{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T07:18:19Z","timestamp":1761895099399,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2010,6,9]],"date-time":"2010-06-09T00:00:00Z","timestamp":1276041600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Localization is one of the most fundamental problems in wireless sensor networks, since the locations of the sensor nodes are critical to both network operations and most application level tasks. A GPS-free localization scheme for wireless sensor networks is presented in this paper. First, we develop a standardized clustering-based approach for the local coordinate system formation wherein a multiplication factor is introduced to regulate the number of master and slave nodes and the degree of connectivity among master nodes. Second, using homogeneous coordinates, we derive a transformation matrix between two Cartesian coordinate systems to efficiently merge them into a global coordinate system and effectively overcome the flip ambiguity problem. The algorithm operates asynchronously without a centralized controller; and does not require that the location of the sensors be known a priori. A set of parameter-setting guidelines for the proposed algorithm is derived based on a probability model and the energy requirements are also investigated. A simulation analysis on a specific numerical example is conducted to validate the mathematical analytical results. We also compare the performance of the proposed algorithm under a variety multiplication factor, node density and node communication radius scenario. Experiments show that our algorithm outperforms existing mechanisms in terms of accuracy and convergence time.<\/jats:p>","DOI":"10.3390\/s100605899","type":"journal-article","created":{"date-parts":[[2010,6,9]],"date-time":"2010-06-09T11:22:42Z","timestamp":1276082562000},"page":"5899-5926","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":37,"title":["GPS-Free Localization Algorithm for Wireless Sensor Networks"],"prefix":"10.3390","volume":"10","author":[{"given":"Lei","family":"Wang","sequence":"first","affiliation":[{"name":"School of Computer Science and Engineering, Xi\u2019an University of Technology, Xi\u2019an 710048, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingzheng","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, Xi\u2019an University of Technology, Xi\u2019an 710048, China"},{"name":"Xi\u2019an Communication Institute, Xi\u2019an 710106, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2010,6,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Stojmenovic, I. (2005). Handbook of Sensor Networks: Algorithms and Architectures, John Wiley and Sons.","DOI":"10.1002\/047174414X"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"961","DOI":"10.1109\/TPDS.2004.67","article-title":"Localization from connectivity in sensor network","volume":"15","author":"Shang","year":"2004","journal-title":"IEEE Trans. Parallel Distrib. Syst"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2529","DOI":"10.1016\/j.comnet.2006.11.018","article-title":"Wireless sensor network localization techniques","volume":"51","author":"Mao","year":"2007","journal-title":"Comput. Networks"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1007\/s11768-010-9187-7","article-title":"A survey on sensor localization","volume":"8","author":"Wang","year":"2010","journal-title":"J. Control Theory Appl"},{"key":"ref_5","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_6","unstructured":"Bahl, P., and Padmanabhan, V.N. (, January March). Radar: an in-building RF-based user location and tracking system. Tel Aviv, Israel."},{"key":"ref_7","unstructured":"Niculescu, D., and Nath, B. (, January November). Ad hoc positioning system (APS). San Antonio, TX, USA."},{"key":"ref_8","unstructured":"Niculescu, D., and Nath, B. (, January April). Ad hoc positioning system (APS) using AOA. San Francisco, CA, USA."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1145\/972627.972630","article-title":"Self-configuring localization systems: Design and experimental evaluation","volume":"3","author":"Bulusu","year":"2004","journal-title":"ACM Trans. Embed. Comput. Syst"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1109\/TNET.2005.850202","article-title":"Novel self-configurable positioning technique for multi-hop wireless networks","volume":"13","author":"Wu","year":"2005","journal-title":"IEEE\/ACM T. Network"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2153","DOI":"10.1016\/j.sigpro.2005.07.042","article-title":"Uwb location and tracking for wireless embedded networks","volume":"86","author":"Yu","year":"2006","journal-title":"Signal Process"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1049\/iet-com.2007.0603","article-title":"Anchor-free localisation algorithm and performance analysis in wireless sensor networks","volume":"3","author":"Yu","year":"2009","journal-title":"IET Commun"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1109\/2.940014","article-title":"Location systems for ubiquitous computing","volume":"34","author":"Hightower","year":"2001","journal-title":"Computer"},{"key":"ref_14","unstructured":"Capkun, S., Hamdi, M., and Hubaux, J.P. (, January January). Gps-free positioning in ad-hoc networks. Maui, HI, USA."