{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T14:31:08Z","timestamp":1774276268233,"version":"3.50.1"},"reference-count":47,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2017,12,11]],"date-time":"2017-12-11T00:00:00Z","timestamp":1512950400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Location localization technology is used in a number of industrial and civil applications. Real time location localization accuracy is highly dependent on the quality of the distance measurements and efficiency of solving the localization equations. In this paper, we provide a novel approach to solve the nonlinear localization equations efficiently and simultaneously eliminate the bad measurement data in range-based systems. A geometric intersection model was developed to narrow the target search area, where Newton\u2019s Method and the Direct Search Method are used to search for the unknown position. Not only does the geometric intersection model offer a small bounded search domain for Newton\u2019s Method and the Direct Search Method, but also it can self-correct bad measurement data. The Direct Search Method is useful for the coarse localization or small target search domain, while the Newton\u2019s Method can be used for accurate localization. For accurate localization, by utilizing the proposed Modified Newton\u2019s Method (MNM), challenges of avoiding the local extrema, singularities, and initial value choice are addressed. The applicability and robustness of the developed method has been demonstrated by experiments with an indoor system.<\/jats:p>","DOI":"10.3390\/s17122869","type":"journal-article","created":{"date-parts":[[2017,12,11]],"date-time":"2017-12-11T12:26:37Z","timestamp":1512995197000},"page":"2869","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["A Practical, Robust and Fast Method for Location Localization in Range-Based Systems"],"prefix":"10.3390","volume":"17","author":[{"given":"Shiping","family":"Huang","sequence":"first","affiliation":[{"name":"State Key Lab of Subtropical Building Science, South China University of Technology, Guangzhou 510640, China"},{"name":"State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhifeng","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Information, Guangdong Communication Polytechnic, Guangzhou 510650, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anil","family":"Misra","sequence":"additional","affiliation":[{"name":"Civil, Environmental and Architectural Engineering, The University of Kansas, Lawrence, KS 66045, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,12,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/S0004-3702(01)00069-8","article-title":"Robust Monte Carlo localization for mobile robots","volume":"128","author":"Thrun","year":"2001","journal-title":"Artif. Intell."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1177\/027836498400300301","article-title":"Model-based recognition and localization from sparse range or tactile data","volume":"3","author":"Grimson","year":"1984","journal-title":"Int. J. Robot. Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1109\/TITS.2012.2213815","article-title":"GPS localization accuracy classification: A context-based approach","volume":"14","author":"Drawil","year":"2013","journal-title":"IEEE Trans. Intell. Trans. Syst."},{"key":"ref_4","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. Part C"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"6611","DOI":"10.3390\/rs5126611","article-title":"Indoor localization algorithms for an ambulatory human operated 3D mobile mapping system","volume":"5","author":"Corso","year":"2013","journal-title":"Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Qian, C., Liu, H., Tang, J., Chen, Y., Kaartinen, H., Kukko, A., Zhu, L., Liang, X., Chen, L., and Hyypp\u00e4, J. (2016). An integrated GNSS\/INS\/LIDAR-SLAM positioning method for highly accurate forest stem mapping. Remote Sens., 9.","DOI":"10.3390\/rs9010003"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Wu, J., Xu, Y., Zhong, X., Sun, Z., and Yang, J. (2017). A three-dimensional localization method for multistatic SAR based on numerical range-doppler algorithm and entropy minimization. Remote Sens., 9.","DOI":"10.3390\/rs9050470"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1109\/TGRS.2010.2051675","article-title":"Combination of advanced inversion techniques for an accurate target localization via GPR for demining applications","volume":"49","author":"Soldovieri","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1109\/98.878533","article-title":"GPS-less low-cost outdoor localization for very small devices","volume":"7","author":"Bulusu","year":"2000","journal-title":"IEEE Pers. Commun."},{"key":"ref_10","first-page":"1","article-title":"Dynamic accuracy of GPS receivers for use in health research: A novel method to assess GPS accuracy in real-world settings","volume":"23","author":"Schipperijn","year":"2014","journal-title":"Emerg. Technol. Promot. Eval. Phys. Act."