General Aviation aircraft mostly fly with Visual Flight Rules (VFR). These are rules in aviation that permit the pilot to fly on sight if the weather conditions offer enough visibility for the pilot to perform the following tasks visually: collision avoidance with terrain or other airborne object, navigation and attitude determination. VFR flight is therefore a very independent way of flying requiring very few on-board instruments, but it is very dependent on weather conditions. Selfly Electronic Detect and Avoid has therefore developed a Collision Avoidance Radar that can support the pilot to detect and avoid the ground and airborne objects. This Frequency Modulated Continuous Wave radar is small, lightweight and can be mounted almost anywhere on the aircraft. This thesis researched if the radar could also be used as Doppler Navigation System to support the pilot for navigation and attitude determination. A method is proposed which uses the radar data of multiple on-board radars to calculate the aircraft states required for navigation and attitude determination. With this method the height, the roll angle and the pitch angle can be determined with the range measurements and the aircraft velocity vector in the body-fixed reference frame can be calculated using the velocity measurements. Assuming a known heading angle, the ground speed of the aircraft can also be determined. The Doppler Navigation System was modeled in Python and flight data was generated with the flight simulator X-Plane 9. The model was used to determine how the aperture angle would affect the accuracy of the obtained states required for navigation and attitude determination and what the optimum on-board radar configuration is. Navigation with the DNS showed an error in the horizontal position of $455m$ for a flight of $728s$ in which the aircraft traveled $84.339 km$. The height of the aircraft can be determined within $20m$ of the actual height of the aircraft along the whole flight. The obtained roll angle was always within $1^{\circ}$ of the actual roll angle when smaller than $10^{\circ}$ and the pitch angle error never exceeded $1^{\circ}$. These result show that this system could be used to navigate with no visibility conditions for a short duration, for example when trapped in a cloud. These results were obtained for a flight over the Dutch coast using a Digital Elevation Map with an accuracy of 3 arc seconds. The DNS performed best with radars with a low depression angle and the azimuth angle did not appear to significantly influence the accuracy of the states. The terrain was however the largest source of error, as the method to calculate the states assumes a flat Earth. The modeling of the radar signal was too computationally intensive to be integrated in the model, therefore the ground velocity and range measurements are assumed to be perfect. In order to improve the accuracy of the system, terrain recognition could be added which would allow the system to determine three or more geographic positions on the surface and use these positions to geometrically determine its position and attitude using triangulation.