{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T09:15:21Z","timestamp":1773652521843,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T00:00:00Z","timestamp":1773446400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42530114"],"award-info":[{"award-number":["42530114"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12273094"],"award-info":[{"award-number":["12273094"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In recent years, the large-scale deployment of Low Earth Orbit (LEO) constellations has made autonomous time synchronization and reference maintenance within constellations a critical enabling technology. Achieving high-precision synchronization with low cost and low power consumption, without relying on onboard atomic clocks or Global Navigation Satellite System (GNSS) signals, remains a significant challenge. This paper proposes an autonomous time synchronization method for LEO constellations that relies solely on high-stability crystal oscillators as local oscillators. By leveraging satellite-to-ground and inter-satellite measurement links, the proposed approach enables constellation-wide time synchronization without external timing references. A satellite-to-ground link visibility time model is established based on orbital parameters and ground station visibility geometry. On this basis, a discrete state-space model is constructed, incorporating temperature-induced frequency perturbation compensation, frequency offset estimation, and control voltage regulation. A combined Kalman filtering and Linear Quadratic Regulator (LQR) control framework is employed to achieve precise time offset synchronization and long-term maintenance. Experimental results demonstrate that, under a Walker-Delta constellation configuration with an orbital altitude of 800 km and an inclination of 55\u00b0, the proposed method introduces a time synchronization performance better than 5 ns (1\u03c3), with a peak-to-peak error below 30 ns. This level of performance satisfies the timing requirements of typical LEO constellation applications, including communication scheduling, high-rate modulation, and critical infrastructure timing services. Moreover, the proposed scheme supports decentralized deployment and provides local physical time signal outputs, making it well suited for large-scale satellite networks requiring high-precision autonomous time synchronization.<\/jats:p>","DOI":"10.3390\/s26061839","type":"journal-article","created":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T08:41:26Z","timestamp":1773650486000},"page":"1839","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["High-Precision Time Synchronization and Autonomous Maintenance for LEO Satellite Constellations Based on High-Stability Crystal Oscillators"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-4360-6306","authenticated-orcid":false,"given":"Lei","family":"Mu","sequence":"first","affiliation":[{"name":"Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China"},{"name":"School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaogong","family":"Hu","sequence":"additional","affiliation":[{"name":"Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mengjie","family":"Wu","sequence":"additional","affiliation":[{"name":"Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6927-0549","authenticated-orcid":false,"given":"Jin","family":"Li","sequence":"additional","affiliation":[{"name":"Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China"},{"name":"School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"131301","DOI":"10.1007\/s11432-020-3218-8","article-title":"An overview on integrated localization and communication towards 6G","volume":"65","author":"Xiao","year":"2022","journal-title":"Sci. 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