Pareto optimality solution of the Gauss-Helmert model
The Pareto optimality method is applied to the parameter estimation of the Gauss-Helmert weighted 2D similarity transformation assuming that there are measurement errors and/or modeling inconsistencies. In some cases of parametric modeling, the residuals to be minimized can be expressed in different...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
Springer
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/21823 |
| _version_ | 1848750698116677632 |
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| author | Palancz, B. Awange, Joseph Völgyesi, L. |
| author_facet | Palancz, B. Awange, Joseph Völgyesi, L. |
| author_sort | Palancz, B. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | The Pareto optimality method is applied to the parameter estimation of the Gauss-Helmert weighted 2D similarity transformation assuming that there are measurement errors and/or modeling inconsistencies. In some cases of parametric modeling, the residuals to be minimized can be expressed in different forms resulting in different values for the estimated parameters. Sometimes these objectives may compete in the Pareto sense, namely a small change in the parameters can result in an increase in one of the objectives on the one hand, and a decrease of the other objective on the other hand. In this study, the Pareto optimality approach was employed to find the optimal trade-off solution between the conflicting objectives and the results compared to those from ordinary least squares (OLS), total least squares (TLS) techniques and the least geometric mean deviation (LGMD) approach. The results indicate that the Pareto optimality can be considered as their generalization since the Pareto optimal solution produces a set of optimal parameters represented by the Pareto-set containing the solutions of these techniques (error models). From the Pareto-set, a single optimal solution can be selected on the basis of the decision maker’s criteria. The application of Pareto optimality needs nonlinear multi-objective optimization, which can be easily achieved in parallel via hybrid genetic algorithms built-in engineering software systems such as Matlab. A real-word problem is investigated to illustrate the effectiveness of this approach. |
| first_indexed | 2025-11-14T07:40:58Z |
| format | Journal Article |
| id | curtin-20.500.11937-21823 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:40:58Z |
| publishDate | 2013 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-218232019-02-19T05:35:00Z Pareto optimality solution of the Gauss-Helmert model Palancz, B. Awange, Joseph Völgyesi, L. Gauss-Helmert transformation parameter estimation pareto optimality genetic algorithm least squares approach measurement and modeling errors The Pareto optimality method is applied to the parameter estimation of the Gauss-Helmert weighted 2D similarity transformation assuming that there are measurement errors and/or modeling inconsistencies. In some cases of parametric modeling, the residuals to be minimized can be expressed in different forms resulting in different values for the estimated parameters. Sometimes these objectives may compete in the Pareto sense, namely a small change in the parameters can result in an increase in one of the objectives on the one hand, and a decrease of the other objective on the other hand. In this study, the Pareto optimality approach was employed to find the optimal trade-off solution between the conflicting objectives and the results compared to those from ordinary least squares (OLS), total least squares (TLS) techniques and the least geometric mean deviation (LGMD) approach. The results indicate that the Pareto optimality can be considered as their generalization since the Pareto optimal solution produces a set of optimal parameters represented by the Pareto-set containing the solutions of these techniques (error models). From the Pareto-set, a single optimal solution can be selected on the basis of the decision maker’s criteria. The application of Pareto optimality needs nonlinear multi-objective optimization, which can be easily achieved in parallel via hybrid genetic algorithms built-in engineering software systems such as Matlab. A real-word problem is investigated to illustrate the effectiveness of this approach. 2013 Journal Article http://hdl.handle.net/20.500.11937/21823 10.1007/s40328-013-0027-3 Springer fulltext |
| spellingShingle | Gauss-Helmert transformation parameter estimation pareto optimality genetic algorithm least squares approach measurement and modeling errors Palancz, B. Awange, Joseph Völgyesi, L. Pareto optimality solution of the Gauss-Helmert model |
| title | Pareto optimality solution of the Gauss-Helmert model |
| title_full | Pareto optimality solution of the Gauss-Helmert model |
| title_fullStr | Pareto optimality solution of the Gauss-Helmert model |
| title_full_unstemmed | Pareto optimality solution of the Gauss-Helmert model |
| title_short | Pareto optimality solution of the Gauss-Helmert model |
| title_sort | pareto optimality solution of the gauss-helmert model |
| topic | Gauss-Helmert transformation parameter estimation pareto optimality genetic algorithm least squares approach measurement and modeling errors |
| url | http://hdl.handle.net/20.500.11937/21823 |