{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T10:36:33Z","timestamp":1781606193805,"version":"3.54.5"},"reference-count":21,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2019,6,29]],"date-time":"2019-06-29T00:00:00Z","timestamp":1561766400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010198","name":"Ministerio de Econom\u00eda, Industria y Competitividad, Gobierno de Espa\u00f1a","doi-asserted-by":"publisher","award":["DPI2016-79960-C3-2-P"],"award-info":[{"award-number":["DPI2016-79960-C3-2-P"]}],"id":[{"id":"10.13039\/501100010198","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Time difference of arrival (TDOA) positioning methods have experienced growing importance over the last few years due to their multiple applications in local positioning systems (LPSs). While five sensors are needed to determine an unequivocal three-dimensional position, systems with four nodes present two different solutions that cannot be discarded according to mathematical standards. In this paper, a new methodology to solve the 3D TDOA problems in a sensor network with four beacons is proposed. A confidence interval, which is defined in this paper as a sphere, is defined to use positioning algorithms with four different nodes. It is proven that the separation between solutions in the four-beacon TDOA problem allows the transformation of the problem into an analogous one in which more receivers are implied due to the geometric properties of the intersection of hyperboloids. The achievement of the distance between solutions needs the application of genetic algorithms in order to find an optimized sensor distribution. Results show that positioning algorithms can be used 96.7% of the time with total security in cases where vehicles travel at less than 25 m\/s.<\/jats:p>","DOI":"10.3390\/s19132892","type":"journal-article","created":{"date-parts":[[2019,7,1]],"date-time":"2019-07-01T03:23:59Z","timestamp":1561951439000},"page":"2892","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":43,"title":["3D Tdoa Problem Solution with Four Receiving\u00a0Nodes"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6566-1630","authenticated-orcid":false,"given":"Javier","family":"D\u00edez-Gonz\u00e1lez","sequence":"first","affiliation":[{"name":"Department of Mechanical, IT and Aerospace Engineering, Universidad de Le\u00f3n, 24071 Le\u00f3n, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rub\u00e9n","family":"\u00c1lvarez","sequence":"additional","affiliation":[{"name":"Positioning Department, Drotium, Universidad de Le\u00f3n, 24071 Le\u00f3n, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0760-1170","authenticated-orcid":false,"given":"Lidia","family":"S\u00e1nchez-Gonz\u00e1lez","sequence":"additional","affiliation":[{"name":"Department of Mechanical, IT and Aerospace Engineering, Universidad de Le\u00f3n, 24071 Le\u00f3n, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6573-8477","authenticated-orcid":false,"given":"Laura","family":"Fern\u00e1ndez-Robles","sequence":"additional","affiliation":[{"name":"Department of Mechanical, IT and Aerospace Engineering, Universidad de Le\u00f3n, 24071 Le\u00f3n, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7112-1983","authenticated-orcid":false,"given":"Hilde","family":"P\u00e9rez","sequence":"additional","affiliation":[{"name":"Department of Mechanical, IT and Aerospace Engineering, Universidad de Le\u00f3n, 24071 Le\u00f3n, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5152-4555","authenticated-orcid":false,"given":"Manuel","family":"Castej\u00f3n-Limas","sequence":"additional","affiliation":[{"name":"Department of Mechanical, IT and Aerospace Engineering, Universidad de Le\u00f3n, 24071 Le\u00f3n, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Xu, J., Ma, M., and Law, C.L. (December, January 30). AOA Cooperative Position Localization. Proceedings of the IEEE Globecom 2008 IEEE Global Telecommunications Conference, New Orleans, LO, USA.","DOI":"10.1109\/GLOCOM.2008.ECP.720"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1109\/TWC.2012.121412.111346","article-title":"Distributed Angle Estimation for Localization in Wireless Sensor Networks","volume":"12","author":"Zhang","year":"2013","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1508","DOI":"10.1109\/TVT.2003.819613","article-title":"On the Accuracy of a Cellular Location System Based on RSS Measurements","volume":"52","author":"Weiss","year":"2003","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1389","DOI":"10.1109\/TWC.2011.031611.101585","article-title":"A New Approach to Sensor Node Localization Using RSS Measurements in Wireless Sensor Networks","volume":"10","author":"Wang","year":"2011","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Passafiume, M., Maddio, S., and Cidronali, A. (2017). An Improved Approach for RSSI-Based only Calibration-Free Real-Time Indoor Localization on IEEE 802.11 and 802.15.4 Wireless Networks. Sensors, 17.","DOI":"10.3390\/s17040717"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2238","DOI":"10.1109\/TWC.2010.07.090465","article-title":"TOA Estimation with the IEEE 802.15. 