Nonlinearity and Least-Squares.
Since almost all functional relations in our geodetic models are nonlinear, it is important, especially from a statistical inference point of view, to know how nonlinearity manifests itself at the various stages of an adjustment. In this paper particular attention is given to the effect of nonlinear...
| Main Authors: | , |
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| Format: | Journal Article |
| Language: | English |
| Published: |
1988
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| Online Access: | http://hdl.handle.net/20.500.11937/47264 |
| _version_ | 1848757786353074176 |
|---|---|
| author | Teunissen, Peter Knickmeyer, E.H. |
| author_facet | Teunissen, Peter Knickmeyer, E.H. |
| author_sort | Teunissen, Peter |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Since almost all functional relations in our geodetic models are nonlinear, it is important, especially from a statistical inference point of view, to know how nonlinearity manifests itself at the various stages of an adjustment. In this paper particular attention is given to the effect of nonlinearity on the first two moments of least squares estimators. Expressions for the moments of least squares estimators of parameters, residuals and functions derived from parameters, are given. The measures of nonlinearity are discussed both from a statistical and differential geometric point of view. Finally, our results are applied to the 2D symmetric Helmert transformation with a rotational invariant covariance structure. |
| first_indexed | 2025-11-14T09:33:38Z |
| format | Journal Article |
| id | curtin-20.500.11937-47264 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T09:33:38Z |
| publishDate | 1988 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-472642017-01-30T15:32:18Z Nonlinearity and Least-Squares. Teunissen, Peter Knickmeyer, E.H. Since almost all functional relations in our geodetic models are nonlinear, it is important, especially from a statistical inference point of view, to know how nonlinearity manifests itself at the various stages of an adjustment. In this paper particular attention is given to the effect of nonlinearity on the first two moments of least squares estimators. Expressions for the moments of least squares estimators of parameters, residuals and functions derived from parameters, are given. The measures of nonlinearity are discussed both from a statistical and differential geometric point of view. Finally, our results are applied to the 2D symmetric Helmert transformation with a rotational invariant covariance structure. 1988 Journal Article http://hdl.handle.net/20.500.11937/47264 en restricted |
| spellingShingle | Teunissen, Peter Knickmeyer, E.H. Nonlinearity and Least-Squares. |
| title | Nonlinearity and Least-Squares. |
| title_full | Nonlinearity and Least-Squares. |
| title_fullStr | Nonlinearity and Least-Squares. |
| title_full_unstemmed | Nonlinearity and Least-Squares. |
| title_short | Nonlinearity and Least-Squares. |
| title_sort | nonlinearity and least-squares. |
| url | http://hdl.handle.net/20.500.11937/47264 |