{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T15:36:09Z","timestamp":1780673769532,"version":"3.54.1"},"reference-count":40,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2021,11,11]],"date-time":"2021-11-11T00:00:00Z","timestamp":1636588800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Key Research and Development Program of China ; Scientific Research and Development Project of Hebei University of Economics and Business,China;New Engineering Research and Practice pro-gram ,China.","award":["No. 2018YFC1504403;No.2021YB03; E-JSJRJ20201310"],"award-info":[{"award-number":["No. 2018YFC1504403;No.2021YB03; E-JSJRJ20201310"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In view of the demand of location awareness in a special complex environment, for an unmanned aerial vehicle (UAV) airborne multi base-station semi-passive positioning system, the hybrid positioning solutions and optimized site layout in the positioning system can effectively improve the positioning accuracy for a specific region. In this paper, the geometric dilution of precision (GDOP) formula of a time difference of arrival (TDOA) and angles of arrival (AOA) hybrid location algorithm is deduced. Mayfly optimization algorithm (MOA) which is a new swarm intelligence optimization algorithm is introduced, and a method to find the optimal station of the UAV airborne multiple base station\u2019s semi-passive positioning system using MOA is proposed. The simulation and analysis of the optimization of the different number of base stations, compared with other station layout methods, such as particle swarm optimization (PSO), genetic algorithm (GA), and artificial bee colony (ABC) algorithm. MOA is less likely to fall into local optimum, and the error of regional target positioning is reduced. By simulating the deployment of four base stations and five base stations in various situations, MOA can achieve a better deployment effect. The dynamic station configuration capability of the multi-station semi-passive positioning system has been improved with the UAV.<\/jats:p>","DOI":"10.3390\/s21227484","type":"journal-article","created":{"date-parts":[[2021,11,11]],"date-time":"2021-11-11T23:04:46Z","timestamp":1636671886000},"page":"7484","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["An Optimal Geometry Configuration Algorithm of Hybrid Semi-Passive Location System Based on Mayfly Optimization Algorithm"],"prefix":"10.3390","volume":"21","author":[{"given":"Aihua","family":"Hu","sequence":"first","affiliation":[{"name":"School of Electronic Engineering, Beijing University of Posts and Communications, Beijing 100876, China"},{"name":"School of Information Technology, Hebei University of Economics and Business, Shijiazhuang 050061, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhongliang","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Beijing University of Posts and Communications, Beijing 100876, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hui","family":"Yang","sequence":"additional","affiliation":[{"name":"Astronaut Research and Training Center, Beijing 100094, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5679-1644","authenticated-orcid":false,"given":"Yao","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Beijing University of Posts and Communications, Beijing 100876, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuhui","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Beijing University of Posts and Communications, Beijing 100876, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Di","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Beijing University of Posts and Communications, Beijing 100876, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,11]]},"reference":[{"key":"ref_1","first-page":"122","article-title":"Illegal radio station localization with UAV-based Q-learning","volume":"15","author":"Wu","year":"2018","journal-title":"China Commun."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"55817","DOI":"10.1109\/ACCESS.2019.2912306","article-title":"LSAR: Multi-UAV Collaboration for Search and Rescue Missions","volume":"7","author":"Alotaibi","year":"2019","journal-title":"IEEE Access"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1016\/j.measurement.2014.09.023","article-title":"Cooperative angle-of-arrival position localization","volume":"59","author":"Xu","year":"2015","journal-title":"Measurement"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1271","DOI":"10.1109\/TCOM.1979.1094559","article-title":"The Effects of Repeater Hard-Limiting, Filter Distortion, and Noise on a Pseudo-Noise, Time-Of-Arrival Estimation System","volume":"27","author":"Weinberg","year":"1979","journal-title":"IEEE Trans. Commun."