{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:47:10Z","timestamp":1760237230671,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,3,20]],"date-time":"2020-03-20T00:00:00Z","timestamp":1584662400000},"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>Since the existing methods cannot evaluate the time delay of different layers of sensor networks, there are some problems such as the low precision of clock error compensation, high time delay, and low efficiency of communication in sensor networks. To solve this problem, a method of clock error compensation in sensor networks based on a cyclic symmetry algorithm is proposed. Based on the basic theory of cyclic symmetry, the cyclic symmetry matrix of the sensor network is constructed; in the communication process, all nodes are extended to get the cumulative delay rate of the sensor network in the specified time domain. Using the cumulative delay rate of the cyclic network and the sensor network, the autoregressive integral sliding mode control model is established to compensate for the cumulative error of clock synchronization. The simulation results show that the compensation accuracy of this method is more than 98%, which can effectively reduce the delay of sensor network. It improves the communication efficiency of the sensor network, meets the communication requirements of the sensor network, and has a very broad application prospect.<\/jats:p>","DOI":"10.3390\/s20061738","type":"journal-article","created":{"date-parts":[[2020,3,20]],"date-time":"2020-03-20T11:42:11Z","timestamp":1584704531000},"page":"1738","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Compensation Method for Sensor Network Clock Error Based on Cyclic Symmetry Algorithm"],"prefix":"10.3390","volume":"20","author":[{"given":"Hailiang","family":"Feng","sequence":"first","affiliation":[{"name":"School of Information and Communication Engineering, Communication University of China, Beijing 100024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhanxin","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Information and Communication Engineering, Communication University of China, Beijing 100024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuhai","family":"Shi","sequence":"additional","affiliation":[{"name":"Internet Technology Institute, Academy of Broadcasting Science, Beijing 100866, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3882-3179","authenticated-orcid":false,"given":"Narjes","family":"Nabipour","sequence":"additional","affiliation":[{"name":"Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,20]]},"reference":[{"key":"ref_1","first-page":"232","article-title":"Asymmetric Interference Alignment for Device-to-Device Underlaying Cellular Networks","volume":"12","author":"Zhang","year":"2017","journal-title":"J. Chin. Acad. Electron. Inf. Technol."},{"key":"ref_2","first-page":"55","article-title":"One Improved EMF Harmonic Adaptive Compensation for PMSG Sensorless Control Method","volume":"15","author":"Chai","year":"2017","journal-title":"J. Power Supply"},{"key":"ref_3","first-page":"1433","article-title":"Compensation Control of Photovoltaic Power Prediction Deviation Based on Energy Storage System","volume":"41","author":"Luo","year":"2017","journal-title":"Chin. J. Power Sources"},{"key":"ref_4","first-page":"149","article-title":"Error Analysis of Phase Difference Magnetic Modulation DC Leakage Current Sensor","volume":"9","author":"Qi","year":"2018","journal-title":"Autom. Instrum."},{"key":"ref_5","first-page":"947","article-title":"Data Compression Algorithm of Sensor Networks Based on Dynamic Adjustment of Threshold of Encoding Transmission","volume":"55","author":"Tao","year":"2017","journal-title":"J. Jilin Univ."},{"key":"ref_6","first-page":"329","article-title":"Simulation of Attack Data Detection Method Based on Wireless Sensor Networks","volume":"35","author":"Wang","year":"2018","journal-title":"Comput. Simul."},{"key":"ref_7","first-page":"1","article-title":"A Temperature Compensation Method for Magneto-Elastic Tension Sensor in Rod-Like Structure Tension Measurement","volume":"54","author":"Zhu","year":"2018","journal-title":"IEEE Trans. Magn."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/s10921-017-0405-9","article-title":"Fault Detection of a Rotating Shaft by Using the Electromechanical Impedance Method and a Temperature Compensation Approach","volume":"36","author":"Rabelo","year":"2017","journal-title":"J. Nondestr. 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