{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:18:34Z","timestamp":1760149114683,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2023,7,11]],"date-time":"2023-07-11T00:00:00Z","timestamp":1689033600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Portuguese Foundation for Science and Technology","doi-asserted-by":"publisher","award":["2022.09452.BD","POCI-01-0247-FEDER-045941","COMPETE2020"],"award-info":[{"award-number":["2022.09452.BD","POCI-01-0247-FEDER-045941","COMPETE2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"name":"K2D: Knowledge and Data from the Deep to Space","award":["2022.09452.BD","POCI-01-0247-FEDER-045941","COMPETE2020"],"award-info":[{"award-number":["2022.09452.BD","POCI-01-0247-FEDER-045941","COMPETE2020"]}]},{"name":"Operational Program for Competitiveness and Internationalization","award":["2022.09452.BD","POCI-01-0247-FEDER-045941","COMPETE2020"],"award-info":[{"award-number":["2022.09452.BD","POCI-01-0247-FEDER-045941","COMPETE2020"]}]},{"name":"MIT Portugal Program","award":["2022.09452.BD","POCI-01-0247-FEDER-045941","COMPETE2020"],"award-info":[{"award-number":["2022.09452.BD","POCI-01-0247-FEDER-045941","COMPETE2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Accurate localization is a critical task in underwater navigation. Typical localization methods use a set of acoustic sensors and beacons to estimate relative position, whose geometric configuration has a significant impact on the localization accuracy. Although there is much effort in the literature to define optimal 2D or 3D sensor placement, the optimal sensor placement in irregular and constrained 3D surfaces, such as autonomous underwater vehicles (AUVs) or other structures, is not exploited for improving localization. Additionally, most applications using AUVs employ commercial acoustic modems or compact arrays, therefore the optimization of the placement of spatially independent sensors is not a considered issue. This article tackles acoustic sensor placement optimization in irregular and constrained 3D surfaces, for inverted ultra-short baseline (USBL) approaches, to improve localization accuracy. The implemented multi-objective memetic algorithm combines an evaluation of the geometric sensor\u2019s configuration, using the Cramer-Rao Lower Bound (CRLB), with the incidence angle of the received signal. A case study is presented over a simulated homing and docking scenario to demonstrate the proposed optimization algorithm.<\/jats:p>","DOI":"10.3390\/s23146316","type":"journal-article","created":{"date-parts":[[2023,7,12]],"date-time":"2023-07-12T01:05:01Z","timestamp":1689123901000},"page":"6316","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Sensor Placement in an Irregular 3D Surface for Improving Localization Accuracy Using a Multi-Objective Memetic Algorithm"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6317-0897","authenticated-orcid":false,"given":"Paula A.","family":"Gra\u00e7a","sequence":"first","affiliation":[{"name":"INESC TEC\u2014Institute for Systems and Computer Engineering, Technology and Science, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"given":"Jos\u00e9 C.","family":"Alves","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5508-0576","authenticated-orcid":false,"given":"Bruno M.","family":"Ferreira","sequence":"additional","affiliation":[{"name":"INESC TEC\u2014Institute for Systems and Computer Engineering, Technology and Science, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/j.fmre.2021.03.002","article-title":"Underwater robot sensing technology: A survey","volume":"1","author":"Cong","year":"2021","journal-title":"Fundam. Res."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"113861","DOI":"10.1016\/j.oceaneng.2023.113861","article-title":"Autonomous Underwater Vehicle navigation: A review","volume":"273","author":"Zhang","year":"2023","journal-title":"Ocean. Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"6403161","DOI":"10.1155\/2020\/6403161","article-title":"A review of underwater localization techniques, algorithms, and challenges","volume":"2020","author":"Su","year":"2020","journal-title":"J. Sens."},{"key":"ref_4","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_5","doi-asserted-by":"crossref","first-page":"100241","DOI":"10.1016\/j.cosrev.2020.100241","article-title":"Localization schemes for Underwater Acoustic Sensor Networks\u2014A Review","volume":"37","author":"Toky","year":"2020","journal-title":"Comput. Sci. Rev."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"101845","DOI":"10.1016\/j.apor.2019.06.002","article-title":"Survey of underwater robot positioning navigation","volume":"90","author":"Wu","year":"2019","journal-title":"Appl. Ocean. Res."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1016\/j.automatica.2009.12.003","article-title":"Optimality analysis of sensor-target localization geometries","volume":"46","author":"Bishop","year":"2010","journal-title":"Automatica"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.oceaneng.2017.06.033","article-title":"Optimal sensor configuration for positioning seafloor geodetic node","volume":"142","author":"Zou","year":"2017","journal-title":"Ocean. