{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T06:58:47Z","timestamp":1760597927301,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,1,25]],"date-time":"2020-01-25T00:00:00Z","timestamp":1579910400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100011354","name":"State Key Laboratory of Geo-Information Engineering","doi-asserted-by":"publisher","award":["SKLGIE2018-Z-1-2"],"award-info":[{"award-number":["SKLGIE2018-Z-1-2"]}],"id":[{"id":"10.13039\/501100011354","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>As a system of ranging and positioning based on time transfer, the timekeeping ability of a navigation satellite constellation is a key factor for accurate positioning and timing services. As the timekeeping performances depend on the frequency stability and predictability of satellite clocks, we propose a method to establish a more stable and predictable space time reference, i.e., inter-satellite link time (ISLT), uniting the satellite clocks through inter-satellite links (ISLs). The joint timekeeping framework is introduced first. Based on the weighted average timescale algorithm, the optimal weights that minimize the increment of the ISLT timescale are determined and allocated to the clock ensemble to improve the frequency stability and predictability in both the long and short term. The time deviations with respect to the system time of nine BeiDou-3 satellites through multi-satellite precise orbit determination (MPOD) are used for joint timekeeping evaluation. According to the Allan deviation, the frequency of the ISLT is more stable than the nine satellite clocks in the short term (averaging time smaller than 7000 s), and its daily stability can reach 6 \u00d7 10\u221215. Meanwhile, the short-term (two hours) and long-term (10 h) prediction accuracy of the ISLT is 0.18 and 1.05 ns, respectively, also better than each satellite clock. Furthermore, the joint timekeeping is verified to be robust against single-satellite malfunction.<\/jats:p>","DOI":"10.3390\/s20030670","type":"journal-article","created":{"date-parts":[[2020,1,27]],"date-time":"2020-01-27T07:41:11Z","timestamp":1580110871000},"page":"670","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Joint Timekeeping of Navigation Satellite Constellation with Inter-Satellite Links"],"prefix":"10.3390","volume":"20","author":[{"given":"Leyuan","family":"Sun","sequence":"first","affiliation":[{"name":"College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wende","family":"Huang","sequence":"additional","affiliation":[{"name":"College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, China"},{"name":"State Key Laboratory of Geo-Information Engineering, Xi\u2019an 710000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuaihe","family":"Gao","sequence":"additional","affiliation":[{"name":"Southwest China Research Institute of Electronic Equipment, China Electronics Technology Group Corporation, Chengdu 610000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Li","sequence":"additional","affiliation":[{"name":"National Time Service Center, Chinese Academy of Science, Xi\u2019an 610000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiye","family":"Guo","sequence":"additional","affiliation":[{"name":"College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/s10291-019-0910-7","article-title":"Relativity effect of Galileo passive hydrogen maser satellite clocks","volume":"23","author":"Kouba","year":"2019","journal-title":"GPS Solut."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"999","DOI":"10.1007\/s10291-016-0587-0","article-title":"Timeslot scheduling of inter-satellite links based on a system of narrow beam with time division","volume":"21","author":"Yang","year":"2017","journal-title":"GPS Solut."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1007\/s10291-018-0706-1","article-title":"Performance of the BDS3 experimental satellite passive hydrogen maser","volume":"22","author":"Wu","year":"2018","journal-title":"GPS Solut."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2889","DOI":"10.1016\/j.asr.2018.01.020","article-title":"Atomic clock performance and combined clock error prediction for the new generation of BeiDou navigation satellites","volume":"63","author":"Wang","year":"2019","journal-title":"Adv. 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