{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T15:43:09Z","timestamp":1783611789608,"version":"3.55.0"},"reference-count":43,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2019,6,16]],"date-time":"2019-06-16T00:00:00Z","timestamp":1560643200000},"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":["51579143"],"award-info":[{"award-number":["51579143"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61701299"],"award-info":[{"award-number":["61701299"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Shanghai Committee of Science and Technology","award":["18040501700"],"award-info":[{"award-number":["18040501700"]}]},{"name":"the Postgraduate Innovation Foundation of Shanghai Maritime University","award":["2017ycx030"],"award-info":[{"award-number":["2017ycx030"]}]},{"name":"the Postgraduate Innovation Foundation of Shanghai Maritime University","award":["2016ycx042"],"award-info":[{"award-number":["2016ycx042"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>As an important means of multidimensional observation on the sea, ocean sensor networks (OSNs) could meet the needs of comprehensive information observations in large-scale and multifactor marine environments. In what concerns OSNs, accurate location information is the basis of the data sets. However, because of the multipath effect\u2014signal shadowing by waves and unintentional or malicious attacks\u2014outlier measurements occur frequently and inevitably, which directly degrades the localization accuracy. Therefore, increasing localization accuracy in the presence of outlier measurements is a critical issue that needs to be urgently tackled in OSNs. In this case, this paper proposed a robust, non-cooperative localization algorithm (RNLA) using received signal strength indication (RSSI) in the presence of outlier measurements in OSNs. We firstly formulated the localization problem using a log-normal shadowing model integrated with a first order Taylor series. Nevertheless, the problem was infeasible to solve, especially in the presence of outlier measurements. Hence, we then converted the localization problem into the optimization problem using squared range and weighted least square (WLS), albeit in a nonconvex form. For the sake of an accurate solution, the problem was then transformed into a generalized trust region subproblem (GTRS) combined with robust functions. Although GTRS was still a nonconvex framework, the solution could be acquired by a bisection approach. To ensure global convergence, a block prox-linear (BPL) method was incorporated with the bisection approach. In addition, we conducted the Cramer\u2013Rao low bound (CRLB) to evaluate RNLA. Simulations were carried out over variable parameters. Numerical results showed that RNLA outperformed the other algorithms under outlier measurements, notwithstanding that the time for RNLA computation was a little bit more than others in some conditions.<\/jats:p>","DOI":"10.3390\/s19122708","type":"journal-article","created":{"date-parts":[[2019,6,17]],"date-time":"2019-06-17T03:24:41Z","timestamp":1560741881000},"page":"2708","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["A Robust, Non-Cooperative Localization Algorithm in the Presence of Outlier Measurements in Ocean Sensor Networks"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1831-4329","authenticated-orcid":false,"given":"Xiaojun","family":"Mei","sequence":"first","affiliation":[{"name":"Merchant Marine College, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3150-3407","authenticated-orcid":false,"given":"Huafeng","family":"Wu","sequence":"additional","affiliation":[{"name":"Merchant Marine College, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiangfeng","family":"Xian","sequence":"additional","affiliation":[{"name":"Merchant Marine College, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bowen","family":"Chen","sequence":"additional","affiliation":[{"name":"Merchant Marine College, Shanghai Maritime University, Shanghai 201306, China"},{"name":"Department of Informatics, Linnaeus University, V\u00e4xj\u00f6 351 06, Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hao","family":"Zhang","sequence":"additional","affiliation":[{"name":"Merchant Marine College, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xia","family":"Liu","sequence":"additional","affiliation":[{"name":"Merchant Marine College, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.inffus.2018.03.005","article-title":"A Comprehensive Survey on the Reliability of Mobile Wireless Sensor Networks: Taxonomy, Challenges, and Future Directions","volume":"44","author":"Yue","year":"2018","journal-title":"Inf. Fusion"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.comcom.2019.01.002","article-title":"Efficient target detection in maritime search and rescue wireless sensor network using data fusion","volume":"136","author":"Wu","year":"2019","journal-title":"Comput. Commun."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.comcom.2018.09.007","article-title":"Missing data recovery using reconstruction in ocean wireless sensor networks","volume":"132","author":"Wu","year":"2018","journal-title":"Comput. Commun."