The theoretical and practical background of the similarity transformation together with the simultaneous estimation of local geoid undulations is presented in Bányai (2011). The mean features of the traditional network adjustment on the local ellipsoids are summarized and the different Hungarian networks and known geoid solutions are shortly described as the basic data of the test computations. The eigenvalue and eigenvector decomposition revealed that the seven parameter similarity transformation cannot be applied together with the simultaneous local geoid estimation because the rotations about the X and Y axes significantly destroy the condition of the normal equations. However, the replacement of the rotations about the X, Y and Z axes by the rotation about the ellipsoidal normal of the datum point can provide a very well-conditioned solution, which takes into account the special role of the datum point of the astro-geodetic network adjustment. Based on the unit weights of the input data an optimal adjustment strategy is demonstrated from a computational point of view, where the five transformation parameters can be estimated together with a very large number of local geoid undulations. The geoid has to be known in the global reference system. The geoid unknowns describe only the relative position of this known geoid with respect to the local 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 concurrently 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. changes, global rotations and scale parameters in one computational step. The proposed method is used to investigate the significance of the impact of global plate motions on regional crustal move-ment network. Simulated data of the regional Cairo network is used for this evaluation. The estimat-B
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