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1905","DOI":"10.1109\/78.301830","article-title":"A simple and efficient estimator for hyperbolic location","volume":"42","author":"Chan","year":"1994","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1109\/TVT.2012.2225074","article-title":"A Semidefinite Relaxation Method for Source Localization Using TDOA and FDOA Measurements","volume":"62","author":"Wang","year":"2013","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3626","DOI":"10.1109\/TWC.2006.256985","article-title":"RSS-Based Location Estimation with Unknown Pathloss Model","volume":"5","author":"Li","year":"2006","journal-title":"IEEE Trans. Wireless Commun."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1687","DOI":"10.1080\/00207179.2013.792606","article-title":"Optimal sensor placement for target localisation and tracking in 2D and 3D","volume":"86","author":"Zhao","year":"2013","journal-title":"Int. J. Control"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1049\/iet-rsn.2017.0117","article-title":"Algebraic solution for three-dimensional TDOA\/AOA localisation in multiple-input\u2013multiple-output passive radar","volume":"12","author":"Noroozi","year":"2018","journal-title":"IET Radar Sonar Navig."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Deng, Z.L., Wang, H.H., Zheng, X.Y., and Yin, L. (2020). Base Station Selection for Hybrid TDOA\/RTT\/DOA Positioning in Mixed LOS\/NLOS Environment. Sensors, 20.","DOI":"10.3390\/s20154132"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Luo, J., Walker, E., Bhattacharya, P., and Chen, X. (2010, January 7\u20139). A new TDOA\/FDOA-based recursive geolocation algorithm. Proceedings of the 2010 42nd Southeastern Symposium on System Theory (SSST), Tyler, TX, USA.","DOI":"10.1109\/SSST.2010.5442839"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1049\/iet-smt.2018.5310","article-title":"Optimal deployment of sensor\u2013emitter geometries for hybrid localisation using TDOA and AOA measurements","volume":"13","author":"Wang","year":"2019","journal-title":"IET Sci. Meas. Technol."},{"key":"ref_13","first-page":"1","article-title":"Simple solution to the optimal deployment of cooperative nodes in two-dimensional TOA-based and AOA-based localization system","volume":"1","author":"Shi","year":"2017","journal-title":"Eurasip J. Wirel. Commun. Netw."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"109181","DOI":"10.1109\/ACCESS.2019.2933584","article-title":"Optimal sensor deployment and velocity configuration with hybrid TDOA and FDOA measurements","volume":"7","author":"Wang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Bishop, A.N., and Jensfelt, P. (2009, January 7\u201310). An optimality analysis of sensor-target geometries for signal strength based localization. Proceedings of the 2009 International Conference on Intelligent Sensors, Sensor Networks and Information Processing (ISSNIP), Melbourne, VIC, Australia.","DOI":"10.1109\/ISSNIP.2009.5416784"},{"key":"ref_16","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":"45","author":"Bishop","year":"2010","journal-title":"Automation"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Bishop, A.N., Fidan, B., and Anderson, B.D.O. (2007, January 3\u20136). Optimality analysis of sensor target geometries in passive localization: Part 1 \u2013 bearing-only localization. Proceedings of the 2017 3rd International Conference on Intelligent Sensors Sensor Networks and Information Processing, Melbourne, VIC, Australia.","DOI":"10.1109\/ISSNIP.2007.4496811"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Bishop, A.N., Fidan, B., and Anderson, B.D.O. (2007, January 3\u20136). Optimality analysis of sensor target geometries in passive localization: Part 2 \u2013 time-of-arrival based localization. Proceedings of the 2017 3rd International Conference on Intelligent Sensors Sensor Networks and Information Processing, Melbourne, VIC, Australia.","DOI":"10.1109\/ISSNIP.2007.4496812"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1016\/j.automatica.2005.12.018","article-title":"Optimal sensor placement and motion coordination for target tracking","volume":"42","author":"Bullo","year":"2006","journal-title":"Automation"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1611","DOI":"10.1109\/LGRS.2016.2597960","article-title":"Constrained Optimal Placements of Heterogeneous Range\/Bearing\/RSS Sensor Networks for Source Localization with Distance-Dependent Noise","volume":"13","author":"Liang","year":"2016","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3371","DOI":"10.1109\/TVT.2009.2017270","article-title":"GDOP Analysis for Positioning System Design","volume":"58","author":"Sharp","year":"2009","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4673","DOI":"10.1109\/TSP.2014.2338835","article-title":"Elliptic Localization: Performance Study and Optimum Receiver Placement","volume":"62","author":"Rui","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2000","DOI":"10.1177\/1550147720920471","article-title":"Analytical evaluation of geometric dilution of precision for three-dimensional angle-of-arrival target localization in wireless sensor networks","volume":"16","author":"Zhang","year":"2020","journal-title":"Int. J. Distrib. Sens. Netw."