{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T18:55:59Z","timestamp":1770749759902,"version":"3.50.0"},"reference-count":21,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,5,3]],"date-time":"2022-05-03T00:00:00Z","timestamp":1651536000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003725","name":"Korea Government (MSIT)","doi-asserted-by":"publisher","award":["2019R1F1A1063111"],"award-info":[{"award-number":["2019R1F1A1063111"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Increasing the number of satellites in a global navigation satellite system (GNSS) improves the positioning accuracy and increases availability. However, it reduces the positioning accuracy improvement rate and increases the calculation loads, which can cause battery usage problems in mobile devices using a GNSS. An appropriate satellite selection method is required. One current method entails the use of ideal satellite placement with respect to the minimum geometric dilution of precision (GDOP). In this study, the described ideal satellite placement with the minimum GDOP were divided in terms of the horizontal dilution of precision (HDOP) and vertical dilution of precision (VDOP). HDOP and VDOP were mathematically derived and analyzed. The derived formula was verified using simulations. The analysis was performed with actual dual GNSS satellite data. The satellites adjacent to the ideal placement were selected and the DOP was calculated. Simply selecting satellites closest to the ideal placement afforded large values for HDOP and VDOP. This issue was addressed using a satellite changing algorithm considering the dual GNSS, resulting in reduced values of the HDOP and VDOP.<\/jats:p>","DOI":"10.3390\/s22093475","type":"journal-article","created":{"date-parts":[[2022,5,3]],"date-time":"2022-05-03T08:26:35Z","timestamp":1651566395000},"page":"3475","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["HDOP and VDOP Analysis in an Ideal Placement Environment for Dual GNSSs"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4720-7757","authenticated-orcid":false,"given":"JinHyeok","family":"Jang","sequence":"first","affiliation":[{"name":"Mechanical and Aerospace Engineering, Konkuk University, Seoul 05029, Korea"}]},{"given":"Dana","family":"Park","sequence":"additional","affiliation":[{"name":"Mechanical and Aerospace Engineering, Konkuk University, Seoul 05029, Korea"}]},{"given":"Sangkyung","family":"Sung","sequence":"additional","affiliation":[{"name":"Mechanical and Aerospace Engineering, Konkuk University, Seoul 05029, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9203-048X","authenticated-orcid":false,"given":"Young Jae","family":"Lee","sequence":"additional","affiliation":[{"name":"Mechanical and Aerospace Engineering, Konkuk University, Seoul 05029, Korea"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Han, K., Lee, S., You, M., and Won, J.H. (2022). A Comprehensive Evaluation of Possible RNSS Signals in the S-Band for the KPS. Sensors, 22.","DOI":"10.3390\/s22062180"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Reid, T.G.R., Pervez, N., Ibrahim, U., Houts, S.E., Pandey, G., Alla, N.K.R., and Hsia, A. (2019, January 16\u201320). Standalone and RTK GNSS on 30,000 Km of North American Highways. Proceedings of the 32nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2019), Miami, FL, USA.","DOI":"10.33012\/2019.16914"},{"key":"ref_3","unstructured":"(2022, January 27). Navigation Center, Available online: https:\/\/www.navcen.uscg.gov\/?Do=constellationStatus."},{"key":"ref_4","unstructured":"Application Consumer Center (2022, January 27). GLONASS. Available online: https:\/\/www.glonass-iac.ru\/glonass\/sostavOG\/."},{"key":"ref_5","unstructured":"(2022, January 27). Constellation Information|European GNSS Service Centre. Available online: https:\/\/www.gsc-europa.eu\/system-service-status\/constellation-information."},{"key":"ref_6","unstructured":"(2022, January 27). Test and Assessment Research Center of China Satellite Navigation Office Available. Available online: http:\/\/www.csno-tarc.cn\/en\/system\/constellation."},{"key":"ref_7","unstructured":"Ramawickrama, Y., Vijayanga, J., Dharmarathne, R., and Wijesooriya, H. (2016, January 12\u201313). The Future of GNSS in the Next Ten Years. Proceedings of the 3rd Asia Pacific Space Generation Workshop (3rd AP-SGW), Los Barnos, Philippines."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"740","DOI":"10.1109\/JSTSP.2009.2028381","article-title":"A Fast Satellite Selection Algorithm: Beyond Four Satellites","volume":"3","author":"Zhang","year":"2009","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1109\/7.937488","article-title":"Recursive Method for Optimum GPS Satellite Selection","volume":"37","author":"Phatak","year":"2001","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/s10291-008-0111-2","article-title":"A Closed-Form Formula for GPS GDOP Computation","volume":"13","author":"Doong","year":"2009","journal-title":"GPS Solut."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s10291-015-0440-x","article-title":"A Closed-Form Formula to Calculate Geometric Dilution of Precision (GDOP) for Multi-GNSS Constellations","volume":"20","author":"Teng","year":"2016","journal-title":"GPS Solut."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1002\/j.2161-4296.1984.tb00856.x","article-title":"A Satellite Selection Method and Accuracy for the Global Positioning System","volume":"31","author":"Kihara","year":"1984","journal-title":"Navigation"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/S0275-1062(04)90009-4","article-title":"Selection of GPS Satellites for the Optimum Geometry","volume":"28","author":"Zheng","year":"2004","journal-title":"Chin. Astron. Astrophys."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Tao, A.L., and Jan, S.S. (2016, January 16\u201320). Optimal Navigation with Multi-Constellation GNSS: A Satellite Selection Algorithm. Proceedings of the 29th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2016), Portland, OR, USA.","DOI":"10.33012\/2016.14725"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1080\/00396265.2016.1171959","article-title":"A New Method for Satellite Selection with Controllable Weighted PDOP Threshold","volume":"49","author":"Nie","year":"2017","journal-title":"Surv. Rev."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Cheng, Y., Dambeck, J., and Holzapfel, F. (2016, January 16\u201320). Satellite Selection in Multi-GNSS Positioning. Proceedings of the 29th International Tech. Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2016), Portland, OR, USA.","DOI":"10.33012\/2016.14694"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"25","DOI":"10.15406\/aaoaj.2021.05.00124","article-title":"A Study on Compatibility and Interoperability among Multi- GNSS","volume":"5","author":"Sarkar","year":"2021","journal-title":"AAOAJ"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/s10291-021-01090-6","article-title":"Impact of Galileo-to-GPS-Time-Offset Accuracy on Multi-GNSS Positioning and Timing","volume":"25","author":"Defraigne","year":"2021","journal-title":"GPS Solut."},{"key":"ref_19","unstructured":"Hofmann-Wellenhof, B., Lichtenegger, H., and Wasle, E. (2008). GNSS\u2014Global Navigation Satellite Systems: GPS, GLONASS, Galileo, and More, Springer."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3241","DOI":"10.1109\/TIM.2012.2205512","article-title":"Weighted DOP With Consideration on Elevation-Dependent Range Errors of GNSS Satellites","volume":"61","author":"Won","year":"2012","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1018","DOI":"10.1017\/S037346331400040X","article-title":"New Characteristics of Geometric Dilution of Precision (GDOP) for Multi-GNSS Constellations","volume":"67","author":"Teng","year":"2014","journal-title":"J. Navig."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/9\/3475\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:05:42Z","timestamp":1760137542000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/9\/3475"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,3]]},"references-count":21,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["s22093475"],"URL":"https:\/\/doi.org\/10.3390\/s22093475","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,3]]}}}