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A closed-form algorithm for the least-squares trilateration problem

Published online by Cambridge University Press:  20 May 2010

Yu Zhou
Yu Zhou*
Affiliation:
Department of Mechanical Engineering, State University of New York at Stony Brook, Stony Brook, NY 11794, USA
*
*Corresponding author. E-mail: yuzhou@notes.cc.sunysb.edu
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Summary

Trilateration is the most adopted external reference-based localization technique for mobile robots, given the correspondence of external references. The nonlinear least-squares trilateration formulation provides an optimal position estimate from a general number (greater than or equal to the dimension of the environment) of reference points and corresponding distance measurements. This paper presents a novel closed-form solution to the nonlinear least-squares trilateration problem. The performance of the proposed algorithm in dealing with erroneous inputs of reference points and distance measurements has been analyzed through representative examples. The proposed trilateration algorithm has low computational complexity, high operational robustness, and reduced systematic error and uncertainty in position estimation. The effectiveness of the proposed algorithm has been further verified through an experimental test.

Keywords

LocalizationTrilaterationMobile robot
Type
Article
Information
Robotica , Volume 29 , Issue 3 , May 2011 , pp. 375 - 389
Copyright
Copyright © Cambridge University Press 2010

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