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Majid, A.S., and Joelianto, E. (2012, January 23\u201326). Optimal sensor deployment in non-convex region using Discrete Particle Swarm Optimization algorithm. Proceedings of the 2012 IEEE Conference on Control, Systems & Industrial Informatics, Bandung, Indonesia.","DOI":"10.1109\/CCSII.2012.6470483"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Li, Z., and Lei, L. (2009, January 25\u201327). Sensor node deployment in wireless sensor networks based on improved particle swarm optimization. Proceedings of the 2009 International Conference on Applied Superconductivity and Electromagnetic Devices, Chengdu, China.","DOI":"10.1109\/ASEMD.2009.5306655"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Xiao, Z., Yan, J., Yan, X., Cheng, G., and Qiang, X. (2015, January 23\u201325). A New Optimal Deployment Algorithm for Actor Node in WSAN. In Proceedings of the 2015 International Conference on Network and Information Systems for Computers, Wuhan, China.","DOI":"10.1109\/ICNISC.2015.58"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Xu, S., and Do\u011fan\u00e7ay, K. (2015, January 19\u201324). Optimal sensor deployment for 3D AOA target localization. Proceedings of the 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), South Brisbane, Australia.","DOI":"10.1109\/ICASSP.2015.7178430"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2002","DOI":"10.1109\/TCOMM.2020.3042267","article-title":"Toward Practical Access Point Deployment for Angle-of-Arrival Based Localization","volume":"69","author":"Zheng","year":"2021","journal-title":"IEEE Trans. Commun."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"63388","DOI":"10.1109\/ACCESS.2021.3075475","article-title":"Finding an Optimal Geometric Configuration for TDOA Location Systems With Reinforcement Learning","volume":"9","author":"Li","year":"2021","journal-title":"IEEE Access"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.cie.2020.106559","article-title":"A mayfly optimization algorithm","volume":"145","author":"Zervoudakis","year":"2020","journal-title":"Comput. Ind. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2173","DOI":"10.1109\/TWC.2018.2789882","article-title":"Exploiting LTE Signals for Navigation: Theory to Implementation","volume":"17","author":"Shamaei","year":"2018","journal-title":"IEEE Trans. Wireless Commun."},{"key":"ref_32","first-page":"487","article-title":"Optimization of Multi-Machine Passive Positioning System Based on PSO","volume":"49","author":"Wang","year":"2021","journal-title":"Comp. Digital Eng."},{"key":"ref_33","unstructured":"Kennedy, J., and Eberhart, R. (December, January 27). Particle swarm optimization. Proceedings of the ICNN\u201995\u2014International Conference on Neural Networks, Perth, Australia."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1023\/A:1022602019183","article-title":"Genetic Algorithms and Machine Learning","volume":"2","author":"Goldberg","year":"1988","journal-title":"Mach. Learn."},{"key":"ref_35","first-page":"36","article-title":"Firefly algorithm: Recent advances and applications","volume":"1","author":"Yang","year":"2013","journal-title":"Int. J. Swarm Intell."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Durmus, A., Kurban, R., and Karakose, E. (2021). A comparison of swarm-based optimization algorithms in linear antenna array synthesis. J. Comput. Electron., 20.","DOI":"10.21203\/rs.3.rs-233415\/v1"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1177\/003754979406200405","article-title":"Constrained optimization via genetic algorithms","volume":"62","author":"Homaifar","year":"1994","journal-title":"Simulation"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1016\/0360-8352(96)00037-X","article-title":"Evolutionary algorithms for constrained engineering problems","volume":"30","author":"Michalewicz","year":"1996","journal-title":"Comput. Ind. Eng."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Haspel, M. (2011, January 7\u20139). Geometric optimization of a time-of-arrival (TOA) based self-positioning terrestrial system. Proceedings of the 2011 IEEE International Conference on Microwaves, Communications, Antennas and Electronic Systems (COMCAS 2011), Tel Aviv, Israel.","DOI":"10.1109\/COMCAS.2011.6105930"},{"key":"ref_40","unstructured":"Dana, P. (2021, September 08). Global Positioning System Overview. Available online: http:\/\/gisweb.massey.ac.nz\/topic\/webreferencesites\/gps\/danagps\/gps.html."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/22\/7484\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:28:23Z","timestamp":1760167703000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/22\/7484"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,11]]},"references-count":40,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2021,11]]}},"alternative-id":["s21227484"],"URL":"https:\/\/doi.org\/10.3390\/s21227484","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,11]]}}}