Two Alternative Methods for Height Transformation

Geodesists have always been dealing with coordinate transformations. There exist various kinds of transformations, like three-dimensional (spatial datum) transformations, two-dimensional (horizontal datum) transformations and one-dimensional (eg, height) transformations. In this article we discuss height transformations. Height data is usually obtained by levelling. The problematic side of levelling is that this technique is very labour intensive and costly. Nowadays as well GPS measurements can be used, which are much faster and cheaper, but in order to use GPS measurements for height determination, we need a precise geoid model to transform GPS heights to heights above sea level. In this article two different approaches to this transformation are presented. At first, the affine transformation is discussed. The method is by nature linear, and employs the barycentric coordinates of the point, the height of which is going to be computed. Secondly, the method of fuzzy modelling is used. By these methods, the transformation surface is determined and the heights of desired points can be determined. As the input data, height information from the precise levelling campaign in Estonia is used. The computed values are tested against height information, gathered from the reference geoid model. The objectives of this research are acquiring insight into using alternative methods for height transformation as well as to statistically characterise the suitability of the proposed methods.