4a Standard","volume":"9","author":"Mengali","year":"2010","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2182","DOI":"10.1109\/TWC.2012.040412.110697","article-title":"Accurate Passive Location Estimation Using TOA Measurements","volume":"11","author":"Shen","year":"2012","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Xu, J., Ma, M., and Law, C.L. (2006, January 24\u201327). Position Estimation Using UWB TDOA Measurements. Proceedings of the 2006 IEEE International Conference on Ultra-Wideband, Waltham, MA, USA.","DOI":"10.1109\/ICU.2006.281617"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Niitso, A., Edelh\u00e4u\u00dfer, T., Eberlein, E., Hadaschik, N., and Mutschler, C. (2019). A Deep Learning Approach to Position Estimation from Channel Impulse Responses. Sensors, 19.","DOI":"10.3390\/s19051064"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"16","DOI":"10.11113\/elektrika.v18n1.133","article-title":"Aircraft Position Estimation Comparison of Multilateration System Lateration Algorithms with Different Reference Selection Techniques","volume":"18","author":"Yaro","year":"2019","journal-title":"Elektrika"},{"key":"ref_11","unstructured":"He, S. (2016). Asynchronous Time Difference of Arrival Positioning System and Implementation. [Ph.D. Thesis, University of Victoria]. Available online: http:\/\/hdl.handle.net\/1828\/7411."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1109\/TSP.2006.885744","article-title":"Source Localization Using TDOA and FDOA Measurements in the Presence of Receiver Location Errors: Analysis and Solution","volume":"55","author":"Ho","year":"2007","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_13","unstructured":"Priyantha, N.B., Balakrishnan, H., Demaine, E.D., and Teller, S. (2005, January 13\u201317). Mobile-assisted localization in wireless sensor networks. Proceedings of the IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies, Miami, FL, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1109\/TSMCC.2007.905750","article-title":"Survey of Wireless Indoor Positioning Techniques and Systems","volume":"37","author":"Liu","year":"2007","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_15","unstructured":"Wang, Y., Jia, X., and Lee, H.K. (2003, January 22\u201325). An indoors wireless positioning system based on wireless local area network infrastructure. Proceedings of the 6th International Symposium on Satellite Navigation Technology Including Mobile Positioning & Location Services, Melbourne, Australia."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"10326","DOI":"10.3390\/s111110326","article-title":"Measuring Time-of-Flight in an Ultrasonic LPS System Using Generalized Cross-Correlation","volume":"11","author":"Villadangos","year":"2011","journal-title":"Sensors"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1080\/1065514021000012129","article-title":"A Synthesizable VHDL Model of the Exact Solution for Three-dimensional Hyperbolic Positioning System","volume":"15","author":"Bucher","year":"2002","journal-title":"VLSI Desgin"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Yang, K., Jianping, A., Zhan, X., and Xiangyuan, B. (2008, January 12\u201314). A Generalized Total Least-Squares Algorithm for Hyperbolic Location. Proceedings of the 2008 4th International Conference on Wireless Communications, Networking and Mobile Computing, Dalian, China.","DOI":"10.1109\/WiCom.2008.822"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Bonan, J., Xiaosu, X., and Zhang, T. (2018). Robust Time-Difference-of-Arrival (TDOA) Localization Using Weighted Least Squares with Cone Tangent Plane Constraint. Sensors, 18.","DOI":"10.3390\/s18030778"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1109\/TASE.2009.2037135","article-title":"Sensor Placement for Triangulation-Based Localization","volume":"7","author":"Tekdas","year":"2010","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_21","first-page":"281","article-title":"Random search for hyper-parameter optimization","volume":"13","author":"Bergstra","year":"2012","journal-title":"J. Mach. Learn. Res."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/13\/2892\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:02:30Z","timestamp":1760187750000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/13\/2892"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,29]]},"references-count":21,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2019,7]]}},"alternative-id":["s19132892"],"URL":"https:\/\/doi.org\/10.3390\/s19132892","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,6,29]]}}}