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Biswas, J., and Veloso, M.M. (2010, January 3\u20137). Wifi localization and navigation for autonomous indoor mobile robots. Proceedings of the 2010 IEEE International Conference on Robotics and Automation (ICRA), Anchorage, AK, USA.","DOI":"10.1109\/ROBOT.2010.5509842"},{"key":"ref_12","unstructured":"Youssef, M.A., Agrawala, A., and Shankar, A.U. (2003, January 26). Wlan location determination via clustering and probability distributions. Proceedings of the First IEEE International Conference on Pervasive Computing and Communications, Fort Worth, TX, USA."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Altini, M., Brunelli, D., Farella, E., and Benini, L. (2010, January 5\u20137). Bluetooth indoor localization with multiple neural networks. Proceedings of the 2010 5th IEEE International Symposium on Wireless Pervasive Computing (ISWPC), Modena, Italy.","DOI":"10.1109\/ISWPC.2010.5483748"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Raghavan, A.N., Ananthapadmanaban, H., Sivamurugan, M.S., and Ravindran, B. (2010, January 3\u20137). Accurate mobile robot localization in indoor environments using bluetooth. Proceedings of the 2010 IEEE International Conference on Robotics and Automation (ICRA), Anchorage, AK, USA.","DOI":"10.1109\/ROBOT.2010.5509232"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1016\/j.compag.2010.08.014","article-title":"ZigBee-based wireless sensor network localization for cattle monitoring in grazing fields","volume":"74","author":"Young","year":"2010","journal-title":"Comput. Electron. Agric."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Cheon, J., Hwang, H., Kim, D., and Jung, Y. (2016). IEEE 802.15. 4 ZigBee-based time-of-arrival estimation for wireless sensor networks. Sensors, 16.","DOI":"10.3390\/s16020203"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3501","DOI":"10.3390\/s130303501","article-title":"Ultrasound indoor positioning system based on a low-power wireless sensor network providing sub-centimeter accuracy","volume":"13","author":"Medina","year":"2013","journal-title":"Sensors"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"698","DOI":"10.1016\/j.pmcj.2007.07.004","article-title":"GSM indoor localization","volume":"3","author":"Varshavsky","year":"2007","journal-title":"Pervasive Mob. Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1109\/TWC.2002.800542","article-title":"Hybrid TDOA\/AOA mobile user location for wideband cdma cellular systems","volume":"1","author":"Cong","year":"2002","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"8051","DOI":"10.1109\/JSEN.2016.2604424","article-title":"Smartphone-based indoor localization system using inertial sensor and acoustic transmitter\/receiver","volume":"16","author":"Yang","year":"2016","journal-title":"IEEE Sens. J."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1109\/TAES.2008.4560210","article-title":"Position error bound for uwb localization in dense cluttered environments","volume":"44","author":"Jourdan","year":"2008","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1677","DOI":"10.1109\/JSAC.2002.805060","article-title":"Ranging in a dense multipath environment using an UWB radio link","volume":"20","author":"Lee","year":"2002","journal-title":"Sel. Areas Commun. IEEE J."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Masiero, A., Fissore, F., and Vettore, A. (2017). A low cost UWB based solution for direct georeferencing UAV photogrammetry. Remote Sens., 9.","DOI":"10.3390\/rs9050414"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"9045","DOI":"10.3390\/s110909045","article-title":"A framework for UWB-based communication and location tracking systems for wireless sensor networks","volume":"11","author":"Valdovinos","year":"2011","journal-title":"Sensors"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"404","DOI":"10.1109\/JPROC.2008.2008846","article-title":"Ranging with ultrawide bandwidth signals in multipath environments","volume":"97","author":"Dardari","year":"2009","journal-title":"Proc. IEEE"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Jachimczyk, B., Dziak, D., and Kulesza, W.J. (2017). Customization of UWB 3D-RTLS based on the new uncertainty model of the AoA ranging technique. Sensors, 17.","DOI":"10.3390\/s17020227"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Patwari, N., and Hero, A.O. (2003, January 19). Using proximity and quantized RSS for sensor localization in wireless networks. Proceedings of the 2nd ACM International Conference on Wireless Sensor Networks and Applications, San Diego, CA, USA.","DOI":"10.1145\/941350.941354"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1109\/TAES.1976.308294","article-title":"Position-location solutions by Taylor-series estimation","volume":"AES-12","author":"Foy","year":"1976","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Nguyen, T.L., and