{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T14:38:19Z","timestamp":1784126299745,"version":"3.55.0"},"reference-count":31,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2020,8,20]],"date-time":"2020-08-20T00:00:00Z","timestamp":1597881600000},"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"}]},{"name":"Shanghai Committee of Science and Technology, China","award":["18040501700"],"award-info":[{"award-number":["18040501700"]}]},{"name":"Top-notch innovative program for postgraduates of Shanghai Maritime University","award":["2019YBR002"],"award-info":[{"award-number":["2019YBR002"]}]},{"name":"Top-notch innovative program for postgraduates of Shanghai Maritime University","award":["2019YBR006"],"award-info":[{"award-number":["2019YBR006"]}]},{"name":"Postgraduate innovation foundation of Shanghai Maritime University","award":["2017ycx030"],"award-info":[{"award-number":["2017ycx030"]}]},{"name":"Postgraduate innovation foundation of Shanghai Maritime University","award":["2016ycx042"],"award-info":[{"award-number":["2016ycx042"]}]},{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["201908310079"],"award-info":[{"award-number":["201908310079"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Localization is an indispensable technology for underwater wireless sensor networks (UWSNs). In what concerns UWSNs, the accurate location information is not only the requirement of the marine field applications but also the basis of the other corresponding research, for instance, network routing and topology control. Recently, an astonishing surge of interest has been drawn in the received signal strength (RSS)-based scheme due to cost-effectiveness and synchronization-free compared with others. However, unlike the terrestrial wireless sensor networks (WSNs), the acoustic signal may suffer the absorption loss in the underwater environment besides the path loss, which degrades the localization accuracy and limits the capability of the RSS-based technology in UWSNs. In this context, a robust localization method with an absorption mitigation technique (AMT) is developed. First, an RSS-based analytically tractable measurement model is conducted, where the maximum likelihood estimator (MLE) is derived. Nevertheless, it is quite challenging to solve the problem using MLE under a non-convex expression. Therefore, by exploiting certain approximations, the considered localization problem is converted into an optimization expression with a maximum absorption loss involved. A min\u2013max strategy is then presented, with which the problem is turned to minimize the worst situation of the absorption loss. After a simple manipulation, the problem is further investigated as a generalized trust region sub-problem (GTRS) framework. Although the GTRS is a non-convex scheme, the solution can be obtained through an iteration method by introducing a multiplier. In addition, the closed-form expression of the Cramer\u2013Rao lower bound (CRLB) of the analytically tractable measurement model is derived. Numerical simulations demonstrate the effectiveness of the proposed method compared with the state-of-the-art approaches in different scenarios.<\/jats:p>","DOI":"10.3390\/s20174698","type":"journal-article","created":{"date-parts":[[2020,8,20]],"date-time":"2020-08-20T09:35:31Z","timestamp":1597916131000},"page":"4698","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["An Absorption Mitigation Technique for Received Signal Strength-Based Target Localization in Underwater Wireless Sensor Networks"],"prefix":"10.3390","volume":"20","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"},{"name":"Institute for Systems and Robotics, Instituto Superior T\u00e9cnico, University of Lisbon, 1049-001 Lisbon, Portugal"}],"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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5123-5139","authenticated-orcid":false,"given":"Nasir","family":"Saeed","sequence":"additional","affiliation":[{"name":"Computer, Electrical, Mathematical Sciences &amp; Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5609-7388","authenticated-orcid":false,"given":"Teng","family":"Ma","sequence":"additional","affiliation":[{"name":"Institute for Systems and Robotics, Instituto Superior T\u00e9cnico, University of Lisbon, 1049-001 Lisbon, Portugal"},{"name":"Science and Technology on Underwater Vehicle Laboratory, Harbin Engineering University, Harbin 150001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiangfeng","family":"Xian","sequence":"additional","affiliation":[{"name":"Merchant Marine College, Shanghai Maritime University, Shanghai 201306, China"},{"name":"Department of Electronics and Telecommunications, Politecnico di Torino, 10129 Torino, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9659-4880","authenticated-orcid":false,"given":"Yanzhen","family":"Chen","sequence":"additional","affiliation":[{"name":"Merchant Marine College, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"690","DOI":"10.1038\/s41467-018-03158-3","article-title":"Ocean science research is key for a sustainable future","volume":"9","author":"Visbeck","year":"2018","journal-title":"Nat. Commun."},{"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":"2652","DOI":"10.1109\/TWC.2019.2906309","article-title":"Localization of Energy Harvesting Empowered Underwater Optical Wireless Sensor Networks","volume":"18","author":"Saeed","year":"2019","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Wu, H., Meng, Q., Xian, J., Mei, X., Claramunt, C., and Cao, J. (2019). An Information Entropy Based Event Boundary Detection Algorithm in Wireless Sensor Networks. Symmetry, 11.","DOI":"10.3390\/sym11040537"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1016\/j.comcom.2020.06.034","article-title":"NMTLAT: A New robust mobile Multi-Target Localization and Tracking Scheme in marine search and rescue wireless sensor networks under Byzantine attack","volume":"160","author":"Xian","year":"2020","journal-title":"Comput. Commun."