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    Pareto optimality solution of the Gauss-Helmert model

    193569_193569.pdf (515.3Kb)
    Access Status
    Open access
    Authors
    Palancz, B.
    Awange, Joseph
    Völgyesi, L.
    Date
    2013
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Palancz, B. and Awange, J.L. and Völgyesi, L. 2013. Pareto optimality solution of the Gauss-Helmert model. Acta Geodetica et Geophysica. 48 (3): pp. 293-304.
    Source Title
    Acta Geodetica et Geophysica
    DOI
    10.1007/s40328-013-0027-3
    ISSN
    2213-5812
    Remarks

    The final publication is available at Springer via http://doi.org/10.1007/s40328-013-0027-3

    URI
    http://hdl.handle.net/20.500.11937/21823
    Collection
    • Curtin Research Publications
    Abstract

    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.

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