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1017\/S0373463318000504","article-title":"Robust Ship Tracking via Multi-view Learning and Sparse Representation","volume":"72","author":"Chen","year":"2019","journal-title":"J. Navig."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1038\/d41586-018-03068-w","article-title":"Ocean sensors can track progress on climate goals","volume":"555","author":"Russell","year":"2018","journal-title":"Nature"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"John, P., Supriya, M.H., and Pillai, P.R.S. (2010, January 20\u201323). Cost effective sensor buoy for ocean environmental monitoring. Proceedings of the OCEANS 2010 MTS\/IEEE SEATTLE, Seattle, WA, USA.","DOI":"10.1109\/OCEANS.2010.5664312"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"29702","DOI":"10.3390\/s151129702","article-title":"SSL: Signal Similarity-Based Localization for Ocean Sensor Networks","volume":"15","author":"Chen","year":"2015","journal-title":"Sensors"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2028","DOI":"10.1109\/COMST.2018.2798591","article-title":"Location of Things (LoT): A Review and Taxonomy of Sensors Localization in IoT Infrastructure","volume":"20","author":"Shit","year":"2018","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Luo, J., Fan, L., Wu, S., and Yan, X. (2018). Research on Localization Algorithms Based on Acoustic Communication for Underwater Sensor Networks. Sensors, 18.","DOI":"10.3390\/s18010067"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.isatra.2017.09.013","article-title":"A novel cooperative localization algorithm using enhanced particle filter technique in maritime search and rescue wireless sensor network","volume":"78","author":"Wu","year":"2018","journal-title":"ISA Trans."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/j.sigpro.2018.08.004","article-title":"Received signal strength based localization in inhomogeneous underwater medium","volume":"154","author":"Poursheikhali","year":"2019","journal-title":"Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"e3445","DOI":"10.1002\/dac.3445","article-title":"Localization under anchor node uncertainty for underwater acoustic sensor networks","volume":"31","author":"Mridula","year":"2018","journal-title":"Int. J. Commun. Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1109\/JOE.2015.2494918","article-title":"Optimal Sensor Placement for Acoustic Underwater Target Positioning With Range-Only Measurements","volume":"41","author":"Pascoal","year":"2016","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2543","DOI":"10.1109\/TVT.2017.2764265","article-title":"Asynchronous Localization With Mobility Prediction for Underwater Acoustic Sensor Networks","volume":"67","author":"Yan","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1108\/SR-06-2017-0105","article-title":"Energy-aware localization algorithm for Ocean Internet of Things","volume":"38","author":"Guo","year":"2018","journal-title":"Sens. Rev."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3915","DOI":"10.1109\/JSEN.2014.2357331","article-title":"UREAL: Underwater Reflection-Enabled Acoustic-Based Localization","volume":"14","author":"Emokpae","year":"2014","journal-title":"IEEE Sens. J."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Yan, Y., Wang, H., Shen, X., Leng, B., and Li, S. (2018). Efficient Convex Optimization for Energy-Based Acoustic Sensor Self-Localization and Source Localization in Sensor Networks. Sensors, 18.","DOI":"10.3390\/s18051646"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Moreno-Salinas, D., Pascoal, A.M., and Aranda, J. (2018). Multiple underwater target positioning with optimally placed acoustic surface sensor networks. Int. J. Distrib. Sens. Netw., 14.","DOI":"10.1177\/1550147718773234"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1016\/j.oceaneng.2017.04.006","article-title":"A robust method for underwater wireless sensor joint localization and synchronization","volume":"137","author":"Mortazavi","year":"2017","journal-title":"Ocean Eng."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Chang, S., Li, Y., He, Y., and Hui, W. (2018). Target Localization in Underwater Acoustic Sensor Networks Using RSS Measurements. Appl. Sci., 8.","DOI":"10.3390\/app8020225"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/j.apacoust.2016.10.005","article-title":"Direct regressions for underwater acoustic source localization in fluctuating oceans","volume":"116","author":"Lefort","year":"2017","journal-title":"Appl. Acoust."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1109\/LSP.2018.2799699","article-title":"AUV-Aided Joint Localization and Time Synchronization for Underwater Acoustic Sensor Networks","volume":"25","author":"Gong","year":"2018","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Luo, J., and Fan, L. (2017). A Two-Phase Time Synchronization-Free Localization Algorithm for Underwater Sensor Networks. Sensors, 17.","DOI":"10.3390\/s17040726"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.adhoc.2016.09.003","article-title":"Fault-resilient localization for underwater sensor networks","volume":"55","author":"Das","year":"2017","journal-title":"Ad Hoc Netw."