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"96879","DOI":"10.1109\/ACCESS.2019.2928876","article-title":"Underwater Wireless Sensor Networks: A Survey on Enabling Technologies, Localization Protocols, and Internet of Underwater Things","volume":"7","author":"Jouhari","year":"2019","journal-title":"IEEE Access"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Mei, X., Wu, H., and Xian, J. (2020). Matrix Factorization based Target Localization via Range Measurements with Uncertainty in Transmit Power. IEEE Wirel. Commun. Lett., 1.","DOI":"10.1109\/LWC.2020.2998609"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/j.isatra.2020.04.007","article-title":"An AUV localization and path planning algorithm for terrain-aided navigation","volume":"103","author":"Teng","year":"2020","journal-title":"ISA Trans."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"101935","DOI":"10.1016\/j.adhoc.2019.101935","article-title":"Underwater optical wireless communications, networking, and localization: A survey","volume":"94","author":"Saeed","year":"2019","journal-title":"Ad Hoc Netw."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Chang, S., Li, Y., He, Y., and Wu, Y. (2019). RSS-Based Target Localization in Underwater Acoustic Sensor Networks via Convex Relaxation. Sensors, 19.","DOI":"10.3390\/s19102323"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"45693","DOI":"10.1109\/ACCESS.2019.2909133","article-title":"Localization and Detection of Targets in Underwater Wireless Sensor Using Distance and Angle Based Algorithms","volume":"7","author":"Ullah","year":"2019","journal-title":"IEEE Access"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Xu, T., Hu, Y., Zhang, B., and Leus, G. (2016, January 20\u201325). RSS-based sensor localization in underwater acoustic sensor networks. Proceedings of the 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Shanghai, China.","DOI":"10.1109\/ICASSP.2016.7472409"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Mei, X., Wu, H., Xian, J., Chen, B., Zhang, H., and Liu, X. (2019). A Robust, Non-Cooperative Localization Algorithm in the Presence of Outlier Measurements in Ocean Sensor Networks. Sensors, 19.","DOI":"10.3390\/s19122708"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1109\/MCOM.2009.4752682","article-title":"Underwater acoustic communication channels: Propagation models and statistical characterization","volume":"47","author":"Stojanovic","year":"2009","journal-title":"IEEE Commun. Mag."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"e3350","DOI":"10.1002\/dac.3350","article-title":"A survey on deployment techniques, localization algorithms, and research challenges for underwater acoustic sensor networks","volume":"30","author":"Tuna","year":"2017","journal-title":"Int. J. Commun. Syst."},{"key":"ref_17","unstructured":"Nasir, S., Abdulkadir, C., Mohamed-Slim, A., and Al-Naffouri, T.Y. (2019). Analysis of 3D Localization in Underwater Optical Wireless Networks with Uncertain Anchor Positions. Sci. CHINA Inf. Sci."},{"key":"ref_18","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_19","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":"Saleheh","year":"2019","journal-title":"Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1109\/LSP.2019.2892225","article-title":"A Linear Estimator for Network Localization Using Integrated RSS and AOA Measurements","volume":"26","author":"Tomic","year":"2019","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1109\/LCOMM.2019.2963834","article-title":"A Majorization-Minimization based Target Localization Problem from Range Measurements","volume":"24","author":"Gao","year":"2020","journal-title":"IEEE Commun. Lett."},{"key":"ref_22","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_23","doi-asserted-by":"crossref","first-page":"3607","DOI":"10.1109\/COMST.2018.2855063","article-title":"A Survey of Enabling Technologies for Network Localization, Tracking, and Navigation","volume":"20","author":"Laoudias","year":"2018","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_24","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_25","doi-asserted-by":"crossref","first-page":"2585","DOI":"10.1007\/s11276-019-02023-5","article-title":"Underwater sensor networks localization based on mobility-constrained beacon","volume":"26","author":"Guo","year":"2020","journal-title":"Wirel. Netw."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Ali, M.F., Jayakody, D.N.K., Chursin, Y.A., Affes, S., and Dmitry, S. (2019). Recent Advances and Future Directions on Underwater Wireless Communications. Arch. Comput. Methods Eng., 1\u201334.","DOI":"10.1007\/s11831-019-09354-8"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Stojanovic, M. (2006, January 25). On the Relationship between Capacity and Distance in an Underwater Acoustic Communication Channel. Proceedings of the 1st ACM International Workshop on Underwater Networks, Los Angeles, CA, USA.","DOI":"10.1145\/1161039.1161049"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3105","DOI":"10.3390\/s19143105","article-title":"An Efficient RSS Localization for Underwater Wireless Sensor Networks","volume":"19","author":"L","year":"2019","journal-title":"Sensors"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"175275","DOI":"10.1155\/2014\/175275","article-title":"Efficient Underwater RSS Value to Distance Inversion Using the Lambert Function","volume":"2014","author":"Hosseini","year":"2014","journal-title":"Math. Probl. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1109\/JOE.2015.2433851","article-title":"Development of Underwater Short-Range Sensor Using Electromagnetic Wave Attenuation","volume":"41","author":"Park","year":"2016","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_31","unstructured":"Kay, S.M. (1993). Fundamentals of Statistical Signal Processing: Estimation Theory, Prentice-Hall."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/17\/4698\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:03:53Z","timestamp":1760177033000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/17\/4698"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,20]]},"references-count":31,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2020,9]]}},"alternative-id":["s20174698"],"URL":"https:\/\/doi.org\/10.3390\/s20174698","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,20]]}}}