{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:12:25Z","timestamp":1760235145804,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2021,7,23]],"date-time":"2021-07-23T00:00:00Z","timestamp":1626998400000},"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":["61971472"],"award-info":[{"award-number":["61971472"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Strategic Priority Research Program (A) of Chinese Academy of Sciences","award":["XDA22030101"],"award-info":[{"award-number":["XDA22030101"]}]},{"name":"Institute of Acoustic, Chinese Academy of Sciences Free Exploration Project","award":["ZYTS202003"],"award-info":[{"award-number":["ZYTS202003"]}]},{"name":"National Key Research and Development Project","award":["2016YFC0300300"],"award-info":[{"award-number":["2016YFC0300300"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Time synchronization plays an important role in the scheduling and position technologies of sensor nodes in underwater acoustic networks (UANs). The time synchronization (TS) algorithms face challenges such as high requirements of energy efficiency, the estimation accuracy of the time-varying clock skew and the suppression of the impulsive noise. To achieve accurate time synchronization for UANs, an energy-efficient TS method based on nonlinear clock skew tracking (NCST) is proposed. First, based on the sea trial temperature data and the crystal oscillators\u2019 temperature\u2013frequency characteristics, a nonlinear model is established to characterize the dynamic of clock skews. Second, a single-way communication scheme based on a receiver-only (RO) paradigm is used in the NCST-TS to save limited energy. Meanwhile, impulsive noises are considered during the communication process and the Gaussian mixture model (GMM) is employed to fit receiving timestamp errors caused by non-Gaussian noise. To combat the nonlinear and non-Gaussian problem, the particle filter (PF)-based algorithm is used to track the time-varying clock state and an accurate posterior probability density function under the GMM error model is also given in PF. The simulation results show that under the GMM error model, the accumulative Root Mean Square Errors (RMSE) of NCST-TS can be reduced from 10\u22124 s to 10\u22125 s compared with existing protocols. It also outperforms the other TS algorithms in the aspect of energy efficiency.<\/jats:p>","DOI":"10.3390\/s21155018","type":"journal-article","created":{"date-parts":[[2021,7,25]],"date-time":"2021-07-25T22:07:00Z","timestamp":1627250820000},"page":"5018","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Energy-Efficient Time Synchronization Based on Nonlinear Clock Skew Tracking for Underwater Acoustic Networks"],"prefix":"10.3390","volume":"21","author":[{"given":"Di","family":"Liu","sequence":"first","affiliation":[{"name":"Ocean Acoustic Technology Center, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Beijing Engineering Technology Research Center of Ocean Acoustic Equipment, Beijing 100190, China"}]},{"given":"Min","family":"Zhu","sequence":"additional","affiliation":[{"name":"Ocean Acoustic Technology Center, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"Beijing Engineering Technology Research Center of Ocean Acoustic Equipment, Beijing 100190, China"},{"name":"State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9679-7522","authenticated-orcid":false,"given":"Dong","family":"Li","sequence":"additional","affiliation":[{"name":"Ocean Acoustic Technology Center, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Beijing Engineering Technology Research Center of Ocean Acoustic Equipment, Beijing 100190, China"}]},{"given":"Xiaofang","family":"Fang","sequence":"additional","affiliation":[{"name":"Ocean Acoustic Technology Center, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"Beijing Engineering Technology Research Center of Ocean Acoustic Equipment, Beijing 100190, China"}]},{"given":"Yanbo","family":"Wu","sequence":"additional","affiliation":[{"name":"Ocean Acoustic Technology Center, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"Beijing Engineering Technology Research Center of Ocean Acoustic Equipment, Beijing 100190, China"},{"name":"State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1707","DOI":"10.1109\/TIE.2020.2970691","article-title":"Underwater Acoustic Sensor Networks with Cost Efficiency for Internet of Underwater Things","volume":"68","author":"Song","year":"2020","journal-title":"IEEE Trans. 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