The steadily increasing popularity of Unmanned Aerial Vehicles (UAVs) is creating new opportunities in diverse fields of technology and business. However, this increase of popularity also raises safety concerns. To tackle the primary concern of keeping the UAV inside a designated region, a novel trajectory estimation algorithm for geo-fencing applications is proposed. We derive the Beta-Trajectory that takes into account constraints in curvature as well as constraints in the change of curvature which is bounded by the maximum roll-rate of the aircraft. We incorporate the Beta-Trajectory into a geo-fencing algorithm. By using our open-source uavAP autopilot, the applicability and necessity of accurate trajectory estimation algorithms for geo-fencing applications are shown on small fixed-wing aircraft. The model and algorithm are validated in high-fidelity simulations as well as in real flight testing.