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.eswa.2015.11.008","article-title":"Sensor placement determination for range-difference positioning using evolutionary multi-objective optimization","volume":"47","author":"Wieser","year":"2016","journal-title":"Expert Syst. Appl."},{"key":"ref_10","first-page":"1550147718773234","article-title":"Multiple underwater target positioning with optimally placed acoustic surface sensor networks","volume":"14","author":"Pascoal","year":"2018","journal-title":"Int. J. Distrib. Sens. Netw."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"D\u00edez-Gonz\u00e1lez, J., Verde, P., Ferrero-Guill\u00e9n, R., \u00c1lvarez, R., and P\u00e9rez, H. (2020). Hybrid memetic algorithm for the node location problem in local positioning systems. Sensors, 20.","DOI":"10.3390\/s20195475"},{"key":"ref_12","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_13","doi-asserted-by":"crossref","unstructured":"Ferreira, B., Matos, A., and Cruz, N. (2013, January 5\u20138). Optimal positioning of autonomous marine vehicles for underwater acoustic source localization using TOA measurements. Proceedings of the 2013 IEEE International Underwater Technology Symposium (UT), Tokyo, Japan.","DOI":"10.1109\/UT.2013.6519898"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/j.oceaneng.2019.04.011","article-title":"Advancements in the field of autonomous underwater vehicle","volume":"181","author":"Sahoo","year":"2019","journal-title":"Ocean. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Rypkema, N.R., Fischell, E.M., and Schmidt, H. (June, January 9). One-way travel-time inverted ultra-short baseline localization for low-cost autonomous underwater vehicles. Proceedings of the 2017 IEEE International Conference on Robotics and Automation (ICRA), Singapore.","DOI":"10.1109\/ICRA.2017.7989570"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Gonz\u00e1lez-Garc\u00eda, J., G\u00f3mez-Espinosa, A., Cuan-Urquizo, E., Garc\u00eda-Valdovinos, L.G., Salgado-Jim\u00e9nez, T., and Cabello, J.A.E. (2020). Autonomous underwater vehicles: Localization, navigation, and communication for collaborative missions. Appl. Sci., 10.","DOI":"10.3390\/app10041256"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Diamant, R., Voronin, V., and Kebkal, K.G. (2019, January 17\u201320). Design Structure of SYMBIOSIS: An Opto-Acoustic System for Monitoring Pelagic Fish. Proceedings of the OCEANS 2019\u2014Marseille, Marseille, France.","DOI":"10.1109\/OCEANSE.2019.8867440"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Costanzi, R., Monnini, N., Ridolfi, A., Allotta, B., and Caiti, A. (2017, January 19\u201322). On field experience on underwater acoustic localization through USBL modems. Proceedings of the OCEANS 2017\u2014Aberdeen, Aberdeen, UK.","DOI":"10.1109\/OCEANSE.2017.8084996"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1109\/JSTSP.2019.2899732","article-title":"An underwater acoustic positioning algorithm for compact arrays with arbitrary configuration","volume":"13","author":"Sun","year":"2019","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Dubrovinskaya, E., Kebkal, V., Kebkal, O., Kebkal, K., and Casari, P. (2020). Underwater localization via wideband Direction-of-Arrival estimation using acoustic arrays of arbitrary shape. Sensors, 20.","DOI":"10.3390\/s20143862"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"D\u00edez-Gonz\u00e1lez, J., \u00c1lvarez, R., Gonz\u00e1lez-B\u00e1rcena, D., S\u00e1nchez-Gonz\u00e1lez, L., Castej\u00f3n-Limas, M., and Perez, H. (2019). Genetic algorithm approach to the 3D node localization in TDOA systems. Sensors, 19.","DOI":"10.3390\/s19183880"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Yang, J., Cai, Y., Tang, D., and Liu, Z. (2019). A novel centralized range-free static node localization algorithm with memetic algorithm and L\u00e9vy flight. Sensors, 19.","DOI":"10.3390\/s19143242"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Villa, M., Ferreira, B., and Cruz, N. (2022). Genetic Algorithm to Solve Optimal Sensor Placement for Underwater Vehicle Localization with Range Dependent Noises. Sensors, 22.","DOI":"10.3390\/s22197205"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1109\/TSMCC.2010.2049649","article-title":"Bio-inspired algorithms for autonomous deployment and localization of sensor nodes","volume":"40","author":"Kulkarni","year":"2010","journal-title":"IEEE Trans. Syst. Man Cybern. Part C (Appl. Rev.)"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Tholen, C., El-Mihoub, T.A., Nolle, L., Ralle, O., and Rofallski, R. (2020, January 9\u201312). Optimal Receiver Configuration Of Short-Baseline Localisation Systems Using Particle Swarm Optimisation. Proceedings of the 34th International ECMS Conference on Modelling and Simulation, Wildau, Germany.","DOI":"10.7148\/2020-0025"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Yan, Z., Li, J., Wu, Y., and Zhang, G. (2019). A real-time path planning algorithm for AUV in unknown underwater environment based on combining PSO and waypoint guidance. Sensors, 19.","DOI":"10.3390\/s19010020"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1109\/TEVC.2005.850260","article-title":"A tutorial for competent memetic algorithms: Model, taxonomy, and design issues","volume":"9","author":"Krasnogor","year":"2005","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Gra\u00e7a, P.A., Alves, J.C., and Ferreira, B.M. (2022, January 17\u201320). Multi-Objective optimization of Sensor Placement in a 3D Body for Underwater Localization. Proceedings of the OCEANS 2022, Hampton Roads, VA, USA.","DOI":"10.1109\/OCEANS47191.2022.9977053"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.apor.2018.05.011","article-title":"Investigation on underwater positioning stochastic model based on acoustic ray incidence angle","volume":"77","author":"Zhao","year":"2018","journal-title":"Appl. Ocean. Res."