{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T15:00:01Z","timestamp":1781017201768,"version":"3.54.1"},"reference-count":28,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2021,6,28]],"date-time":"2021-06-28T00:00:00Z","timestamp":1624838400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Time synchronization is the basis of many applications. Aiming at the limitations of the existing clock synchronization algorithms in underwater wireless sensor networks, we propose a pairwise synchronization algorithm called K-Sync, which is based on the Kalman filter. The algorithm does not need the assistance of the position sensor or the speed sensor, and the high time synchronization accuracy can be realized only by utilizing the time-stamps information in the process of message exchange. The K-Sync uses the general constraints of the motion characteristics of the sensor nodes to establish the recursive equations of the clock skew, clock offset, relative mobility velocity, and relative distance. At the same time, the time-stamps are viewed as the observation variables and the system observation equation is obtained. The K-Sync estimates the normalized clock skew and offset of the node via the Kalman filter to achieve high-precision clock synchronization between the two nodes. The simulation shows that the K-Sync has obvious advantages in the key indicators such as the estimated accuracy of clock skew and clock offset, convergence speed, etc. In addition, the K-Sync is more robust to a variety of underwater motion scenes.<\/jats:p>","DOI":"10.3390\/s21134426","type":"journal-article","created":{"date-parts":[[2021,6,28]],"date-time":"2021-06-28T13:39:22Z","timestamp":1624887562000},"page":"4426","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Pair Nodes Clock Synchronization Algorithm Based on Kalman Filter for Underwater Wireless Sensor Networks"],"prefix":"10.3390","volume":"21","author":[{"given":"Xiaomeng","family":"Ni","sequence":"first","affiliation":[{"name":"School of Informatics, Xiamen University, Xiamen 361005, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ting","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Informatics, Xiamen University, Xiamen 361005, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sijia","family":"Ye","sequence":"additional","affiliation":[{"name":"School of Informatics, Xiamen University, Xiamen 361005, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yunsi","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Informatics, Xiamen University, Xiamen 361005, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pengfei","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Informatics, Xiamen University, Xiamen 361005, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lingyu","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Informatics, Xiamen University, Xiamen 361005, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1098\/rsta.2011.0214","article-title":"Underwater sensor networks: Applications, advances and challenges","volume":"370","author":"Heidemann","year":"2012","journal-title":"Philos. Trans. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/j.adhoc.2005.01.004","article-title":"Underwater acoustic sensor networks: Research challenges","volume":"3","author":"Akyildiz","year":"2005","journal-title":"Ad Hoc Netw."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"576","DOI":"10.1109\/58.393101","article-title":"Fundamental limits on the frequency stabilities of crystal oscillators","volume":"42","author":"Walls","year":"1995","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"101844","DOI":"10.1109\/ACCESS.2019.2931117","article-title":"Integrated time synchronization and multiple access protocol for underwater acoustic sensor networks","volume":"7","author":"Jin","year":"2019","journal-title":"IEEE Access"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"590","DOI":"10.3390\/a8030590","article-title":"An overview of a class of clock synchronization algorithms for wireless sensor networks: A statistical signal processing perspective","volume":"8","author":"Wang","year":"2015","journal-title":"Algorithms"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Liu, G., Yan, S., Mao, L., and Sui, Z. (2020, January 21\u201324). Time Synchronization and Clock Parameter Estimation for Wireless Sensor Networks with Unequal Propagation Delays. Proceedings of the 2020 IEEE International Conference on Signal Processing, Communications and Computing (ICSPCC), Macau, China.","DOI":"10.1109\/ICSPCC50002.2020.9259527"},{"key":"ref_7","unstructured":"Liu, J., Wang, Z., Peng, Z., Zuba, M., Cui, J.H., and Zhou, S. (2011, January 5\u20139). TSMU: A time synchronization scheme for mobile underwater sensor networks. Proceedings of the 2011 IEEE Global Telecommunications Conference\u2014GLOBECOM 2011, Houston, TX, USA."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"708","DOI":"10.1016\/j.adhoc.2010.02.003","article-title":"SDRT: A reliable data transport protocol for underwater sensor networks","volume":"8","author":"Xie","year":"2010","journal-title":"Ad Hoc Netw."