{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T14:39:07Z","timestamp":1774449547471,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,1,16]],"date-time":"2019-01-16T00:00:00Z","timestamp":1547596800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51207042"],"award-info":[{"award-number":["51207042"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006579","name":"Ministry of Industry and Information Technology of the People's Republic of China","doi-asserted-by":"publisher","award":["12-MC-KY-14"],"award-info":[{"award-number":["12-MC-KY-14"]}],"id":[{"id":"10.13039\/501100006579","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003482","name":"Department of Education of Hebei Province","doi-asserted-by":"publisher","award":["ZD2017216"],"award-info":[{"award-number":["ZD2017216"]}],"id":[{"id":"10.13039\/501100003482","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Accurate localization of the radio transmitter is an important work in radio management. Previous research is more focused on two-dimensional (2-D) scenarios, but the localization of an unknown radio transmitter under three-dimensional (3-D) scenarios has more practical significance. In this paper, we propose a novel 3-D localization algorithm with received signal strength difference (RSSD) information and factor graph (FG), which is suitable for both line-of-sight (LOS) and non-line-of-sight (NLOS) condition. Considering the stochastic properties of measurement errors caused by the indoor environment, RSSD measurements are processed with mean and variance in the form of Gaussian distribution in the FG framework. A new 3-D RSSD-based FG model is constructed with the relationship between RSSD and location coordinates by local linearization technique. The soft-information computation and iterative process of the proposed model are derived by using the sum-product algorithm. In addition, the impacts of different grid distances and number of signal receivers on positioning accuracy are explored. Finally, the performance of our proposed approach is experimentally evaluated in a real scenario. The results show that the positioning performance of the proposed algorithm is not only superior to the k-nearest neighbors (kNN) algorithm and least square (LS) algorithm, but also it can achieve a mean localization error as low as 1.15 m. Our proposed scheme provides a good solution for the accurate detection of an unknown radio transmitter under indoor 3-D space and has a good application prospect.<\/jats:p>","DOI":"10.3390\/s19020338","type":"journal-article","created":{"date-parts":[[2019,1,16]],"date-time":"2019-01-16T03:09:13Z","timestamp":1547608153000},"page":"338","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Indoor 3-D Localization Based on Received Signal Strength Difference and Factor Graph for Unknown Radio Transmitter"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9088-9610","authenticated-orcid":false,"given":"Liyang","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Artificial Intelligence, Hebei University of Technology, Tianjin 300130, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1487-4596","authenticated-orcid":false,"given":"Taihang","family":"Du","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Hebei University of Technology, Tianjin 300130, China"},{"name":"Control Engineering Research Center of Hebei, Tianjin 300130, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chundong","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Hebei University of Technology, Tianjin 300130, China"},{"name":"Control Engineering Research Center of Hebei, Tianjin 300130, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2488","DOI":"10.1109\/LCOMM.2017.2737985","article-title":"A Robust Bisection-based Estimator for TOA-based Target Localization in NLOS Environments","volume":"21","author":"Tomic","year":"2017","journal-title":"IEEE Commun. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1430","DOI":"10.1109\/LCOMM.2017.2787739","article-title":"Semidefinite Programming for NLOS Error Mitigation in TDOA Localization","volume":"22","author":"Su","year":"2018","journal-title":"IEEE Commun. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"6524","DOI":"10.1109\/TWC.2015.2456057","article-title":"An Asymptotically Efficient Estimator in Closed-form for 3-D AOA Localization Using a Sensor Network","volume":"14","author":"Wang","year":"2015","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_4","first-page":"6524","article-title":"RSS Distribution-Based Passive Localization and Its Application in Sensor Networks","volume":"14","author":"Liu","year":"2016","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1340","DOI":"10.1109\/TVT.2015.2397598","article-title":"Distance-Based Interpolation and Extrapolation Methods for RSS-Based Localization with Indoor Wireless Signals","volume":"64","author":"Talvitie","year":"2015","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1474","DOI":"10.1109\/LCOMM.2018.2833544","article-title":"Performance Metric on the Best Achievable Accuracy for Hybrid TOA\/AOA Target Localization","volume":"22","author":"Li","year":"2018","journal-title":"IEEE Commun. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3197","DOI":"10.1109\/TVT.2016.2589923","article-title":"3-D Target Localization in Wireless Sensor Networks Using RSS and AoA Measurements","volume":"66","author":"Tomic","year":"2017","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"626","DOI":"10.1109\/LCOMM.2004.835319","article-title":"The Cramer-Rao Bounds of Hybrid TOA\/RSS and TDOA\/RSS Location Estimation Schemes","volume":"8","author":"Catovic","year":"2004","journal-title":"IEEE Commun. Lett."