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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 927031, 18 pages
Research Article

Geometric Buildup Algorithms for Sensor Network Localization

1Department of Mathematics, University of California, Irvine, CA 92697, USA
2School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China
3Department of Mathematics, Iowa State University, Ames, IA 50011, USA

Received 6 June 2011; Revised 22 August 2011; Accepted 22 August 2011

Academic Editor: Jinling Liang

Copyright © 2012 Zhenzhen Zheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a geometric buildup algorithm for solving the sensor network localization problem with either accurate or noisy distance data. The algorithm determines the locations of the sensors, one at a time, by using the distances between the determined sensors and the undetermined ones. Each time, only a small system of distance equations needs to be solved and therefore, in an ideal case when the required distances are available for every sensor to be determined, the computation can be completed in n steps if n sensors are to be determined. An algorithm with two buildup phases is also implemented to handle not only noisy but also sparse distance data with for example only a few distant anchors. We show our test results and compare them with other approaches.