The NetSat mission by the Zentrum für Telematik e.V. and the University of Würzburg consistsof four identical CubeSats which are supposed to launch in early 2019 to demonstrate inorbitformation flying. The satellites are equipped with an attitude control system and fourelectrical thrusters pointing in the same direction. This enables the controlled change of orbitalparameters to change or hold a certain position relative to the other satellites.Besides actuation, precise information about the relative positions of the satellites in terms ofthe orbital elements is required to successfully complete the mission. GNSS provides a reliablesolution to determine the absolute positions and velocity in LEO. This information can be usedto determine the orbital elements, both absolute and relative to a reference point as the virtualleader of the satellite formation. Exchanging the satellite’s states via an inter-satellite linkallows the satellites to know their position within the formation and adjust them accordingly,thus enable active control of the formation.Due to the small dimensions of CubeSats, GPS patch antennas are mostly used for such missions.The performance of these antennas strongly relies on the dimensions of their ground plane as wellas their position on the plane to obtain the right center frequency and a reasonable bandwidth.The overall system behaviour such as measurement accuracy and false-positive fixes can bedescribed by evaluation and comparison of data from both known reference antennas and thepatch antennas. However, the position fixes provided by the GPS-sensors are erroneous, so thata correction of the data needs to be done by using additional information. The most commonway for such a state estimation is the Kalman filter, which takes mathematical systems andsensor models besides the actual sensor data into account to calculate the most probable statewith the help of gaussian distributions. This filter can then also be used to propagate a futurestate, e.g. for mission or manoeuvre planning.The thesis will cover the implementation of the GPS-based navigation in both hard- and software.The work is divided into three parts, namely testing of the hardware including theperformance measurements of both reference and patch antennas, the description of the overallGPS system with the resulting test data, and the implementation of a Kalman filter for orbitdetermination and propagation. The final goal of the thesis is to have a fully tested and analyzedGPS antenna and receiver system as well as a working Kalman filter for orbit determinationand propagation from fused GPS sensor data and on-board orbit propagation data.