{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T23:50:20Z","timestamp":1767916220662,"version":"3.49.0"},"reference-count":32,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2020,8,28]],"date-time":"2020-08-28T00:00:00Z","timestamp":1598572800000},"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":["41874008"],"award-info":[{"award-number":["41874008"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Since the observation precision of the Global Navigation Satellite System (GNSS) carrier phase is on the order of millimeters, if the phase ambiguity is correctly solved, while calibrating the receiver inter-frequency bias, time synchronization on the order of tens of picoseconds is expected. In this contribution, a method that considers the prior constraints of the between-receiver inter-frequency bias (IFB) and its random variation characteristics is proposed for the estimation of the between-receiver clock difference, based on the uncombined GNSS carrier phase and pseudorange observations of the zero and short baselines. The proposed method can rapidly achieve the single-difference ambiguity resolution of the zero and short baselines, and then obtain the high-precision relative clock offset, by using only the carrier phase observations, along with the between-receiver IFBs being simultaneously determined. Our numerical tests, carried out using GNSS observations sampled every 30 s by a dedicatedly selected set of zero and short baselines, show that the method can fix the between-receiver single-difference ambiguity successfully within an average of fewer than 2 epochs (interval 30 s). Then, a clock difference between two receivers with millimeter precision is obtained, achieving time synchronization on tens of picoseconds level, and deriving a frequency stability of 5 \u00d7 10\u221214 for averaging times of 30,000 s. Furthermore, the proposed approach is compared with the precise point positioning (PPP) time transfer method. The results show that, for different types of receivers, the agreement between the two methods is between \u22126.7 ns and 0.2 ns.<\/jats:p>","DOI":"10.3390\/s20174882","type":"journal-article","created":{"date-parts":[[2020,8,28]],"date-time":"2020-08-28T09:17:08Z","timestamp":1598606228000},"page":"4882","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Fast Time Synchronization on Tens of Picoseconds Level Using Uncombined GNSS Carrier Phase of Zero\/Short Baseline"],"prefix":"10.3390","volume":"20","author":[{"given":"Yinghao","family":"Zhao","sequence":"first","affiliation":[{"name":"Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu 611756, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8541-0989","authenticated-orcid":false,"given":"Letao","family":"Zhou","sequence":"additional","affiliation":[{"name":"Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu 611756, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Feng","sequence":"additional","affiliation":[{"name":"Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu 611756, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shaoguang","family":"Xu","sequence":"additional","affiliation":[{"name":"Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu 611756, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1109\/TIM.1985.4315283","article-title":"Accuracy of international time and frequency comparisons via global positioning system satellites in common-view","volume":"IM-34","author":"Allan","year":"1985","journal-title":"IEEE Trans. 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