Properties of the total least squares estimation
Through theoretical derivation, some properties of the total least squares estimation are found. The total least squares estimation is the linear transformation of the least squares estimation, and the total least squares estimation is unbiased. The condition number of the total least squares estima...
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| Format: | Article |
| Language: | English |
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KeAi Communications Co., Ltd.
2012-11-01
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| Series: | Geodesy and Geodynamics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1674984715301361 |
| _version_ | 1829141432221302784 |
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| author | Wang Leyang |
| author_facet | Wang Leyang |
| author_sort | Wang Leyang |
| collection | DOAJ |
| description | Through theoretical derivation, some properties of the total least squares estimation are found. The total least squares estimation is the linear transformation of the least squares estimation, and the total least squares estimation is unbiased. The condition number of the total least squares estimation is greater than the least squares estimation, so the total least squares estimation is easier to be affected by the data error than the least squares estimation. Then through the further derivation, the relationships of solutions, residuals and unit weight variance estimations between the total least squares and the least squares are given. |
| first_indexed | 2024-12-14T20:13:43Z |
| format | Article |
| id | doaj.art-e2d1af7eb515455eb60261162e6dcde5 |
| institution | Directory Open Access Journal |
| issn | 1674-9847 |
| language | English |
| last_indexed | 2024-12-14T20:13:43Z |
| publishDate | 2012-11-01 |
| publisher | KeAi Communications Co., Ltd. |
| record_format | Article |
| series | Geodesy and Geodynamics |
| spelling | doaj.art-e2d1af7eb515455eb60261162e6dcde52022-12-21T22:48:54ZengKeAi Communications Co., Ltd.Geodesy and Geodynamics1674-98472012-11-0134394610.3724/SP.J.1246.2012.00039.1Properties of the total least squares estimationWang Leyang0Faculty of Geomatics, East China Institute of Technology, Nanchang 330013, ChinaThrough theoretical derivation, some properties of the total least squares estimation are found. The total least squares estimation is the linear transformation of the least squares estimation, and the total least squares estimation is unbiased. The condition number of the total least squares estimation is greater than the least squares estimation, so the total least squares estimation is easier to be affected by the data error than the least squares estimation. Then through the further derivation, the relationships of solutions, residuals and unit weight variance estimations between the total least squares and the least squares are given.http://www.sciencedirect.com/science/article/pii/S1674984715301361total least squares (TLS)least squares (LS)singular value decomposition (SVD)residualsunit weight variance |
| spellingShingle | Wang Leyang Properties of the total least squares estimation Geodesy and Geodynamics total least squares (TLS) least squares (LS) singular value decomposition (SVD) residuals unit weight variance |
| title | Properties of the total least squares estimation |
| title_full | Properties of the total least squares estimation |
| title_fullStr | Properties of the total least squares estimation |
| title_full_unstemmed | Properties of the total least squares estimation |
| title_short | Properties of the total least squares estimation |
| title_sort | properties of the total least squares estimation |
| topic | total least squares (TLS) least squares (LS) singular value decomposition (SVD) residuals unit weight variance |
| url | http://www.sciencedirect.com/science/article/pii/S1674984715301361 |
| work_keys_str_mv | AT wangleyang propertiesofthetotalleastsquaresestimation |