{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T03:00:56Z","timestamp":1760151656598,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,4,18]],"date-time":"2022-04-18T00:00:00Z","timestamp":1650240000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000270","name":"Natural Environment Research Council","doi-asserted-by":"publisher","award":["NE\/N012070\/1"],"award-info":[{"award-number":["NE\/N012070\/1"]}],"id":[{"id":"10.13039\/501100000270","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["NE\/N012070\/1"],"award-info":[{"award-number":["NE\/N012070\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>Particle swarm optimisation (PSO) is a swarm intelligence algorithm used for controlling robotic swarms in applications such as source localisation. However, conventional PSO algorithms consider only the intensity of the received signal. Wavefield signals, such as propagating underwater acoustic waves, permit the measurement of higher order statistics that can be used to provide additional information about the location of the source and thus improve overall swarm performance. Wavefield correlation techniques that make use of such information are already used in multi-element hydrophone array systems for the localisation of underwater marine sources. Additionally, the simplest model of a multi-element array (a two-element array) is characterised by operational simplicity and low-cost, which matches the ethos of robotic swarms. Thus, in this paper, three novel approaches are introduced that enable PSO to consider the higher order statistics available in wavefield measurements. In simulations, they are shown to outperform the standard intensity-based PSO in terms of robustness to low signal-to-noise ratio (SNR) and convergence speed. The best performing approach, cross-correlation bearing PSO (XB-PSO), is capable of converging to the source from as low as \u22125 dB initial SNR. The original PSO algorithm only manages to converge at 10 dB and at this SNR, XB-PSO converges 4 times faster.<\/jats:p>","DOI":"10.3390\/robotics11020052","type":"journal-article","created":{"date-parts":[[2022,4,19]],"date-time":"2022-04-19T02:39:31Z","timestamp":1650335971000},"page":"52","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Source Localisation Using Wavefield Correlation-Enhanced Particle Swarm Optimisation"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0522-812X","authenticated-orcid":false,"given":"George","family":"Rossides","sequence":"first","affiliation":[{"name":"Marine Robotics Innovation Centre, Cyprus Marine and Maritime Institute, Larnaca 6023, Cyprus"},{"name":"Department of Electronic & Electrical Engineering, University of Bath, Bath BA2 7AY, UK"}]},{"given":"Alan","family":"Hunter","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4279-8930","authenticated-orcid":false,"given":"Benjamin","family":"Metcalfe","sequence":"additional","affiliation":[{"name":"Department of Electronic & Electrical Engineering, University of Bath, Bath BA2 7AY, UK"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"100565","DOI":"10.1016\/j.swevo.2019.100565","article-title":"Review of methodologies and tasks in swarm robotics towards standardization","volume":"50","author":"Nedjah","year":"2019","journal-title":"Swarm Evol. Comput."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Lon\u010dar, I., Babi\u0107, A., Arbanas, B., Vasiljevi\u0107, G., Petrovi\u0107, T., Bogdan, S., and Mi\u0161kovi\u0107, N. (2019). A Heterogeneous Robotic Swarm for Long-Term Monitoring of Marine Environments. Appl. Sci., 9.","DOI":"10.3390\/app9071388"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Gupta, R., and Bayal, R.K. (2020, January 14\u201316). Source Detection of Oil Spill using Modified Glowworm Swarm optimization. Proceedings of the 2020 5th International Conference on Computing, Communication and Security (ICCCS), Patna, India.","DOI":"10.1109\/ICCCS49678.2020.9276960"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Griffiths S\u00e0nchez, N.D., Vargas, P.A., and Couceiro, M.S. (2018, January 8\u201313). A Darwinian Swarm Robotics Strategy Applied to Underwater Exploration. Proceedings of the 2018 IEEE Congress on Evolutionary Computation (CEC), Rio de Janeiro, Brazil.","DOI":"10.1109\/CEC.2018.8477738"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1016\/j.robot.2015.08.010","article-title":"Search and tracking algorithms for swarms of robots: A survey","volume":"75","author":"Senanayake","year":"2016","journal-title":"Robot. Auton. Syst."},{"key":"ref_6","unstructured":"Kennedy, J., and Eberhart, R. (1995, January 10\u201313). Particle swarm optimization. Proceedings of the ICNN\u201995\u2014International Conference on Neural Networks, Nanjing, China."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/s11721-008-0021-5","article-title":"Glowworm swarm optimization for simultaneous capture of multiple local optima of multimodal functions","volume":"3","author":"Krishnanand","year":"2009","journal-title":"Swarm Intell."