This paper proposes a discrete-time, multi-time-scale estimation and control design for quadrotors in the presence of external disturbances and model uncertainties. Assuming that not all state measurements are available, they will need to be estimated. The sample-data Extended High-Gain Observers are used to estimate unmeasured states, system uncertainties, and external disturbances. Discretized dynamic inversion utilizes those estimates and deals with an uncertain principal inertia matrix. In the plant dynamics, the proposed control forces the rotational dynamics to be faster than the translational dynamics. Numerical simulations and experimental results verify the proposed estimation and control algorithm. All sensing and computation is done on-board the vehicle.