Trilateration Analysis for Movement Planning in a Group of Mobile Robots
AIMSA '08 Proceedings of the 13th international conference on Artificial Intelligence: Methodology, Systems, and Applications
Ad-Hoc Communication and Localization System for Mobile Robots
Proceedings of the FIRA RoboWorld Congress 2009 on Advances in Robotics
Distributed sensor localization in random environments using minimal number of anchor nodes
IEEE Transactions on Signal Processing
An efficient least-squares trilateration algorithm for mobile robot localization
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
New iterative algorithm for hyperbolic positioning used in an ultrasonic local positioning system
ETFA'09 Proceedings of the 14th IEEE international conference on Emerging technologies & factory automation
An experimental measuring instrument to characterize partial discharges by sensor fusion
ICICS'09 Proceedings of the 7th international conference on Information, communications and signal processing
Timing-Based Mobile Sensor Localization in Wireless Sensor and Actor Networks
Mobile Networks and Applications
Beacon scheduling algorithm for localization of a mobile robot
ICIRA'11 Proceedings of the 4th international conference on Intelligent Robotics and Applications - Volume Part I
Benefits of averaging lateration estimates obtained using overlapped subgroups of sensor data
Digital Signal Processing
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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.