The use of autonomous UAV’s is a progressively expanding industry. This thesisfocuses on the landing procedure with the main goal to be independent of visualaids. That means that the landing site can be hidden from the air, the landingcan be done in bad weather conditions and in the dark. In this thesis the use ofradio signals is investigated as an alternative to the visual sensor based systems.A localization system is needed to perform the landing without knowing wherethe landing site is. In this thesis an Extended Kalman Filter (EKF) is derived andused for the localization, based on the received signal strength from a radio beaconat the landing site. There are two main goals that are included in the landing,to land as accurate and as fast as possible. To combine these two goals a simultaneoustrajectory optimization and target estimation problem is set up that can bepartially solved while flying. The optimal solution to this problem produces thepath that the UAV will travel to get the best target localization while still reachingthe target. It is shown that trying to move directly towards the estimated landingsite is not the best strategy. Instead, the optimal trajectory is a spiral that jointlyoptimizes the information from the sensors and minimizes the arrival time.