Shin, Y. (2016). Matrix completion optimization for localization in wireless sensor networks for intelligent IoT. Sensors, 16.","DOI":"10.3390\/s16050722"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Leugner, S., Pelka, M., and Hellbr\u00fcck, H. (2016, January 19\u201320). Comparison of wired and wireless synchronization with clock drift compensation suited for U-TDoA localization. Proceedings of the 2016 13th Workshop on Positioning, Navigation and Communications (WPNC), Bremen, Germany.","DOI":"10.1109\/WPNC.2016.7822846"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1109\/LAWP.2005.852577","article-title":"Low-cost PCB antenna for UWB applications","volume":"4","author":"Low","year":"2005","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1002\/mop.11392","article-title":"A new ultra-wideband antenna for UWB applications","volume":"40","author":"Choi","year":"2004","journal-title":"Microw. Opt. Technol. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1109\/4234.660801","article-title":"On the robustness of ultra-wide bandwidth signals in dense multipath environments","volume":"2","author":"Win","year":"1998","journal-title":"IEEE Commun. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1613","DOI":"10.1109\/JSAC.2002.805031","article-title":"Characterization of ultra-wide bandwidth wireless indoor channels: A communication-theoretic view","volume":"20","author":"Win","year":"2002","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"829","DOI":"10.3390\/s130100829","article-title":"About non-line-of-sight satellite detection and exclusion in a 3D map-aided localization algorithm","volume":"13","author":"Peyraud","year":"2013","journal-title":"Sensors"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"M\u00fcller, C.A., and Delande, D. (arXiv, 2010). Disorder and interference: Localization phenomena, arXiv.","DOI":"10.1093\/acprof:oso\/9780199603657.003.0009"},{"key":"ref_37","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 Proc."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Kelley, C.T. (2003). Solving Nonlinear Equations with Newton\u2019s Method, SIAM.","DOI":"10.1137\/1.9780898718898"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Yang, L., Cao, J., and Yang, W. (2016, January 6\u201310). TDOA location based on modified newton method. Proceedings of the 2016 IEEE 13th International Conference on Signal Processing (ICSP), Chengdu, China.","DOI":"10.1109\/ICSP.2016.7878079"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2181","DOI":"10.1109\/JSEN.2013.2249660","article-title":"A distributed localization algorithm for wireless sensor networks based on the solutions of spatially-constrained local problems","volume":"13","author":"Rosiles","year":"2013","journal-title":"IEEE Sens. J."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Duff, I.S., Erisman, A.M., and Reid, J.K. (2017). Direct Methods for Sparse Matrices, Oxford University Press.","DOI":"10.1093\/acprof:oso\/9780198508380.001.0001"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1145\/356004.356007","article-title":"Efficient Gaussian elimination method for symbolic determinants and linear systems","volume":"8","author":"Sasaki","year":"1982","journal-title":"ACM Trans. Math. Softw."},{"key":"ref_43","first-page":"197","article-title":"Micromechanics based stress-displacement relationships of rough contacts: Numerical implementation under combined normal and shear loading","volume":"52","author":"Misra","year":"2009","journal-title":"Comput. Model. Eng. Sci"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Huber, P.J. (2011). Robust Statistics, Springer.","DOI":"10.1007\/978-3-642-04898-2_594"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"5801","DOI":"10.1109\/TWC.2009.12.090319","article-title":"Localization with a mobile beacon based on geometric constraints in wireless sensor networks","volume":"8","author":"Lee","year":"2009","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"839","DOI":"10.3390\/s120100839","article-title":"A low-complexity geometric bilateration method for localization in wireless sensor networks and its comparison with least-squares methods","volume":"12","author":"Rosiles","year":"2012","journal-title":"Sensors"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1007\/s11704-008-0018-7","article-title":"A robust localization algorithm in wireless sensor networks","volume":"2","author":"Li","year":"2008","journal-title":"Front. Comput. Sci. China"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/12\/2869\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:53:28Z","timestamp":1760208808000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/12\/2869"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12,11]]},"references-count":47,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2017,12]]}},"alternative-id":["s17122869"],"URL":"https:\/\/doi.org\/10.3390\/s17122869","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,12,11]]}}}