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"6464","DOI":"10.1109\/TWC.2013.103013.130811","article-title":"Distributed clock parameters tracking in wireless sensor network","volume":"12","author":"Luo","year":"2013","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Syed, A.A., and Heidemann, J.S. (2006, January 23\u201329). Time Synchronization for High Latency Acoustic Networks. Proceedings of the Infocom, Barcelona, Spain.","DOI":"10.1109\/INFOCOM.2006.161"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Chirdchoo, N., Soh, W.S., and Chua, K.C. (2008, January 15). MU-Sync: A time synchronization protocol for underwater mobile networks. Proceedings of the 3rd ACM International Workshop on Underwater Networks, San Francisco, CA, USA.","DOI":"10.1145\/1410107.1410115"},{"key":"ref_12","unstructured":"Vonlopvisut, P., Annur, R., Wuttisittikulkij, L., and Chridchoo, N. (2014, January 1\u20134). Enhancement of MU-Sync: A Time Synchronization Protocol for Underwater Mobile Networks. Proceedings of the 29th International Technical Conference on Circuit\/Systems Computers and Communications, Phuket, Thailand."},{"key":"ref_13","unstructured":"Lu, F., Mirza, D., and Schurgers, C. (October, January 30). D-sync: Doppler-based time synchronization for mobile underwater sensor networks. Proceedings of the Fifth ACM International Workshop on UnderWater Networks, Woods Hole, MA, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"582","DOI":"10.1109\/TMC.2013.13","article-title":"DA-Sync: A Doppler-assisted time-synchronization scheme for mobile underwater sensor networks","volume":"13","author":"Liu","year":"2013","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1109\/TPDS.2012.71","article-title":"Mobi-sync: Efficient time synchronization for mobile underwater sensor networks","volume":"24","author":"Liu","year":"2012","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1109\/JOE.2015.2469955","article-title":"A robust, opportunistic clock synchronization algorithm for ad hoc underwater acoustic networks","volume":"40","author":"Vermeij","year":"2015","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2026","DOI":"10.3390\/s120202026","article-title":"Localization algorithms of underwater wireless sensor networks: A survey","volume":"12","author":"Han","year":"2012","journal-title":"Sensors"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1109\/TMC.2012.100","article-title":"Underwater localization with time-synchronization and propagation speed uncertainties","volume":"12","author":"Diamant","year":"2012","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1109\/TMC.2015.2410777","article-title":"A joint time synchronization and localization design for mobile underwater sensor networks","volume":"15","author":"Liu","year":"2015","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"26932","DOI":"10.1109\/ACCESS.2017.2778425","article-title":"Joint synchronization and localization for underwater sensor networks considering stratification effect","volume":"5","author":"Zhang","year":"2017","journal-title":"IEEE Access"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Hyakudome, T., Nakatani, T., Yoshida, H., Tani, T., Ito, H., and Sugihara, K. (2016, January 6\u20139). Development of fuel cell system for long cruising lange Autonomous Underwater Vehicle. Proceedings of the 2016 IEEE\/OES Autonomous Underwater Vehicles (AUV), Tokyo, Japan.","DOI":"10.1109\/AUV.2016.7778666"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Mar\u00f3ti, M., Kusy, B., Simon, G., and L\u00e9deczi, A. (2004, January 3\u20135). The flooding time synchronization protocol. Proceedings of the 2nd International Conference on Embedded Networked Sensor Systems, Baltimore, MD, USA.","DOI":"10.1145\/1031495.1031501"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Serpedin, E., and Chaudhari, Q.M. (2009). Synchronization in Wireless Sensor Networks: Parameter Estimation, Performance Benchmarks, and Protocols, Cambridge University Press.","DOI":"10.1017\/CBO9780511627194"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1109\/MSP.2008.926661","article-title":"Distributed synchronization in wireless networks","volume":"25","author":"Simeone","year":"2008","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1109\/81.847872","article-title":"Phase noise in oscillators: A unifying theory and numerical methods for characterization","volume":"47","author":"Demir","year":"2000","journal-title":"IEEE Trans. Circuits Syst. I Fundam. Theory Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"933","DOI":"10.1109\/TC.1987.5009516","article-title":"Clock synchronization in distributed real-time systems","volume":"100","author":"Kopetz","year":"1987","journal-title":"IEEE Trans. Comput."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1386","DOI":"10.1109\/78.668800","article-title":"Posterior Cram\u00e9r-Rao bounds for discrete-time nonlinear filtering","volume":"46","author":"Tichavsky","year":"1998","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1111\/j.1752-1688.2007.00017.x","article-title":"Chaotic Behavior and Pollution Dispersion Characteristics in Engineered Tidal Embayments: A Numerical Investigation 1","volume":"43","author":"Bagtzoglou","year":"2007","journal-title":"JAWRA J. Am. Water Resour. 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