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EIV Models and Pareto Optimalitity

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Geospatial Algebraic Computations

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Abstract

In some geospatial 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 is often the case in multiobjective problems. Such is often 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 Chapter, 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 to 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. 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.

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Authors and Affiliations

  1. Curtin University, Perth, West Australia, Australia

    Joseph L. Awange

  2. Budapest University of Technology and Economics, Budapest, Hungary

    Béla Paláncz

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  1. Joseph L. Awange
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  2. Béla Paláncz
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Awange, J.L., Paláncz, B. (2016). EIV Models and Pareto Optimalitity. In: Geospatial Algebraic Computations. Springer, Cham. https://doi.org/10.1007/978-3-319-25465-4_10

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