In many geodetic (surveying) applications positions of points in the terrain need to be determined with high precision (cm-accuracy or even better). The Global Positioning System (GPS) is very suitable for this purpose. High positioning accuracy is in principle feasible when a relative measurement setup is used and in the processing procedure certain systematic errors in the GPS observations are properly taken into account. The largest of these errors is due to the propagation of the GPS signals through the ionosphere, the part of the atmosphere from about 80 km altitude. When the distance between the GPS receivers in the relative measurement setup is sufficiently short (e.g. a few km) it is known that these errors almost cancel, such that the positioning can be conducted using only a short time span of measurements, which is very favorable from an economical point of view. For longer distances the necessary time span increases enormously since unknown parameters for among others the ionospheric errors need to be estimated in the processing. In this thesis a procedure is outlined for the processing of relative GPS observations over medium distances (max. 50 km), while at the same time it should allow a user a short time span of measurements. An important requirement to this procedure is the availability of a permanent network of GPS reference stations. From the observations this permanent network collects, it is possible to generate information about the ionospheric delays, which a user can consequently apply to correct his own GPS observations. Much attention in the thesis is paid to the mathematical modelling aspects of this procedure.