Direct polynomial approach to nonlinear distance (ranging) problems
In GPS atmospheric sounding, geodetic positioning, robotics and photogrammetric (perspective center and intersection) problems, distances (ranges) as observables play a key role in determining the unknown parameters. The measured distances (ranges) are however normally related to the desired paramet...
| Main Authors: | , , , |
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| Format: | Journal Article |
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Terra Scientific Publishing Company
2003
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| Online Access: | http://www.terrapub.co.jp/journals/EPS/pdf/2003/5505/55050231.pdf http://hdl.handle.net/20.500.11937/40047 |
| _version_ | 1848755759749267456 |
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| author | Awange, Joseph Grafarend, E. Fukuda, Y. Takemoto, S. |
| author_facet | Awange, Joseph Grafarend, E. Fukuda, Y. Takemoto, S. |
| author_sort | Awange, Joseph |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In GPS atmospheric sounding, geodetic positioning, robotics and photogrammetric (perspective center and intersection) problems, distances (ranges) as observables play a key role in determining the unknown parameters. The measured distances (ranges) are however normally related to the desired parameters via nonlinear equations or nonlinear system of equations that require explicit or exact solutions. Procedures for solving such equations are either normally iterative, and thus require linearization or the existing analytical procedures require laborious forward and backward substitutions. We present in the present contribution direct procedures for solving distance nonlinear system of equations without linearization, iteration, forward and backward substitution. In particular, we exploit the advantage of faster computers with large storage capacities and the computer algebraic softwares of Mathematica, Maple and Matlab to test polynomial based approaches. These polynomial (algebraic based) approaches turn out to be the key to solving distance nonlinear system of equations. The algebraic techniques discussed here does not however solve all general types of nonlinear equations but only those nonlinear system of equations that can be converted into algebraic (polynomial) form. |
| first_indexed | 2025-11-14T09:01:25Z |
| format | Journal Article |
| id | curtin-20.500.11937-40047 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:01:25Z |
| publishDate | 2003 |
| publisher | Terra Scientific Publishing Company |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-400472017-01-30T14:39:19Z Direct polynomial approach to nonlinear distance (ranging) problems Awange, Joseph Grafarend, E. Fukuda, Y. Takemoto, S. In GPS atmospheric sounding, geodetic positioning, robotics and photogrammetric (perspective center and intersection) problems, distances (ranges) as observables play a key role in determining the unknown parameters. The measured distances (ranges) are however normally related to the desired parameters via nonlinear equations or nonlinear system of equations that require explicit or exact solutions. Procedures for solving such equations are either normally iterative, and thus require linearization or the existing analytical procedures require laborious forward and backward substitutions. We present in the present contribution direct procedures for solving distance nonlinear system of equations without linearization, iteration, forward and backward substitution. In particular, we exploit the advantage of faster computers with large storage capacities and the computer algebraic softwares of Mathematica, Maple and Matlab to test polynomial based approaches. These polynomial (algebraic based) approaches turn out to be the key to solving distance nonlinear system of equations. The algebraic techniques discussed here does not however solve all general types of nonlinear equations but only those nonlinear system of equations that can be converted into algebraic (polynomial) form. 2003 Journal Article http://hdl.handle.net/20.500.11937/40047 http://www.terrapub.co.jp/journals/EPS/pdf/2003/5505/55050231.pdf Terra Scientific Publishing Company restricted |
| spellingShingle | Awange, Joseph Grafarend, E. Fukuda, Y. Takemoto, S. Direct polynomial approach to nonlinear distance (ranging) problems |
| title | Direct polynomial approach to nonlinear distance (ranging) problems |
| title_full | Direct polynomial approach to nonlinear distance (ranging) problems |
| title_fullStr | Direct polynomial approach to nonlinear distance (ranging) problems |
| title_full_unstemmed | Direct polynomial approach to nonlinear distance (ranging) problems |
| title_short | Direct polynomial approach to nonlinear distance (ranging) problems |
| title_sort | direct polynomial approach to nonlinear distance (ranging) problems |
| url | http://www.terrapub.co.jp/journals/EPS/pdf/2003/5505/55050231.pdf http://hdl.handle.net/20.500.11937/40047 |