{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T13:38:39Z","timestamp":1768484319600,"version":"3.49.0"},"reference-count":37,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,2,26]],"date-time":"2024-02-26T00:00:00Z","timestamp":1708905600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Beihang University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Low Earth orbit (LEO) satellite constellations have emerged as an effective alternative for the provision of high-accuracy positioning, navigation and timing (PNT) solutions which are based on high-precision orbit and clock information. Determining an orbit with high precision is dependent on the number and distribution of ground tracking stations. Therefore, it is important to investigate methodologies that can ensure the adequate observing coverage of LEO navigation constellations. In this study, an evolutionary algorithm is applied to optimize the number and deployment of ground stations for tracking LEO constellations. According to the distribution area, two schemes of study are analyzed: (a) global deployment\u2014the ground stations are deployed throughout the globe; (b) regional deployment\u2014a selected region is used for deployment. For global deployment, the optimization objectives are focused on the ground station and observing rate for k-heavy observing coverage (HC), while the sole objective for the regional deployment scheme is the satellite position dilution of precision (SPDOP). It is shown that a deployment of 95 ground stations is optimal for achieving 3-HC with an observing rate of 97.37% and 4-HC with an observing rate of 92.01%. For regional distribution, 15, 20 and 25 ground stations are used for three optimal configurations of SPDOP at 2.058, 1.399 and 1.330, respectively. The results are significantly enhanced using intersatellite links for SPDOP evaluation, from 2.058, 1.399 and 1.330 to 0.439, 0.422 and 0.409, with 15, 20 and 25 ground stations, respectively.<\/jats:p>","DOI":"10.3390\/rs16050810","type":"journal-article","created":{"date-parts":[[2024,2,26]],"date-time":"2024-02-26T10:40:17Z","timestamp":1708944017000},"page":"810","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Optimizing the Deployment of Ground Tracking Stations for Low Earth Orbit Satellite Constellations Based on Evolutionary Algorithms"],"prefix":"10.3390","volume":"16","author":[{"given":"Mansour","family":"Kralfallah","sequence":"first","affiliation":[{"name":"SNARS Laboratory, School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0298-9476","authenticated-orcid":false,"given":"Falin","family":"Wu","sequence":"additional","affiliation":[{"name":"SNARS Laboratory, School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-7159-6445","authenticated-orcid":false,"given":"Afnan","family":"Tahir","sequence":"additional","affiliation":[{"name":"SNARS Laboratory, School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191, China"},{"name":"Pakistan Space and Upper Atmosphere Research Commission (SUPARCO), SUPARCO Rd, P.O. Box 8402, Karachi 75270, Pakistan"}]},{"given":"Amel","family":"Oubara","sequence":"additional","affiliation":[{"name":"SNARS Laboratory, School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191, China"}]},{"given":"Xiaohong","family":"Sui","sequence":"additional","affiliation":[{"name":"Institute of Remote Sensing Satellite, China Academy of Space Technology, Beijing 100094, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1002\/j.2161-4296.2010.tb01773.x","article-title":"Analysis of Iridium-augmented GPS for floating carrier phase positioning","volume":"57","author":"Joerger","year":"2010","journal-title":"Navigation"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"83412","DOI":"10.1109\/ACCESS.2019.2924470","article-title":"New method for positioning using IRIDIUM satellite signals of opportunity","volume":"7","author":"Tan","year":"2019","journal-title":"IEEE Access"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Ke, M., Lv, J., Chang, J., Dai, W., Tong, K., and Zhu, M. (2015, January 15\u201317). Integrating GPS and LEO to accelerate convergence time of precise point positioning. Proceedings of the 2015 International Conference on Wireless Communications & Signal Processing (WCSP), Nanjing, China.","DOI":"10.1109\/WCSP.2015.7341230"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1007\/s00190-018-1195-2","article-title":"LEO constellation-augmented multi-GNSS for rapid PPP convergence","volume":"93","author":"Li","year":"2019","journal-title":"J. Geod."