The miniature tailsitter is a unique aircraft with inherent advantages over typical unmanned aerial vehicles. With the capabilities of both hover and level flight, these small, portable systems can produce efficient maneuvers for enhanced surveillance and autonomy with little threat to surroundings and the system itself. Such vehicles are accompanied with control challenges due to the two different flight regimes. Problems with the conventional attitude representation arise in estimation and control as the system departs from level flight conditions. Furthermore, changing dynamics and limitations in modeling and sensing give rise to significant attitude control design challenges. Restrictions in computation also result from the limited size and weight capacity of the miniature airframe. In this research, the inherent control challenges discussed above are addressed with a computationally efficient adaptive quaternion control algorithm. A backstepping method for model cancellation and consistent tracking of reference model attitude dynamics is derived. This is used in conjunction with two different algorithms designed for the identification of system parameters. For a metric of baseline performance, gain-scheduled quaternion feedback control is developed. With a regularized data-weighting recursive least-squares parameter estimation algorithm, the adaptive quaternion controller is shown to be better than the baseline method in simulation and hardware results. This method is also shown to produce universal performance for all aircraft with the three conventional control surface actuators (aileron, elevator, and rudder) barring saturation and assuming accurate system identification. Testing of attitude control algorithms requires development in quaternion-based navigational control and attitude estimation. A novel technique for hover north/east position control is derived. Also, altitude tracking in hover, given an inconsistent thrust system, is addressed with an original method of on-line throttle system identification. Means for quaternion-based level flight control are produced from adaptations made to existing techniques employed in the Brigham Young University Multi-Agent Coordination and Control Lab. Also generated are simple trajectories for transitions between flight modes. A method for the estimation of quaternion attitude is developed, which uses multiple sensors combined in a filtering technique similar to the fixed-gain Kalman filter. Simulation and hardware results of these methods are presented for concept validation. A discussion of the development and production of these testing means (a simulation environment and hardware flight test system) is provided. In culmination, a fully autonomous miniature tailsitter system is produced with results demonstrating its various capabilities.