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The paper discusses a novel vision-based estimation and control approach to enable fully autonomous tracking and landing of vertical take-off and landing (VTOL) capable unmanned aerial vehicles (UAVs) on moving platforms without relying on a GPS signal. A unique feature of the present method is that it accomplishes this task without tracking the landing pad itself; however, by utilizing a standardized visual cue installed normal to the landing pad and parallel to the pilot's/vehicle's line of sight. A computer vision system using a single monocular camera is developed to detect the visual cue and then accurately estimate the heading of the UAV and its relative distances in all three directions to the landing pad. Through comparison with a Vicon-based motion capture system, the capability of the present vision system to measure distances in real-time within an accuracy of less than a centimeter and heading within a degree with the right visual cue, is demonstrated. A gain-scheduled proportional integral derivative (PID) control system is integrated with the vision system and then implemented on a quad-rotor-UAV dynamic model in a realistic simulation program called Gazebo. Extensive simulations are conducted to demonstrate the ability of the controller to achieve robust tracking and landing on platforms moving in arbitrary trajectories. Repeated flight tests, using both stationary and moving platforms are successfully conducted with less than 5 centimeters of landing error.