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1016\/j.asr.2020.04.031","article-title":"LEO constellation optimization for LEO enhanced global navigation satellite system (LeGNSS)","volume":"66","author":"Ge","year":"2020","journal-title":"Adv. Space Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/s10291-021-01217-9","article-title":"LEO-constellation-augmented multi-GNSS real-time PPP for rapid re-convergence in harsh environments","volume":"26","author":"Li","year":"2021","journal-title":"GPS Solut."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/978-981-16-3142-9_18","article-title":"LEO Constellation Design Based on Dual Objective Optimization and Study on PPP Performance","volume":"Volume 773","author":"Yang","year":"2021","journal-title":"China Satellite Navigation Conference (CSNC 2021) 2021 Proceedings"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1911","DOI":"10.1016\/j.asr.2020.07.021","article-title":"Orbital design of LEO navigation constellations and assessment of their augmentation to BDS","volume":"66","author":"Zhang","year":"2020","journal-title":"Adv. Space Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/j.cja.2020.09.005","article-title":"LEO navigation augmentation constellation design with the multi-objective optimization approaches","volume":"34","author":"Han","year":"2021","journal-title":"Chin. J. Aeronaut."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Yang, M., Dong, X., and Hu, M. (2016, January 12\u201314). Design and simulation for hybrid LEO communication and navigation constellation. Proceedings of the 2016 IEEE Chinese Guidance, Navigation and Control Conference (CGNCC), Nanjing, China.","DOI":"10.1109\/CGNCC.2016.7829041"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1007\/978-981-13-0005-9_54","article-title":"Design of Mega-Constellations of LEO Satellites for Positioning","volume":"Volume 497","author":"Sun","year":"2018","journal-title":"China Satellite Navigation Conference (CSNC 2018) 2018 Proceedings"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Guan, M., Xu, T., Gao, F., Nie, W., and Yang, H. (2020). Optimal walker constellation design of LEO-based global navigation and augmentation system. Remote Sens., 12.","DOI":"10.3390\/rs12111845"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1134\/S2075108713040056","article-title":"Optimization of the global network of tracking stations to provide GLONASS users with precision navigation and timing service","volume":"4","author":"Dvorkin","year":"2013","journal-title":"Gyroscopy Navig."},{"key":"ref_14","first-page":"441","article-title":"Real-time GPS satellite clock offset determination based on the TIN global station-selecting method","volume":"34","author":"Li","year":"2017","journal-title":"J. Geomat. Sci. Technol."},{"key":"ref_15","first-page":"216","article-title":"Optimal Estimation of Dynamic Parameters of BDS Orbit for Optimal Selection of Tracking Stations","volume":"36","author":"Zhang","year":"2016","journal-title":"J. Geod. Geodyn."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Shah Sadman, A.A.M., and Hossam-E-Haider, M. (2021, January 1\u20133). Study of GNSS Parameters and Environmental Factors over Bangladesh Intended for Selecting Ideal Ground Station Location for SBAS. Proceedings of the 2021 2nd Global Conference for Advancement in Technology (GCAT), Bangalore, India.","DOI":"10.1109\/GCAT52182.2021.9587629"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"7579185","DOI":"10.1155\/2019\/7579185","article-title":"Random optimization algorithm on GNSS monitoring stations selection for ultra-rapid orbit determination and real-time satellite clock offset estimation","volume":"2019","author":"Yang","year":"2019","journal-title":"Math. Probl. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2177","DOI":"10.1016\/j.asr.2015.07.045","article-title":"Impact of tracking station distribution structure on BeiDou satellite orbit determination","volume":"56","author":"Zhang","year":"2015","journal-title":"Adv. Space Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4069","DOI":"10.1016\/j.asr.2021.07.022","article-title":"Optimization of ground tracking stations for BDS-3 satellite orbit determination","volume":"68","author":"Zhang","year":"2021","journal-title":"Adv. Space Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4011","DOI":"10.1016\/j.asr.2021.02.027","article-title":"Orbit determination of BDS-3 satellite based on regional ground tracking station and inter-satellite link observations","volume":"67","author":"Zhang","year":"2021","journal-title":"Adv. Space Res."