{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:15:29Z","timestamp":1760217329348,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2015,9,3]],"date-time":"2015-09-03T00:00:00Z","timestamp":1441238400000},"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 essential for node localization, target tracking, data fusion, and various other Wireless Sensor Network (WSN) applications. To improve the estimation accuracy of continuous clock offset and skew of mobile nodes in WSNs, we propose a novel time synchronization algorithm, the Rao-Blackwellised (RB) particle filter time synchronization algorithm based on the Dirichlet process mixture (DPM) model. In a state-space equation with a linear substructure, state variables are divided into linear and non-linear variables by the RB particle filter algorithm. These two variables can be estimated using Kalman filter and particle filter, respectively, which improves the computational efficiency more so than if only the particle filter was used. In addition, the DPM model is used to describe the distribution of non-deterministic delays and to automatically adjust the number of Gaussian mixture model components based on the observational data. This improves the estimation accuracy of clock offset and skew, which allows achieving the time synchronization. The time synchronization performance of this algorithm is also validated by computer simulations and experimental measurements. The results show that the proposed algorithm has a higher time synchronization precision than traditional time synchronization algorithms.<\/jats:p>","DOI":"10.3390\/s150922249","type":"journal-article","created":{"date-parts":[[2015,9,3]],"date-time":"2015-09-03T10:57:07Z","timestamp":1441277827000},"page":"22249-22265","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["RB Particle Filter Time Synchronization Algorithm Based on the DPM Model"],"prefix":"10.3390","volume":"15","author":[{"given":"Chunsheng","family":"Guo","sequence":"first","affiliation":[{"name":"College of Communication Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jia","family":"Shen","sequence":"additional","affiliation":[{"name":"College of Communication Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yao","family":"Sun","sequence":"additional","affiliation":[{"name":"College of Automation Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Na","family":"Ying","sequence":"additional","affiliation":[{"name":"College of Communication Engineering, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,9,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1247","DOI":"10.1109\/JPROC.2003.814918","article-title":"Sensor networks: Evolution, opportunities, and challenges","volume":"8","author":"Chong","year":"2003","journal-title":"IEEE Proceed."},{"doi-asserted-by":"crossref","unstructured":"Jafari, R., Encarnacao, A., Zahoory, A., Dabiri, F., Noshadi, H., and Sarrafzadeh, M. (2005, January 1). Wireless sensor networks for health monitoring. Proceedings of the 2th Annual International Conference on Mobile and Ubiquitous Systems, San Diego, CA, USA.","key":"ref_2","DOI":"10.1109\/MOBIQUITOUS.2005.65"},{"unstructured":"Elson, J., and Romer, K. (2002, January 28\u201329). Wireless sensor networks: A new regime for time synchronization. Proceedings of the First Workshop on Hot Topics In Networks, Princeton, NJ, USA.","key":"ref_3"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1109\/MNET.2004.1316761","article-title":"Time synchronization in sensor networks: A survey","volume":"4","author":"Sivrikaya","year":"2004","journal-title":"IEEE Netw."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1007\/s11036-012-0361-7","article-title":"Accurate and Efficient Node Localization for Mobile Sensor Networks","volume":"1","author":"Chen","year":"2013","journal-title":"Mobile Netw. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1007\/s11036-010-0281-3","article-title":"Mobility-Assisted Node Localization Based on TOA Measurements Without Time Synchronization in Wireless Sensor Networks","volume":"1","author":"Chen","year":"2012","journal-title":"Mobile Netw. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3532","DOI":"10.1109\/TWC.2010.090210.100146","article-title":"Asymmetrical Round Trip Based Synchronization-Free Localization in Large-Scale Underwater Sensor Networks","volume":"11","author":"Liu","year":"2010","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"7625","DOI":"10.3390\/s110807625","article-title":"Enhanced Precision Time Synchronization for Wireless Sensor Networks","volume":"11","author":"Cho","year":"2011","journal-title":"Sensors"},{"unstructured":"Bulusu, N., and Jha, S. (2005). Wireless Sensor Networks: A Systems Perspective,  Artech House.","key":"ref_9"},{"doi-asserted-by":"crossref","unstructured":"Elson, J., Girod, L., and Estrin, D. (2002, January 9\u201311). Fine-Grained Network Time Synchronization using Reference Broadcasts. Proceedings of the Fifth Symposium on Operating Systems Design and Implementation (OSDI2002), Boston, MA, USA.","key":"ref_10","DOI":"10.1145\/1060289.1060304"},{"doi-asserted-by":"crossref","unstructured":"Maroti, M., Kusy, B., Simon, G., and Ledeczi, A. (2004, January 3\u20135). The flooding time synchronization protocol. Proceedings of the 2nd International Conference on Embedded Networked Sensor Systems, Baltimore, MA, USA.","key":"ref_11","DOI":"10.1145\/1031495.1031501"},{"doi-asserted-by":"crossref","unstructured":"Ganeriwal, S., Kumar, R., and Srivastava, M.B. (2003, January 5\u20137). Timing-Sync Protocol for Sensor Networks. Proceedings of the 1st International Conference on Embedded Networked Sensor Systems, Los Angeles, CA, USA.","key":"ref_12","DOI":"10.1145\/958491.958508"},{"unstructured":"Ping, S. (2003). Delay Measurement Time Synchronization for Wireless Sensor Networks, Technical Report for Intel Research Berkeley Lab.","key":"ref_13"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1109\/TCOMM.2004.840668","article-title":"On maximum-likelihood estimation of clock offset","volume":"1","author":"Jeske","year":"2005","journal-title":"IEEE Trans. Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"766","DOI":"10.1109\/TCOMM.2007.894102","article-title":"Novel Clock Phase Offset and Skew Estimation Using Two-Way Timing Message Exchanges for Wireless Sensor Networks","volume":"4","author":"Noh","year":"2007","journal-title":"IEEE Trans. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1685","DOI":"10.1109\/TSP.2007.910536","article-title":"On Maximum Likelihood Estimation of Clock Offset and Skew in Networks with Exponential Delays","volume":"4","author":"Chaudhari","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2893","DOI":"10.1109\/TIT.2010.2046233","article-title":"On Minimum Variance Unbiased Estimation of Clock Offset in a Two-Way Message Exchange Mechanism","volume":"6","author":"Chaudhari","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1155","DOI":"10.1016\/j.sigpro.2008.12.021","article-title":"A robust estimation scheme for clock phase offsets in wireless sensor networks in the presence of non-Gaussian random delays","volume":"6","author":"Kim","year":"2009","journal-title":"Signal Process."},{"doi-asserted-by":"crossref","unstructured":"Kim, J.S., Lee, J., Serpedin, E., and Qaraqe, K. (2010). A Robust Approach for Clock Offsets Estimation in Wireless Sensor Networks. EURASIP J. Adv. Sig. Proc., 2010.","key":"ref_19","DOI":"10.1155\/2010\/132381"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3035","DOI":"10.1109\/TSP.2011.2141660","article-title":"Robust Clock Synchronization in Wireless Sensor Networks through Noise Density Estimation","volume":"7","author":"Kim","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_21","first-page":"6","article-title":"Hierarchical Dirichlet Processes","volume":"1","author":"Teh","year":"2004","journal-title":"J. Am. Statist. Assoc."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2279","DOI":"10.1109\/TSP.2005.849151","article-title":"Marginalized particle filters for mixed linear\/nonlinear state-space models","volume":"7","author":"Schon","year":"2005","journal-title":"IEEE Trans. Signal Process."},{"unstructured":"Ota, K., Duflos, E., Vanheeghe, P., and Yanagida, M. (April, January 31). Speech recognition with speech density estimation by the Dirichlet Process Mixture. Proceedings of the IEEE International Conference on Speech and Signal Processing (ICASSP), Las Vegas, NV, USA.","key":"ref_23"},{"doi-asserted-by":"crossref","unstructured":"Cherian, A., Morellas, V., Papanikolopoulos, N., and Bedros, S.J. (2011, January 20\u201325). Dirichlet process mixture models on symmetric positive definite matrices for appearance clustering in video surveillance applications. Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition (CVPR), Providence, RI, USA.","key":"ref_24","DOI":"10.1109\/CVPR.2011.5995723"},{"doi-asserted-by":"crossref","unstructured":"Rabaoui, A., Viandier, N., Marais, J., and Duflos, E. (2011, January 22\u201327). On selecting the hyperparameters of the DPM models for the density estimation of observation errors. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech Republic.","key":"ref_25","DOI":"10.1109\/ICASSP.2011.5947252"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1109\/TRO.2010.2085490","article-title":"Efficient Unbiased Tracking of Multiple Dynamic Obstacles under Large Viewpoint Changes","volume":"1","author":"Miller","year":"2011","journal-title":"IEEE Trans. Robot."},{"doi-asserted-by":"crossref","unstructured":"Maddern, W., Milford, M., and Wyeth, G. (2011, January 9\u201313). Continuous appearance-based trajectory SLAM. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China.","key":"ref_27","DOI":"10.1109\/ICRA.2011.5979963"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4408","DOI":"10.1109\/TSP.2005.857061","article-title":"Complexity analysis of the marginalized particle filter","volume":"11","author":"Karlsson","year":"2005","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1109\/LCOMM.2010.04.092364","article-title":"Advanced self-correcting time synchronization in wireless sensor networks","volume":"4","author":"Liu","year":"2010","journal-title":"IEEE Commun. Lett."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/15\/9\/22249\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:47:58Z","timestamp":1760215678000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/15\/9\/22249"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9,3]]},"references-count":29,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2015,9]]}},"alternative-id":["s150922249"],"URL":"https:\/\/doi.org\/10.3390\/s150922249","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2015,9,3]]}}}