Programming of ellipsoidal heights to orthometric heights transformation with matlab

Positioning information which is high accurate is produced with GNSS techniques quickly and economically. However, ellipsoidal heights determined by these techniques are expressed geometrically, and show discrepancy depending on the position of the reference ellipsoid. For this reason, since the ellipsoidal heights cannot be used directly for geodetic purposes, the ellipsoidal heights determined with GNSS have to be transformed to orthometric height. In this study, the transformation of the ellipsoidal heights to the orthometric height has been investigated. A program was developed in the MATLAB programming language to transform from the ellipsoidal heights to the orthometric height using interpolation methods. By means of this program, taking advantage of the known points with ellipsoidal height and orthometric height in the test area, the orthometric heights of other known points with only ellipsoidal heigths are able to be calculated with inverse distance weighted methods, polynomial surfaces and multiquadratic methods. The prepared program was tested using 76 points which are known ellipsoidal and orthometric heights. In practice, 40 of these points were used as reference points and 36 as test points. In addition, the height of the points in the test area were determined with Turkey Jeoid 2003 (TG03). When the differences between the known orthometric heights of the test points and the heights determined by interpolation and the root mean square errors(rms) are examined, it is seen that k=2 in invers distance weighted methods, the cubic surface in the orthogonal polynomial, and bi-cubic surface in the non-orthogonal polynomial gave the best results. When the obtained interpolation results and the values calculated according to TG03 are evaluated together, it is seen that multiquadratic interpolation method gives better for the test area than the others.