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In this paper, we describe a system that enables a low-cost quadrocopter coupled with a ground-based laptop to navigate autonomously in previously unknown and GPS-denied environments. Our system consists of three components: a monocular SLAM system, an extended Kalman filter for data fusion and state estimation and a PID controller to generate steering commands. Next to a working system, the main contribution of this paper is a novel, closed-form solution to estimate the absolute scale of the generated visual map from inertial and altitude measurements. In an extensive set of experiments, we demonstrate that our system is able to navigate in previously unknown environments at absolute scale without requiring artificial markers or external sensors. Furthermore, we show (1) its robustness to temporary loss of visual tracking and significant delays in the communication process, (2) the elimination of odometry drift as a result of the visual SLAM system and (3) accurate, scale-aware pose estimation and navigation.