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1109\/MCI.2006.329691","article-title":"Ant colony optimization","volume":"1","author":"Dorigo","year":"2006","journal-title":"IEEE Comput. Intell. Mag."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1504\/IJBIC.2010.032124","article-title":"Firefly Algorithm, Stochastic Test Functions and Design Optimisation","volume":"2","author":"Yang","year":"2010","journal-title":"Int. J. Bio-Inspired Comput."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1007\/s10514-006-7567-0","article-title":"Particle swarm-based olfactory guided search","volume":"20","author":"Marques","year":"2006","journal-title":"Auton. Robot."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"10415","DOI":"10.3390\/s111110415","article-title":"Collective Odor Source Estimation and Search in Time-Variant Airflow Environments Using Mobile Robots","volume":"11","author":"Meng","year":"2011","journal-title":"Sensors"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"106228","DOI":"10.1016\/j.buildenv.2019.106228","article-title":"Source localization in dynamic indoor environments with natural ventilation: An experimental study of a particle swarm optimization-based multi-robot olfaction method","volume":"161","author":"Feng","year":"2019","journal-title":"Build. Environ."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1221","DOI":"10.1080\/01691864.2013.819605","article-title":"A PSO multi-robot exploration approach over unreliable MANETs","volume":"27","author":"Couceiro","year":"2013","journal-title":"Adv. Robot."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"76328","DOI":"10.1109\/ACCESS.2019.2921621","article-title":"Extended PSO Based Collaborative Searching for Robotic Swarms with Practical Constraints","volume":"7","author":"Yang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Rossides, G., Metcalfe, B., and Hunter, A. (2021). Particle Swarm Optimization\u2014An Adaptation for the Control of Robotic Swarms. Robotics, 10.","DOI":"10.3390\/robotics10020058"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Hereford, J.M., Siebold, M., and Nichols, S. (2007, January 1\u20135). Using the Particle Swarm Optimization Algorithm for Robotic Search Applications. Proceedings of the 2007 IEEE Swarm Intelligence Symposium, Honolulu, HI, USA.","DOI":"10.1109\/SIS.2007.368026"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Perreault, L., Wittie, M.P., and Sheppard, J. (2014, January 9\u201312). Communication-aware distributed PSO for dynamic robotic search. Proceedings of the 2014 IEEE Symposium on Swarm Intelligence, Orlando, FL, USA.","DOI":"10.1109\/SIS.2014.7011777"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"226484","DOI":"10.1109\/ACCESS.2020.3045177","article-title":"A Novel Approach for Swarm Robotic Target Searches Based on the DPSO Algorithm","volume":"8","author":"Du","year":"2020","journal-title":"IEEE Access"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1007\/s11277-019-06743-x","article-title":"A Dynamic Inertial Weight Strategy in Micro PSO for Swarm Robots","volume":"110","author":"Bakhale","year":"2020","journal-title":"Wirel. Pers. Commun."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Poursheikhali, S., and Zamiri-Jafarian, H. (2015, January 29). TDOA based target localization in inhomogenous underwater wireless sensor network. Proceedings of the 2015 5th International Conference on Computer and Knowledge Engineering (ICCKE), Mashhad, Iran.","DOI":"10.1109\/ICCKE.2015.7365873"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"36645","DOI":"10.1109\/ACCESS.2018.2852636","article-title":"Underwater Source Localization Using TDOA and FDOA Measurements with Unknown Propagation Speed and Sensor Parameter Errors","volume":"6","author":"Zhang","year":"2018","journal-title":"IEEE Access"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Li, P., Zhang, X., and Zhang, W. (2019). Direction of Arrival Estimation Using Two Hydrophones: Frequency Diversity Technique for Passive Sonar. Sensors, 19.","DOI":"10.3390\/s19092001"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11721-017-0141-x","article-title":"Particle swarm stability: A theoretical extension using the non-stagnate distribution assumption","volume":"12","author":"Cleghorn","year":"2018","journal-title":"Swarm Intell."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Yang, S., Ong, Y.S., and Jin, Y. (2007). Particle Swarm Optimization in Dynamic Environments. Evolutionary Computation in Dynamic and Uncertain Environments, Springer.","DOI":"10.1007\/978-3-540-49774-5"},{"key":"ref_25","unstructured":"Carlisle, A., and Dozier, G. (2000, January 11\u201314). Adapting Particle Swarm Optimization to Dynamic Environments. Proceedings of the International Conference on Artificial Intelligence, Acapulco, Mexico."