Polynomial methods in noisy network localization

In this paper we introduce a polynomial method for addressing sensor network localization problems when the inter-sensor measurements are noisy. We compare the results obtained applying this method with the results obtained by other localization methods in the literature. Later in the paper we propose tools from algebraic geometry to aid us solve the problem in a more computationally appealing way.

[1]  C. B. García,et al.  On the Number of Solutions to Polynomial Systems of Equations , 1980 .

[2]  J. Carroll.  Vulnerability Assessment of the U.S. Transportation Infrastructure that Relies on the Global Positioning System , 2003 .

[3]  Federico Thomas,et al.  Revisiting trilateration for robot localization , 2005, IEEE Transactions on Robotics.

[4]  Brian D. O. Anderson,et al.  Wireless sensor network localization techniques , 2007, Comput. Networks.

[5]  David E. Culler,et al.  The effects of ranging noise on multihop localization: an empirical study , 2005, IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005..

[6]  Pablo A. Parrilo,et al.  Minimizing Polynomial Functions , 2001, Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science.

[7]  Pablo A. Parrilo,et al.  Semidefinite programming relaxations for semialgebraic problems , 2003, Math. Program..

[8]  J. Lasserre,et al.  Detecting global optimality and extracting solutions in GloptiPoly , 2003 .

[9]  Brian D. O. Anderson,et al.  Circumnavigation using distance measurements , 2009, 2009 European Control Conference (ECC).

[10]  Jian Li,et al.  Exact and Approximate Solutions of Source Localization Problems , 2008, IEEE Transactions on Signal Processing.

[11]  Ali H. Sayed,et al.  Network-based wireless location , 2005 .

[12]  Brian D. O. Anderson,et al.  Cooperative Self-Localization of Mobile Agents , 2011, IEEE Transactions on Aerospace and Electronic Systems.

[13]  Stergios I. Roumeliotis,et al.  Robot-to-Robot Relative Pose Estimation From Range Measurements , 2008, IEEE Transactions on Robotics.

[14]  Brian D. O. Anderson,et al.  Sensor network localization with imprecise distances , 2006, Syst. Control. Lett..