Ranging algebraically with more observations than unknowns
In the recently developed Spatial Reference System that is designed to check and control the accuracy of the three-dimensional coordinate measuring machines and tooling equipment (Metronom US., Inc., Ann Arbor: <a href="http://www.metronomus.com),">http://www.metronomus.com),</a&g...
| Main Authors: | , , , , |
|---|---|
| Format: | Journal Article |
| Published: |
Terra Scientific Publishing Company
2003
|
| Online Access: | http://www.terrapub.co.jp/journals/EPS/pdf/2003/5507/55070387.pdf http://hdl.handle.net/20.500.11937/28433 |
| _version_ | 1848752535522770944 |
|---|---|
| author | Awange, Joseph Fukuda, Y. Takemoto, S. Ateya, I. Grafarend, E. |
| author_facet | Awange, Joseph Fukuda, Y. Takemoto, S. Ateya, I. Grafarend, E. |
| author_sort | Awange, Joseph |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In the recently developed Spatial Reference System that is designed to check and control the accuracy of the three-dimensional coordinate measuring machines and tooling equipment (Metronom US., Inc., Ann Arbor: <a href="http://www.metronomus.com),">http://www.metronomus.com),</a> the coordinates of the edges of the instrument are computed from distances of the bars. The use of distances in industrial application is fast gaining momentum just as in Geodesy and in Geophysical applications and thus necessitating efficient algorithms to solve the nonlinear distance equations. Whereas the ranging problem with minimum known stations was considered in our previous contribution in the same Journal, the present contribution extends to the case where one is faced with many distance observations than unknowns (overdetermined case) as is usually the case in practise. Using the Gauss-Jacobi Combinatorial approach, we demonstrate how one can proceed to position without reverting to iterative and linearizing procedures such as Newton's or Least Squares approach. |
| first_indexed | 2025-11-14T08:10:10Z |
| format | Journal Article |
| id | curtin-20.500.11937-28433 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:10:10Z |
| publishDate | 2003 |
| publisher | Terra Scientific Publishing Company |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-284332017-01-30T13:04:57Z Ranging algebraically with more observations than unknowns Awange, Joseph Fukuda, Y. Takemoto, S. Ateya, I. Grafarend, E. In the recently developed Spatial Reference System that is designed to check and control the accuracy of the three-dimensional coordinate measuring machines and tooling equipment (Metronom US., Inc., Ann Arbor: <a href="http://www.metronomus.com),">http://www.metronomus.com),</a> the coordinates of the edges of the instrument are computed from distances of the bars. The use of distances in industrial application is fast gaining momentum just as in Geodesy and in Geophysical applications and thus necessitating efficient algorithms to solve the nonlinear distance equations. Whereas the ranging problem with minimum known stations was considered in our previous contribution in the same Journal, the present contribution extends to the case where one is faced with many distance observations than unknowns (overdetermined case) as is usually the case in practise. Using the Gauss-Jacobi Combinatorial approach, we demonstrate how one can proceed to position without reverting to iterative and linearizing procedures such as Newton's or Least Squares approach. 2003 Journal Article http://hdl.handle.net/20.500.11937/28433 http://www.terrapub.co.jp/journals/EPS/pdf/2003/5507/55070387.pdf Terra Scientific Publishing Company restricted |
| spellingShingle | Awange, Joseph Fukuda, Y. Takemoto, S. Ateya, I. Grafarend, E. Ranging algebraically with more observations than unknowns |
| title | Ranging algebraically with more observations than unknowns |
| title_full | Ranging algebraically with more observations than unknowns |
| title_fullStr | Ranging algebraically with more observations than unknowns |
| title_full_unstemmed | Ranging algebraically with more observations than unknowns |
| title_short | Ranging algebraically with more observations than unknowns |
| title_sort | ranging algebraically with more observations than unknowns |
| url | http://www.terrapub.co.jp/journals/EPS/pdf/2003/5507/55070387.pdf http://hdl.handle.net/20.500.11937/28433 |