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Fernandez-Marquez, J.L., and Arcos, J.L. (2009, January 8\u201312). An Evaporation Mechanism for Dynamic and Noisy Multimodal Optimization. Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation (GECCO \u201909), Montreal, QC, Canada.","DOI":"10.1145\/1569901.1569905"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"193","DOI":"10.3758\/BF03192887","article-title":"Forgetting functions","volume":"29","author":"White","year":"2001","journal-title":"Anim. Learn. Behav."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Munoz, D., Bouchereau, F., Vargas, C., and Enriquez, R. (2009). CHAPTER 2\u2014Signal Parameter Estimation for the Localization Problem. Position Location Techniques and Applications, Academic Press.","DOI":"10.1016\/B978-0-12-374353-4.00008-9"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Zhang, J., Cao, L., Zhang, Z., and Xu, J. (2017, January 17\u201319). Research on the signal separation method based on multi-sensor cross-correlation fusion algorithm. Proceedings of the 2017 3rd IEEE International Conference on Control Science and Systems Engineering (ICCSSE), Beijing, China.","DOI":"10.1109\/CCSSE.2017.8087995"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Mikhael, M.R.M., Alink, M.S.O., and Kokkeler, A.B.J. (2019, January 22\u201325). Using Multiple Chains in Cross-Correlation Receivers to Improve Sensitivity. Proceedings of the 2019 IEEE 90th Vehicular Technology Conference (VTC2019-Fall), Honolulu, HI, USA.","DOI":"10.1109\/VTCFall.2019.8891593"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Schneider, P.J., and Eberly, D.H. (2003). CHAPTER 7-INTERSECTION IN 2D. Geometric Tools for Computer Graphics, Morgan Kaufmann.","DOI":"10.1016\/B978-155860594-7\/50010-2"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Railey, K. (2018). Demonstration of Passive Acoustic Detection and Tracking of Unmanned Underwater Vehicles. [Ph.D. Thesis, Massachusetts Institute of Technology].","DOI":"10.1575\/1912\/10414"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3942","DOI":"10.1121\/10.0002954","article-title":"An acoustic remote sensing method for high-precision propeller rotation and speed estimation of unmanned underwater vehicles","volume":"148","author":"Railey","year":"2020","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"A34","DOI":"10.1121\/10.0004444","article-title":"Passive acoustic detection and tracking of an unmanned underwater vehicle from motor noise","volume":"149","author":"Railey","year":"2021","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_35","unstructured":"(2021, August 20). Open Cooperation for European mAritime awareNess. Ocean2020 Mediterranean Sea Trials. Available online: https:\/\/ocean2020.eu\/sea-trials\/."},{"key":"ref_36","unstructured":"Steele, J.H. (2001). Acoustics, Deep Ocean. Encyclopedia of Ocean Sciences, Academic Press."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"EL351","DOI":"10.1121\/1.4754419","article-title":"Aspect-dependent radiated noise analysis of an underway autonomous underwater vehicle","volume":"132","author":"Gebbie","year":"2012","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1109\/JOE.2004.836996","article-title":"Decreasing the radiated acoustic and vibration noise of a mid-size AUV","volume":"30","author":"Zimmerman","year":"2005","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"65007","DOI":"10.1121\/1.3492795","article-title":"An overview of unmanned underwater vehicle noise in the low to mid frequencies bands","volume":"9","author":"Holmes","year":"2010","journal-title":"Proc. Meet. Acoust."},{"key":"ref_40","first-page":"224","article-title":"Cost-Effective, Cognitive Undersea Network for Timely and Reliable Near-Field Tsunami Warning","volume":"6","author":"Xerandy","year":"2015","journal-title":"Int. J. Adv. Comput. Sci. Appl."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.marpolbul.2019.01.009","article-title":"A review of unmanned vehicles for the detection and monitoring of marine fauna","volume":"140","author":"Verfuss","year":"2019","journal-title":"Mar. Pollut. Bull."},{"key":"ref_42","unstructured":"Reynolds, J.E., Perrin, W.F., Reeves, R.R., and Montgomery, S. (2005). Impacts of Anthropogenic Sound on Cetaceans. Marine Mammal Research: Conservation Beyond Crisis, Johns Hopkins University Press."}],"container-title":["Robotics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-6581\/11\/2\/52\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:56:06Z","timestamp":1760136966000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-6581\/11\/2\/52"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,18]]},"references-count":42,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,4]]}},"alternative-id":["robotics11020052"],"URL":"https:\/\/doi.org\/10.3390\/robotics11020052","relation":{},"ISSN":["2218-6581"],"issn-type":[{"type":"electronic","value":"2218-6581"}],"subject":[],"published":{"date-parts":[[2022,4,18]]}}}