Two alternative techniques for fitting the gravimetric geoid for Egypt
In this paper, two proposed geoid fitting techniques for Egypt's gravimetrically determined geoid and Global Positioning System GPS/levelling-derived geoid are introduced. First, any errors in the available GPS stations are ruled out. These methods rely on the absolute geoid difference, which is the gravimetric geoid height minus the geoid obtained through comparing GPS and levelling. The suggested geoid fitting techniques use an optimization algorithm scheme to choose the minimum number of the best-suited GPS stations to be used for fitting the gravimetric geoid. The least-squares collocation method is used to determine each GPS point's impact on the remaining GPS points. The GPS stations with the least impact on the other points are used for external validations, till an acceptable limit of the influence of the GPS points on the remaining ones (when the lowest standard deviation of the differences between gravimetric and geometric geoids is achieved with minimum average or standard deviation is larger than the accuracy of GPS observations, or standard deviation is larger than the target accuracy for geoid; or until a maximum of 30% of the GPS/levellings are excluded). This method operates in a way that automatically selects the fewest GPS stations that are most suitable for usage in the geoid fitting procedure. The geoid quality is then checked externally using the remaining GPS stations. A kriging trend surface is then taken out of the absolute geoid difference to complete the fitting. The proposed geoid fitting techniques are compared with that using polynomial regression of different degrees. The results proved that the proposed techniques give extremely better results. The findings of this study affirm that the adoption of the proposed techniques yields a geoid with an external accuracy of approximately 19 cm for Egypt.