Concise proof of Tienstra's formula

The resection problem consists in finding the location of an observer by measuring the angles sub-tended by lines of sight from this observer to three known stations. Many researchers and practitioners recognize that Tienstra’s formula provides the most compact and elegant solution to this problem....

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Bibliographic Details
Authors: Porta Pleite, Josep Maria|||0000-0002-5056-1717, Thomas, Federico|||0000-0001-9341-5528
Format: article
Publication Date:2009
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/7474
Online Access:https://hdl.handle.net/2117/7474
Access Level:Open access
Keyword:Global Positioning System
Triangulation
Tienstra's formula Triangulation Resection Global localization Barycentric coordinates
Robòtica
Classificació INSPEC::Automation::Robots
Àrees temàtiques de la UPC::Informàtica::Robòtica
Description
Summary:The resection problem consists in finding the location of an observer by measuring the angles sub-tended by lines of sight from this observer to three known stations. Many researchers and practitioners recognize that Tienstra’s formula provides the most compact and elegant solution to this problem. Un- fortunately, all available proofs for this remarkable formula are intricate. This paper shows how, by using barycentric coordinates for the observer in terms of the locations of the stations, a neat and short proof is straightforwardly derived.