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Graphical properties of easily localizable sensor networks


The sensor network localization problem is one of determining the Euclidean positions of all sensors in a network given knowledge of the Euclidean positions of some, and knowledge of a number of inter-sensor distances. This paper identifies graphical properties which can ensure unique localizability, and further sets of properties which can ensure not only unique localizability but also provide guarantees on the associated computational complexity, which can even be linear in the number of sensors on occasions. Sensor networks with minimal connectedness properties in which sensor transmit powers can be increased to increase the sensing radius lend themselves to the acquiring of the needed graphical properties. Results are presented for networks in both two and three dimensions.

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Author information

Correspondence to Brian D. O. Anderson.

Additional information

B. D. O. Anderson supported by National ICT Australia, which is funded by the Australian Government’s Department of Communications, Information Technology and the Arts and the Australian Research Council through the Backing Australia’s Ability initiative and the ICT Centre of Excellence Program.

A. S. Morse supported by US Army Research Office and US National Science Foundation.

W. Whiteley supported in part by grants from NSERC (Canada) and NIH (USA).

Y. R. Yang supported in part by US National Science Foundation.

Brian Anderson is a Distinguished Professor at the Research School of Information Sciences and Engineering, The Australian National University, Australia. Professor Anderson took his undergraduate degrees in Mathematics and Electrical Engineering at Sydney University, and his doctoral degree in Electrical Engineering at Stanford University. He worked in industry in the United States and at Stanford University before serving as Professor of Electrical Engineering at the University of Newcastle, Australia from 1967 through 1981. At that time, he took up a post as Professor and Head of the Department of Systems Engineering at the Australian National University in Canberra, where he was Director of the Research School of Information Sciences and Engineering from 1994 to 2002. For approximately one year to May 2003, he was the inaugural CEO of the newly formed National ICT Australia, established by the Australian Government through the Department of Communications, Information Technology and the Arts and the Australian Research Council under the Information and Communication Technologies Centre of Excellence program. Professor Anderson has served as a member of a number of government bodies, including the Australian Science and Technology Council and the Prime Minister’s Science, Engineering and Innovation Council. He was a member of the Board of Cochlear Limited, the world’s major supplier of cochlear implants from its listing until 2005. He is a Fellow of the Australian Academy of Science and Academy of Technological Sciences and Engineering, the Institute of Electrical and Electronic Engineers, and an Honorary Fellow of the Institution of Engineers, Australia. In 1989, he became a Fellow of the Royal Society, London, and in 2002 a Foreign Associate of the US National Academy of Engineering. He holds honorary doctorates of the Catholic University of Louvain in Belgium, the Swiss Federal Institute of Technology, and the Universities of Sydney, Melbourne and New South Wales. He was appointed an Officer of the Order of Australia in 1993. He was President of the International Federation of Automatic Control for the triennium 1990 to 1993, and served as President of the Australian Academy of Science for four years from 1998 to 2002. Professor Anderson became the Chief Scientist of National ICT Australia in May 2003 and served in that role till September 2006.

Tolga Eren received the B.S. degree in electrical engineering from Bilkent University, Ankara, Turkey, the M.S.E.E. degree in electrical engineering from the University of Massachusetts, the M.S. and the Ph.D. degrees in engineering and applied science from Yale University, New Haven, Connecticut, in 1994, 1998, 1999, and 2003, respectively. From October 2003 to July 2005, he was a postdoctoral research scientist at the Computer Science Department at Columbia University in the City of New York. Since September 2005, he has been at the department of Electrical Engineering at Kirikkale University, Turkey. His research interests are multi-agent (multi-robot, multi-vehicle) systems, sensor networks, computer vision, graph theory, and computational geometry.

A. Stephen Morse was born in Mt. Vernon, New York. He received a BSEE degree from Cornell University, MS degree from the University of Arizona, and a Ph.D. degree from Purdue University. From 1967 to 1970 he was associated with the Office of Control Theory and Application OCTA at the NASA Electronics Research Center in Cambridge, Mass. Since 1970 he has been with Yale University where he is presently the Dudley Professor of Engineering and a Professor of Computer Science. His main interest is in system theory and he has done research in network synthesis, optimal control, multivariable control, adaptive control, urban transportation, vision-based control, hybrid and nonlinear systems, sensor networks, and coordination and control of large grouping of mobile autonomous agents. He is a Fellow of the IEEE, a Distinguished Lecturer of the IEEE Control System Society, and a co-recipient of the Society’s 1993 and 2005 George S. Axelby Outstanding Paper Awards. He has twice received the American Automatic Control Council’s Best Paper Award and is a co-recipient of the Automatica Theory/Methodology Prize . He is the 1999 recipient of the IEEE Technical Field Award for Control Systems. He is a member of the National Academy of Engineering and the Connecticut Academy of Science and Engineering.

Walter Whiteley (B.Sc. 66, Queen’s University at Kingston, Canada) received his Ph.D. in Mathematics from MIT, Cambridge Mass in 1971. He is currently the Director of Applied Mathematics at York University, and a member of the graduate programs in Mathematics, in Computer Science, and in Education. His research focuses on the rigidity and flexibility of systems of geometric constraints (distances, angles, directions, projections, …). Recent work has included applications of this theory to location in networks, control of formations of autonomous agents, built structures in structural engineering, linkages in mechanical engineering, geometric constraints in computational geometry and CAD, and algorithms for protein flexibility in biochemistry. He is also active in geometry education and development of visual reasoning at all levels of mathematics education and in applications of mathematics.

Yang Richard Yang received the B.E. degree in Computer Science and Technology from Tsinghua University, Beijing, China, in 1993, and the M.S. and Ph.D. degrees in Computer Science from the University of Texas at Austin in 1998 and 2001, respectively. Since 2001, he has been with the Department of Computer Science, Yale University, New Haven, CT, where currently he is an Associate Professor of Computer Science and Electrical Engineering. His current research interests are in computer networks, mobile computing, and sensor networks. He leads the Laboratory of Networked Systems (LANS) at Yale University.

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Anderson, B.D.O., Belhumeur, P.N., Eren, T. et al. Graphical properties of easily localizable sensor networks. Wireless Netw 15, 177–191 (2009). https://doi.org/10.1007/s11276-007-0034-9

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  • Localization
  • Sensor networks
  • Global rigidity
  • Graph theory