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....
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2009 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/7474 |
| Acceso en línea: | https://hdl.handle.net/2117/7474 |
| Access Level: | acceso abierto |
| Palabra clave: | 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 |
| Sumario: | 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. |
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