award":["41904038"],"award-info":[{"award-number":["41904038"]}]},{"name":"National Natural Science Foundation of China","award":["42090053"],"award-info":[{"award-number":["42090053"]}]},{"name":"National Natural Science Foundation of China","award":["42127802"],"award-info":[{"award-number":["42127802"]}]},{"name":"National Natural Science Foundation of China","award":["41941019"],"award-info":[{"award-number":["41941019"]}]},{"name":"National Natural Science Foundation of China","award":["2019YFC1509802"],"award-info":[{"award-number":["2019YFC1509802"]}]},{"name":"National Natural Science Foundation of China","award":["2018YFC1505105"],"award-info":[{"award-number":["2018YFC1505105"]}]},{"name":"National Natural Science Foundation of China","award":["2019M662713"],"award-info":[{"award-number":["2019M662713"]}]},{"name":"National Key Research and Development Plan of China","award":["41731066"],"award-info":[{"award-number":["41731066"]}]},{"name":"National Key Research and Development Plan of China","award":["41904038"],"award-info":[{"award-number":["41904038"]}]},{"name":"National Key Research and Development Plan of China","award":["42090053"],"award-info":[{"award-number":["42090053"]}]},{"name":"National Key Research and Development Plan of China","award":["42127802"],"award-info":[{"award-number":["42127802"]}]},{"name":"National Key Research and Development Plan of China","award":["41941019"],"award-info":[{"award-number":["41941019"]}]},{"name":"National Key Research and Development Plan of China","award":["2019YFC1509802"],"award-info":[{"award-number":["2019YFC1509802"]}]},{"name":"National Key Research and Development Plan of China","award":["2018YFC1505105"],"award-info":[{"award-number":["2018YFC1505105"]}]},{"name":"National Key Research and Development Plan of China","award":["2019M662713"],"award-info":[{"award-number":["2019M662713"]}]},{"name":"The China Postdoctoral Science Foundation","award":["41731066"],"award-info":[{"award-number":["41731066"]}]},{"name":"The China Postdoctoral Science Foundation","award":["41904038"],"award-info":[{"award-number":["41904038"]}]},{"name":"The China Postdoctoral Science Foundation","award":["42090053"],"award-info":[{"award-number":["42090053"]}]},{"name":"The China Postdoctoral Science Foundation","award":["42127802"],"award-info":[{"award-number":["42127802"]}]},{"name":"The China Postdoctoral Science Foundation","award":["41941019"],"award-info":[{"award-number":["41941019"]}]},{"name":"The China Postdoctoral Science Foundation","award":["2019YFC1509802"],"award-info":[{"award-number":["2019YFC1509802"]}]},{"name":"The China Postdoctoral Science Foundation","award":["2018YFC1505105"],"award-info":[{"award-number":["2018YFC1505105"]}]},{"name":"The China Postdoctoral Science Foundation","award":["2019M662713"],"award-info":[{"award-number":["2019M662713"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Real-time satellite clock offset is a crucial element for real-time precise point positioning (RT-PPP). However, the elapsed time for undifferenced (UD) multi-global navigation satellite system (GNSS) real-time satellite clock offset estimation at each epoch is increased with the growth of stations, which may fall short of real-time application requirements. Therefore, a rapid estimation method for UD multi-GNSS real-time satellite clock offset is proposed to improve the computation efficiency, in which both the dimension of the normal equation (NEQ) and the number of redundant observations are calculated before adjustment; if these two values are larger than the predefined thresholds, the elevation mask is gradually increased until they are less than the predefined thresholds. Then, the clock offset estimation is conducted; this method is called clock offset estimation using partial observations. Totals of 50, 60, 70 and 80 stations are applied to perform experiments. Compared to clock offset estimation using all observations, the elapsed times of clock offset estimation using partial observations can be reduced from 6.80 to 3.10 s, 7.93 to 2.97 s, 12.04 to 3.14 s for 60, 70 and 80 stations, respectively. By using the proposed method, the elapsed time of the clock offset estimation at each epoch is less than 5 s. The estimated clock offset accuracy for GPS, BDS-3, Galileo and GLONASS satellites are better than 0.04, 0.05, 0.03 and 0.16 ns when using the partial observations to estimate clock offset with 50, 60, 70 and 80 stations, respectively. For the multi-GNSS kinematic PPP using the estimated clock offset from 50, 60, 70 and 80 stations with partial observations, the positioning accuracy at 95% confidence level in the east, north and up direction are better than 2.70, 2.20 and 5.60 cm, respectively.<\/jats:p>","DOI":"10.3390\/rs15071776","type":"journal-article","created":{"date-parts":[[2023,3,27]],"date-time":"2023-03-27T02:18:27Z","timestamp":1679883507000},"page":"1776","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Rapid Estimation of Undifferenced Multi-GNSS Real-Time Satellite Clock Offset Using Partial Observations"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6817-198X","authenticated-orcid":false,"given":"Wei","family":"Xie","sequence":"first","affiliation":[{"name":"College of Geology Engineering and Geomatics, Chang\u2019an University, Xi\u2019an 710054, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guanwen","family":"Huang","sequence":"additional","affiliation":[{"name":"College of Geology Engineering and Geomatics, Chang\u2019an University, Xi\u2019an 710054, China"},{"name":"Key Laboratory of Ecological Geology and Disaster Prevention, Ministry of Natural Resources, Xi\u2019an 710054, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenju","family":"Fu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8269-4779","authenticated-orcid":false,"given":"Shi","family":"Du","sequence":"additional","affiliation":[{"name":"German Research Centre for Geosciences (GFZ), Telegrafenberg, 14473 Potsdam, Germany"},{"name":"Institute of Geodesy and Geoinformation Science, Technische Universit\u00e4t Berlin, Stra\u00dfe des 17. Juni 135, 10623 Berlin, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bobin","family":"Cui","sequence":"additional","affiliation":[{"name":"German Research Centre for Geosciences (GFZ), Telegrafenberg, 14473 Potsdam, Germany"},{"name":"Institute of Geodesy and Geoinformation Science, Technische Universit\u00e4t Berlin, Stra\u00dfe des 17. Juni 135, 10623 Berlin, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mengyuan","family":"Li","sequence":"additional","affiliation":[{"name":"College of Geology Engineering and Geomatics, Chang\u2019an University, Xi\u2019an 710054, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yue","family":"Tan","sequence":"additional","affiliation":[{"name":"College of Geology Engineering and Geomatics, Chang\u2019an University, Xi\u2019an 710054, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5005","DOI":"10.1029\/96JB03860","article-title":"Precise point positioning for the efficient and robust analysis of GPS data from large networks","volume":"102","author":"Zumberge","year":"1997","journal-title":"J. Geophys. 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