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Free adjustment of a triangulation net
It is often useful to determine the measures of precision of the directly observed quantities in a triangulation net. Provided the net is not strained these measures are unique to a particular set of observations and weights. Unique measures for the precision of the indirectly observed quantities ca...
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| Format: | Thesis |
| Language: | English |
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School of Architecture, Planning and Geomatics
2016
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| _version_ | 1867613169385472000 |
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| access_status_str | Open Access |
| author | Jackson, Jonathan |
| author2 | Merry, Charles |
| author_browse | Jackson, Jonathan Merry, Charles |
| author_facet | Merry, Charles Jackson, Jonathan |
| author_sort | Jackson, Jonathan |
| collection | Thesis |
| description | It is often useful to determine the measures of precision of the directly observed quantities in a triangulation net. Provided the net is not strained these measures are unique to a particular set of observations and weights. Unique measures for the precision of the indirectly observed quantities cannot be found by classical means although several ad hoc approaches can be used to approximate to this measure of the 'inherent strength' of a net. Bjerhammar's theory of generalised matrix inverses can be used to derive measures of precision for the indirectly observed quantities, which may be interpreted as reflecting the inherent strength of the net. The theory of adjustment of a triangulation net by the method of variation of co-ordinates is described, followed by an explanation of the theory bf generalised inverses. Methods for the practical derivation of particular inverses are described, following Mittermayer. The characteristics of Normal, Transnormal and Stochastic Ring inverses in solution of Normal equations BX = R, are described. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/16626 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:31:52.071Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | School of Architecture, Planning and Geomatics |
| publisherStr | School of Architecture, Planning and Geomatics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/16626 Free adjustment of a triangulation net Jackson, Jonathan Merry, Charles Geomatics It is often useful to determine the measures of precision of the directly observed quantities in a triangulation net. Provided the net is not strained these measures are unique to a particular set of observations and weights. Unique measures for the precision of the indirectly observed quantities cannot be found by classical means although several ad hoc approaches can be used to approximate to this measure of the 'inherent strength' of a net. Bjerhammar's theory of generalised matrix inverses can be used to derive measures of precision for the indirectly observed quantities, which may be interpreted as reflecting the inherent strength of the net. The theory of adjustment of a triangulation net by the method of variation of co-ordinates is described, followed by an explanation of the theory bf generalised inverses. Methods for the practical derivation of particular inverses are described, following Mittermayer. The characteristics of Normal, Transnormal and Stochastic Ring inverses in solution of Normal equations BX = R, are described. 2016-02-01T10:00:20Z 2016-02-01T10:00:20Z 1976 Master Thesis Masters MSc (Eng) http://hdl.handle.net/11427/16626 eng application/pdf School of Architecture, Planning and Geomatics Faculty of Engineering and the Built Environment University of Cape Town |
| spellingShingle | Geomatics Jackson, Jonathan Free adjustment of a triangulation net |
| thesis_degree_str | Master's |
| title | Free adjustment of a triangulation net |
| title_full | Free adjustment of a triangulation net |
| title_fullStr | Free adjustment of a triangulation net |
| title_full_unstemmed | Free adjustment of a triangulation net |
| title_short | Free adjustment of a triangulation net |
| title_sort | free adjustment of a triangulation net |
| topic | Geomatics |
| url | http://hdl.handle.net/11427/16626 |
| work_keys_str_mv | AT jacksonjonathan freeadjustmentofatriangulationnet |