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1023\/A:1013933626682","article-title":"Gps-free positioning in mobile ad hoc networks","volume":"5","author":"Capkun","year":"2002","journal-title":"Cluster Comput"},{"key":"ref_16","unstructured":"Iyengar, R., and Sikdar, B. (, January May). Scalable and distributed GPS free positioning for sensor networks. Anchorage, AK, USA."},{"key":"ref_17","unstructured":"Li, H.J., Wang, J.W., Li, X., Ma, H., and Huang, Q.W. (, January August). A distributed 3 dimension relative localization algorithm for mobile wireless sensor networks. Harbin, China."},{"key":"ref_18","unstructured":"Yu, G.J., and Wang, S.C. (, January July). A hierarchical MDS-based localization algorithm for wireless sensor networks. Budapest, Hungary."},{"key":"ref_19","unstructured":"He, R., Ghavami, M., and Aghvami, H. (, January September). Ultra wide-band (UWB) positioning routing in ad hoc networks. Athens, Greece."},{"key":"ref_20","unstructured":"Wen, C.Y., and Hsiao, Y.C. (, January October). Decentralized anchor-free localization for wireless ad-hoc sensor networks. Singapore."},{"key":"ref_21","unstructured":"Moore, D., Leonard, J., Rus, D., and Teller, S. (, January November). Robust distributed network localization with noisy range measurements. Baltimore, MD, USA."},{"key":"ref_22","unstructured":"Kannan, A.A., Mao, G.Q., and Vucetic, B. (, January May). Simulated annealing based wireless sensor network localization with flip ambiguity mitigation. Melbourne, Australia."},{"key":"ref_23","first-page":"155","article-title":"Backbone based GPS-free localization in mobile ad hoc networks","volume":"16","author":"Tian","year":"2007","journal-title":"Chinese J. Electron"},{"key":"ref_24","unstructured":"Chen, J.J., Xu, B.C., and Ding, Li. (, January April). Relative localization systems and algorithms for wireless sensor networks. Sanya, China."},{"key":"ref_25","unstructured":"Rappaport, T.S. (2001). Wireless Communications: Principles and Practice, Prentice Hall. [2nd ed]."},{"key":"ref_26","unstructured":"Damosso, E. (1999). Digital Mobile Radio towards Future Generation Systems\u2013Cost 231 Final Report, European Commission."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1109\/TWC.2003.819035","article-title":"Super-resolution TOA estimation with diversity for indoor geolocation","volume":"3","author":"Li","year":"2004","journal-title":"IEEE Trans. Wireless Commun"},{"key":"ref_28","unstructured":"Lanzisera, S., Lin, D.T., and Pister, K.S.J. (, January June). Rf time of flight ranging for wireless sensor network localization. Vienna, Austria."},{"key":"ref_29","unstructured":"Priyantha, N.B., Chakraborty, A., and Balakrishnan, H. (, January August). The cricket location-support system. Boston, MA, USA."},{"key":"ref_30","first-page":"686","article-title":"Automatic decentralized clustering for wireless sensor networks","volume":"28","author":"Wen","year":"2005","journal-title":"Eurasip J. Wirel. Comm"},{"key":"ref_31","unstructured":"Hearn, D., and Baker, M.P. (2003). Computer Graphics with OpenGL, Prentice Hall. [3rd ed]."},{"key":"ref_32","unstructured":"Vince, J. (2005). Mathematics for Computer Graphics, Springer. [2nd ed]."},{"key":"ref_33","unstructured":"Eren, T., Goldenberg, D.K., Whiteley, W., Yang, Y.R., Morse, A.S., Anderson, B.D.O., and Belhumeur, P.N. (, January March). Rigidity, computation, and randomization in network localization. Hong Kong, China."},{"key":"ref_34","unstructured":"Santi, P., Blough, D.M., and Vainstein, F. (, January October). A probabilistic analysis for the range assignment problem in ad hoc networks. Long Beach, CA, USA."},{"key":"ref_35","first-page":"69","article-title":"Measure the range of sensor networks","volume":"47","author":"See","year":"2008","journal-title":"Microwave. RF"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/10\/6\/5899\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:02:40Z","timestamp":1760220160000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/10\/6\/5899"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,6,9]]},"references-count":35,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2010,6]]}},"alternative-id":["s100605899"],"URL":"https:\/\/doi.org\/10.3390\/s100605899","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2010,6,9]]}}}