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Watson, S., Duecker, D.A., and Groves, K. (2020). Localisation of unmanned underwater vehicles (UUVs) in complex and confined environments: A review. Sensors, 20.","DOI":"10.3390\/s20216203"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Lin, R., Zhang, F., Li, D., Lin, M., Zhou, G., and Yang, C. (2021). An improved localization method for the transition between autonomous underwater vehicle homing and docking. Sensors, 21.","DOI":"10.3390\/s21072468"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"e02319","DOI":"10.1016\/j.heliyon.2019.e02319","article-title":"New approaches for Delaunay triangulation and optimisation","volume":"5","author":"Perumal","year":"2019","journal-title":"Heliyon"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2316","DOI":"10.1109\/TSP.2020.2985645","article-title":"Optimal sensor placement for 2-D range-only target localization in constrained sensor geometry","volume":"68","author":"Sadeghi","year":"2020","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"8228","DOI":"10.1109\/TWC.2018.2875432","article-title":"Underwater anchor-AUV localization geometries with an isogradient sound speed profile: A CRLB-based optimality analysis","volume":"17","author":"Zhang","year":"2018","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1109\/JOE.2006.880386","article-title":"Robust range-only beacon localization","volume":"31","author":"Olson","year":"2006","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_36","first-page":"34","article-title":"Crossover operators in genetic algorithms: A review","volume":"162","author":"Kora","year":"2017","journal-title":"Int. J. Comput. Appl."},{"key":"ref_37","unstructured":"Hoos, H.H., and St\u00fctzle, T. (2015). Springer Handbook of Computational Intelligence, Springer."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"103382","DOI":"10.1016\/j.robot.2019.103382","article-title":"A survey of underwater docking guidance systems","volume":"124","author":"Yazdani","year":"2020","journal-title":"Robot. Auton. Syst."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1729881418801739","DOI":"10.1177\/1729881418801739","article-title":"A single acoustic beacon-based positioning method for underwater mobile recovery of an AUV","volume":"15","author":"Zhou","year":"2018","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1007\/s00773-018-0577-8","article-title":"AUV docking based on USBL navigation and vision guidance","volume":"24","author":"Fan","year":"2019","journal-title":"J. Mar. Sci. Technol."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Piskura, J.C., Purcell, M., Stokey, R., Austin, T., Tebo, D., Christensen, R., and Jaffre, F. (2016, January 19\u201323). Development of a robust Line Capture, Line Recovery (LCLR) technology for autonomous docking of AUVs. Proceedings of the OCEANS 2016 MTS\/IEEE Monterey, Monterey, CA, USA.","DOI":"10.1109\/OCEANS.2016.7761255"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Ferreira, B., Matos, A., and Cruz, N. (2010, January 20\u201323). Single beacon navigation: Localization and control of the MARES AUV. Proceedings of the OCEANS 2010 MTS\/IEEE SEATTLE, Seattle, WA, USA.","DOI":"10.1109\/OCEANS.2010.5664518"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.robot.2014.09.035","article-title":"Homing a robot with range-only measurements under unknown drifts","volume":"67","author":"Ferreira","year":"2015","journal-title":"Robot. Auton. Syst."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Cruz, N.A., Matos, A.C., Almeida, R.M., and Ferreira, B.M. (2017, January 21\u201324). A lightweight docking station for a hovering AUV. Proceedings of the 2017 IEEE Underwater Technology (UT), Busan, Republic of Korea.","DOI":"10.1109\/UT.2017.7890314"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"19","DOI":"10.4031\/MTSJ.44.2.5","article-title":"Modeling and control of the MARES autonomous underwater vehicle","volume":"44","author":"Ferreira","year":"2010","journal-title":"Mar. Technol. Soc. J."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/14\/6316\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:10:55Z","timestamp":1760127055000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/14\/6316"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,11]]},"references-count":45,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["s23146316"],"URL":"https:\/\/doi.org\/10.3390\/s23146316","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2023,7,11]]}}}