In this article, the problem of robust state observer design for a class of unmanned aerial vehicles (UAVs) is addressed. A prototype four-rotors helicopter robot for indoors and outdoors applications is considered: the drone is not equipped with GPS related devices, so we describe a strategy to estimate its translational velocity vector based on acceleration, angles and angular speeds measurements only. Since the linearised system is non-observable at the equilibrium point, a nonlinear observability verification is performed for persistently exciting trajectories. A global exponential solution to this open problem is provided in the framework of adaptive observation theory when exact measurements are available. A modified observer is presented to enhance velocity estimation robustness in the realistic case of noisy measurements. The results are compared with a classical estimation strategy based on the extended Kalman filter to test the algorithm's performance.