Publication
Revisiting trilateration for robot localization
Journal Article (2005)
Journal
IEEE Transactions on Robotics
Pages
93-101
Volume
21
Number
1
Doc link
http://dx.doi.org/10.1109/TRO.2004.833793
File
Abstract
Locating a robot from its distances, or range measurements, to three other known points or stations is a common operation, known as trilateration. This problem has been traditionally solved either by algebraic or numerical methods. An approach that avoids the direct algebrization of the problem is proposed here. Using constructive geometric arguments, a coordinate-free formula containing a small number of Cayley-Menger determinants is derived. This formulation accommodates a more thorough investigation of the effects caused by all possible sources of error, including round-off errors, for the first time in this context. New formulas for the variance and bias of the unknown robot location estimation, due to station location and range measurements errors, are derived and analyzed. They are proved to be more tractable compared with previous ones, because all their terms have geometric meaning, allowing a simple analysis of their asymptotic behavior near singularities.
Categories
robots.
Author keywords
cayley-menger determinants, error analysis, numerical conditioning, robot localization, trilateration
Scientific reference
F. Thomas and L. Ros. Revisiting trilateration for robot localization. IEEE Transactions on Robotics, 21(1): 93-101, 2005.
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