Multi Parametric Evaluation of Back Propagation Artificial Neural Network in Determination of Geoid Undulations
G. Pantazis

Abstract
The increased use of GNSS for technical constructions and infrastructure works makes necessary the calculation of local accurate geoid undulation’s models for the determination of accurate orthometric heights. Apart from the conventional methods, artificial neural networks (ANN) are also used for this purpose. Specially, back propagation artificial neural networks (BPANN) are widely applied for engineering practice. It is well known that the training of ANNs consists a "black box", as the user cannot interlope in the procedure. The aim of this work is to investigate the impact of some crucial parameters to the accuracy, of geoid undulations determination, when BPANN is used. Parameters as the different types of input data (ellipsoidal or Cartesian coordinates, ellipsoidal or orthometric heights etc.), the allocation of the known points at a concrete area, the number of neurons and the number of hidden layers are examined. The results are evaluated by means of the achieved RMSEs, they are compared to each other and to the initial approximation by a polynomial interpolation using GNSS/leveling data. For the trial run an urban region of Athens city was used, where 37 points of known geoid undulations are located at 12Km2 area. Useful diagrams illustrate the evaluation of the 176 BPANNs that were tested. It is concluded that the number of the known points is not as crucial as their regular and equidistant allocation. Also the increment of neurons in the hidden layers, optimize the results. Moreover simple input data set with two or three neurons including the coordinates of the known points is adequate as it provides better assessments.

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