Application of pareto optimality to linear models with errors-in-all-variables
In some geodetic and geoinformatic parametric modeling, the objectives to be minimized are often expressed in different forms, resulting in different parametric values for the estimated parameters at non-zero residuals. Sometimes, these objectives may compete in a Pareto sense, namely a small change...
| Main Authors: | , |
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| Format: | Journal Article |
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Springer - Verlag
2011
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| Online Access: | http://hdl.handle.net/20.500.11937/21160 |
| _version_ | 1848750512217784320 |
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| author | Palancz, B. Awange, Joseph |
| author_facet | Palancz, B. Awange, Joseph |
| author_sort | Palancz, B. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In some geodetic and geoinformatic parametric modeling, the objectives to be minimized are often expressed in different forms, resulting in different parametric values for the estimated parameters at non-zero residuals. Sometimes, these objectives may compete in a Pareto sense, namely a small change in the parameters results in the increase of one objective and a decrease of the other, as frequently occurs in multiobjective problems. Such is the case with errors-in-all-variables (EIV) models, e.g., in the geodetic and photogrammetric coordinate transformation problems often solved using total least squares solution (TLS) as opposed to ordinary least squares solution (OLS). In this contribution, the application of Pareto optimality to solving parameter estimation for linear models with EIV is presented. The method is tested to solve two well-known geodetic problems of linear regression and linear conformal coordinate transformation. The results are compared with those from OLS, Reduced Major Axis Regression (TLS solution), and the least geometric mean deviation (GMD) approach. It is shown that the TLS and GMD solutions applied to the EIV models are just special cases of the Pareto optimal solution, since both of them belong to the Pareto-set of the problems. The Pareto balanced optimum (PBO) solution as a member of this Pareto optimal solution set has special features and is numerically equal to the GMD solution. |
| first_indexed | 2025-11-14T07:38:00Z |
| format | Journal Article |
| id | curtin-20.500.11937-21160 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:38:00Z |
| publishDate | 2011 |
| publisher | Springer - Verlag |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-211602017-09-13T16:09:21Z Application of pareto optimality to linear models with errors-in-all-variables Palancz, B. Awange, Joseph Error-in-all-variables Gauss–Markov model (GM) Pareto optimality Nonlinear adjustment Least squares solution Multiobjective optimization Least geometric mean deviation (GMD) Total least squares solution In some geodetic and geoinformatic parametric modeling, the objectives to be minimized are often expressed in different forms, resulting in different parametric values for the estimated parameters at non-zero residuals. Sometimes, these objectives may compete in a Pareto sense, namely a small change in the parameters results in the increase of one objective and a decrease of the other, as frequently occurs in multiobjective problems. Such is the case with errors-in-all-variables (EIV) models, e.g., in the geodetic and photogrammetric coordinate transformation problems often solved using total least squares solution (TLS) as opposed to ordinary least squares solution (OLS). In this contribution, the application of Pareto optimality to solving parameter estimation for linear models with EIV is presented. The method is tested to solve two well-known geodetic problems of linear regression and linear conformal coordinate transformation. The results are compared with those from OLS, Reduced Major Axis Regression (TLS solution), and the least geometric mean deviation (GMD) approach. It is shown that the TLS and GMD solutions applied to the EIV models are just special cases of the Pareto optimal solution, since both of them belong to the Pareto-set of the problems. The Pareto balanced optimum (PBO) solution as a member of this Pareto optimal solution set has special features and is numerically equal to the GMD solution. 2011 Journal Article http://hdl.handle.net/20.500.11937/21160 10.1007/s00190-011-0536-1 Springer - Verlag restricted |
| spellingShingle | Error-in-all-variables Gauss–Markov model (GM) Pareto optimality Nonlinear adjustment Least squares solution Multiobjective optimization Least geometric mean deviation (GMD) Total least squares solution Palancz, B. Awange, Joseph Application of pareto optimality to linear models with errors-in-all-variables |
| title | Application of pareto optimality to linear models with errors-in-all-variables |
| title_full | Application of pareto optimality to linear models with errors-in-all-variables |
| title_fullStr | Application of pareto optimality to linear models with errors-in-all-variables |
| title_full_unstemmed | Application of pareto optimality to linear models with errors-in-all-variables |
| title_short | Application of pareto optimality to linear models with errors-in-all-variables |
| title_sort | application of pareto optimality to linear models with errors-in-all-variables |
| topic | Error-in-all-variables Gauss–Markov model (GM) Pareto optimality Nonlinear adjustment Least squares solution Multiobjective optimization Least geometric mean deviation (GMD) Total least squares solution |
| url | http://hdl.handle.net/20.500.11937/21160 |