  Using the context of trajectory estimation and tracking for multi-rotor
unmanned aerial vehicles (UAVs), we explore the challenges in applying
high-gain observers to highly dynamic systems. The multi-rotor will operate in
the presence of external disturbances and modeling errors. At the same time,
the reference trajectory is unknown and generated from a reference system with
unknown or partially known dynamics. We assume the only measurements that are
available are the position and orientation of the multi-rotor and the position
of the reference system. We adopt an extended high-gain observer (EHGO)
estimation framework to estimate the unmeasured multi-rotor states, modeling
errors, external disturbances, and the reference trajectory. We design a robust
output feedback controller for trajectory tracking that comprises a feedback
linearizing controller and the EHGO. The proposed control method is rigorously
analyzed to establish its stability properties. Finally, we illustrate our
theoretical results through numerical simulation and experimental validation in
which a multi-rotor tracks a moving ground vehicle with an unknown trajectory
and dynamics and successfully lands on the vehicle while in motion.
