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This paper presents a fast and robust approach for estimating the flight altitude of multirotor Unmanned Aerial Vehicles (UAVs) using 3D point cloud sensors in cluttered, unstructured, and dynamic indoor environments. The objective is to present a flight altitude estimation algorithm, replacing the conventional sensors such as laser altimeters, barometers, or accelerometers, which have several limitations when used individually. Our proposed algorithm includes two stages: in the first stage, a fast clustering of the measured 3D point cloud data is performed, along with the segmentation of the clustered data into horizontal planes. In the second stage, these segmented horizontal planes are mapped based on the vertical distance with respect to the point cloud sensor frame of reference, in order to provide a robust flight altitude estimation even in presence of several static as well as dynamic ground obstacles. We validate our approach using the IROS 2011 Kinect dataset available in the literature, estimating the altitude of the RGB-D camera using the provided 3D point clouds. We further validate our approach using a point cloud sensor on board a UAV, by means of several autonomous real flights, closing its altitude control loop using the flight altitude estimated by our proposed method, in presence of several different static as well as dynamic ground obstacles. In addition, the implementation of our approach has been integrated in our open-source software framework for aerial robotics called Aerostack.