},{"key":"ref_9","unstructured":"Bahl, P., and Padmanabhan, V.N. (2000, January 26\u201330). RADAR: An In-building RF-based User Location and Tracking System. Proceedings of the IEEE INFOCOM 2000, Tel Aviv, Israel."},{"key":"ref_10","unstructured":"Ni, L.M., Liu, Y., Lau, Y.C., and Patil, A.P. (2003, January 26). LANDMARC: Indoor location sensing using active RFID. Proceedings of the First IEEE International Conference on Pervasive Computing and Communications, Fort Worth, TX, USA."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"10208","DOI":"10.1109\/JSEN.2018.2874453","article-title":"A Soft Range Limited K-Nearest Neighbors Algorithm for Indoor Localization Enhancement","volume":"18","author":"Hoang","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1055","DOI":"10.1109\/LCOMM.2014.2318031","article-title":"RSS-based Source Localization When Path-loss Model Parameters are Unknown","volume":"18","author":"Xu","year":"2014","journal-title":"IEEE Commun. Lett."},{"key":"ref_13","unstructured":"Guo, X., Zhu, S., Lin, L., Hu, F., and Ansari, N. (2018). Accurate WiFi Localization by Unsupervised Fusion of Extended Candidate Location Set. IEEE Internet Things J., Available online: https:\/\/ieeexplore.ieee.org\/document\/8466583."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3261","DOI":"10.1109\/TSP.2017.2684741","article-title":"Robust Differential Received Signal Strength-based Localization","volume":"65","author":"Hu","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1109\/TMC.2011.243","article-title":"SSD: A roubst RF Location Fingerprint Addressing Mobile Devices Heterogeneity","volume":"12","author":"Hossain","year":"2013","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1784","DOI":"10.1109\/TCOMM.2015.2410300","article-title":"Unknown Transmit Power RSSD Based Source Localization with Sensor Position Uncertainty","volume":"163","author":"Lohrasbipeydeh","year":"2015","journal-title":"IEEE Trans. Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1109\/LWC.2014.2326879","article-title":"A Minimax SDP Method for Energy Based Source Localization with Unknown Transmit Power","volume":"3","author":"Lohrasbipeydeh","year":"2014","journal-title":"IEEE Commun. Lett."},{"key":"ref_18","first-page":"2696","article-title":"Network-Side Mobile Position Location Using Factor Graphs","volume":"63","author":"Chen","year":"2016","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1764","DOI":"10.1109\/TWC.2012.040412.110520","article-title":"A Factor-graph-based TOA Location Estimator","volume":"11","author":"Jhi","year":"2012","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_20","first-page":"1","article-title":"Positioning Based on Factor Graphs","volume":"1","author":"Mensing","year":"2007","journal-title":"EURASIP J. Adv. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3050","DOI":"10.1109\/TWC.2009.080452","article-title":"A Novel Indoor RSS-based Position Location Algorithm Using Factor Graphs","volume":"8","author":"Huang","year":"2009","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_22","unstructured":"Aziz, M.R.K., Anwar, K., and Matsumoto, T. (2016, January 18\u201320). DRSS-based Factor Graph Geolocation Technique for Position Detection of Unknown Radio Emitter. Proceedings of the International Workshop on Advanced PHY and MAC Layer Design for 5G Mobile Networks and Internet of Things in conjunction with European Wireless, Oulu, Finland."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1109\/18.910572","article-title":"Factor graphs and the sum-Product algorithm","volume":"47","author":"Kschischang","year":"2001","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1109\/TWC.2002.800542","article-title":"Hybrid TDOA\/AOA Mobile User Location for Wideband CDMA Celluar Systems","volume":"1","author":"Cong","year":"2002","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1109\/MSP.2005.1458287","article-title":"Locating the nodes: Cooperative localization in wireless sensor networks","volume":"22","author":"Patwari","year":"2005","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_26","unstructured":"Wylie, M.P., and Holtzman, J. (1996, January 2). The Non-line of Sight Problem in Mobile Location Estimation. Proceedings of the 5th International Conference on Universal Personal Communications, Cambridge, MA, USA."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1050","DOI":"10.1109\/TSP.2011.2177264","article-title":"On the Product of Independent Complex Gaussians","volume":"60","author":"Moura","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Cheffena, M., and Mohamed, M. (2018). The Application of Lognormal Mixture Shadowing Model for B2B Channels. IEEE Sens. Lett., 2.","DOI":"10.1109\/LSENS.2018.2848296"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/2\/338\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:26:21Z","timestamp":1760185581000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/2\/338"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,16]]},"references-count":28,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,1]]}},"alternative-id":["s19020338"],"URL":"https:\/\/doi.org\/10.3390\/s19020338","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,16]]}}}