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Liu, X., Ge, Y., Zhao, C., Li, B., and Zhou, R. (2021, January 14\u201316). A Study on Global Monitoring Station Optimization Deployment Method Based on Navigation Satellite Quadruple Observing Coverage. Proceedings of the 2021 International Conference on Communications, Information System and Computer Engineering (CISCE), Beijing, China.","DOI":"10.1109\/CISCE52179.2021.9446011"},{"key":"ref_22","unstructured":"Kopacz, J., Roney, J., and Herschitz, R. (2019, January 3\u20138). Optimized ground station placement for a mega constellation using a genetic algorithm. Proceedings of the 33rd Annual AIAA\/USU Conference on Small Satellites, Logan, UT, USA."},{"key":"ref_23","unstructured":"Carlton-Wippern, K.C. (1997, January 4\u20137). Satellite Position Dilution of Precision (SPDOP). Proceedings of the 1997 AAS\/AIAA Astrodynamics Specialist Conference, Sun Valley, ID, USA."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1671","DOI":"10.1016\/j.asr.2017.01.011","article-title":"The Multi-GNSS Experiment (MGEX) of the International GNSS Service (IGS)\u2014Achievements, prospects and challenges","volume":"59","author":"Montenbruck","year":"2017","journal-title":"Adv. Space Res."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1447","DOI":"10.1007\/s00190-017-1035-9","article-title":"Improving BeiDou precise orbit determination using observations of onboard MEO satellite receivers","volume":"91","author":"Ge","year":"2017","journal-title":"J. Geod."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1249","DOI":"10.1109\/TAES.2004.1386878","article-title":"Performance Evaluation of GPS Augmentation Using Quasi-Zenith Satellite System","volume":"40","author":"Wu","year":"2004","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/s00190-007-0187-4","article-title":"Resolution of GPS carrier-phase ambiguities in precise point positioning (PPP) with daily observations","volume":"82","author":"Ge","year":"2008","journal-title":"J. Geod."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1007\/PL00012883","article-title":"Precise point positioning using IGS orbit and clock products","volume":"5","author":"Kouba","year":"2001","journal-title":"GPS Solut."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/j.actaastro.2019.07.029","article-title":"Contribution analysis of inter-satellite ranging observation to BDS-2 satellite orbit determination based on regional tracking stations","volume":"164","author":"Zhang","year":"2019","journal-title":"Acta Astronaut."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s40328-020-00322-4","article-title":"The application of inter-satellite links connectivity schemes in various satellite navigation systems for orbit and clock corrections determination: Simulation study","volume":"56","author":"Kur","year":"2021","journal-title":"Acta Geod. Geophys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1017\/S0373463319000523","article-title":"Inter-satellite link enhanced orbit determination for BeiDou-3","volume":"73","author":"Yang","year":"2020","journal-title":"J. Navig."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1007\/s10291-019-0823-5","article-title":"Precise orbit determination for BDS-3 satellites using satellite-ground and inter-satellite link observations","volume":"23","author":"Xie","year":"2019","journal-title":"GPS Solut."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1186\/s43020-022-00083-1","article-title":"Precise orbit determination for a large LEO constellation with inter-satellite links and the measurements from different ground networks: A simulation study","volume":"3","author":"He","year":"2022","journal-title":"Satell. Navig."},{"key":"ref_34","unstructured":"NOAA (2023, August 10). National Oceanic and Atmospheric Administration, Available online: www.ngdc.noaa.gov."},{"key":"ref_35","unstructured":"Heris, M.K. (2023, April 15). NSGA-III: Non-dominated Sorting Genetic Algorithm, the Third Version\u2014MATLAB Implementation. Yarpiz. Available online: https:\/\/yarpiz.com\/456\/ypea126-nsga3."},{"key":"ref_36","unstructured":"Mostapha, K.H. (2023, September 20). Strength Pareto Evolutionary Algorithm 2 (SPEA2). Available online: https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/52871-strength-pareto-evolutionary-algorithm-2-spea2."},{"key":"ref_37","unstructured":"V\u00edctor, M.-C. (2023, August 11). Multi-Objective Particle Swarm Optimization (MOPSO). Available online: https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/62074-multi-objective-particle-swarm-optimization-mopso."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/5\/810\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:04:51Z","timestamp":1760105091000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/5\/810"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,26]]},"references-count":37,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["rs16050810"],"URL":"https:\/\/doi.org\/10.3390\/rs16050810","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2,26]]}}}