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Li, Y., Wang, Y., and Guan, X. (2018, January 28\u201330). Belief Propagation Based Multi-AUV Cooperative Localization in Anchor-free Environments. Proceedings of the 2018 Fourth Underwater Communications and Networking Conference (UComms), Lerici, Italy.","DOI":"10.1109\/UComms.2018.8493170"},{"key":"ref_26","first-page":"12","article-title":"Ship tracking of wireless sensor network based on improved adaptive particle filter","volume":"39","author":"Mei","year":"2018","journal-title":"J. Shanghai Marit. Univ."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Zaeemzadeh, A., Joneidi, M., Shahrasbi, B., and Rahnavard, N. (2017, January 22\u201325). Robust Target Localization Based on Squared Range Iterative Reweighted Least Squares. Proceedings of the 2017 IEEE 14th International Conference on Mobile Ad Hoc and Sensor Systems (MASS), Orlando, FL, USA.","DOI":"10.1109\/MASS.2017.50"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1109\/JOE.2016.2578218","article-title":"Kernel-Function-Based Models for Acoustic Localization of Underwater Vehicles","volume":"42","author":"Pinheiro","year":"2017","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1109\/TCOMM.2018.2875083","article-title":"Outlier Detection and Optimal Anchor Placement for 3-D Underwater Optical Wireless Sensor Network Localization","volume":"67","author":"Saeed","year":"2019","journal-title":"IEEE Trans. Commun."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.1109\/JOE.2017.2736951","article-title":"LocDyn: Robust Distributed Localization for Mobile Underwater Networks","volume":"42","author":"Soares","year":"2017","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1386","DOI":"10.1121\/1.395273","article-title":"Nonlinear and non-Gaussian ocean noise","volume":"82","author":"Brockett","year":"1987","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1080\/10556789308805542","article-title":"Generalizations of the trust region problem","volume":"2","author":"More","year":"1993","journal-title":"Optim. Methods Softw."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Peng, H., and Fan, Y. (2017, January 4\u20139). A General Framework for Sparsity Regularized Feature Selection via Iteratively Reweighted Least Square Minimization. Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, San Francisco, CA, USA.","DOI":"10.1609\/aaai.v31i1.10833"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Lerman, G., and Maunu, T. (2018). Fast, Robust and Non-convex Subspace Recovery. arXiv.","DOI":"10.1093\/imaiai\/iax012"},{"key":"ref_35","first-page":"1248","article-title":"Robust statistics","volume":"78","author":"Huber","year":"2011","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1007\/s10915-017-0376-0","article-title":"A Globally Convergent Algorithm for Nonconvex Optimization Based on Block Coordinate Update","volume":"72","author":"Xu","year":"2017","journal-title":"J. Sci. Comput."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"465","DOI":"10.2307\/1269750","article-title":"Fundamentals of Statistical Signal Processing: Estimation Theory","volume":"37","author":"Sengupta","year":"1995","journal-title":"Technometrics"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"3197","DOI":"10.1109\/TVT.2016.2589923","article-title":"3-D Target Localization in Wireless Sensor Networks Using RSS and AoA Measurements","volume":"66","author":"Tomic","year":"2017","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1835","DOI":"10.1016\/j.patcog.2009.11.017","article-title":"Restoration of images corrupted by Gaussian and uniform impulsive noise","volume":"43","year":"2010","journal-title":"Pattern Recognit."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Lathuili\u00e8re, S., Mesejo, P., Alameda-Pineda, X., and Horaud, R. (2018). DeepGUM: Learning Deep Robust Regression with a Gaussian-Uniform Mixture Model. arXiv.","DOI":"10.1007\/978-3-030-01228-1_13"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"3545","DOI":"10.1109\/TIM.2015.2469434","article-title":"Using Gaussian-Uniform Mixture Models for Robust Time-Interval Measurement","volume":"64","author":"Carbone","year":"2015","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_42","unstructured":"Sgurev, V., Jotsov, V., and Kacprzyk, J. (2018). Clustering Non-Gaussian Data Using Mixture Estimation with Uniform Components BT\u2014Practical Issues of Intelligent Innovations. Practical Issues of Intelligent Innovations, Springer International Publishing."},{"key":"ref_43","first-page":"188","article-title":"Real-time localization algorithm for maritime search and rescue wireless sensor network","volume":"2013","author":"Wu","year":"2013","journal-title":"Int. J. Distrib. Sens. Netw."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/12\/2708\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:58:53Z","timestamp":1760187533000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/12\/2708"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,16]]},"references-count":43,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2019,6]]}},"alternative-id":["s19122708"],"URL":"https:\/\/doi.org\/10.3390\/s19122708","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,6,16]]}}}