In this paper we propose a new control method for quadrotor autonomous landing on a visual target without linear velocity measurements. Only onboard sensing is exploited, such that only the images of the landing pad from a down-looking camera, along with data from an Inertial Measurement Unit's gyro, are used. The control system consists of an image-based nonlinear observer that estimates online the linear velocity of the vehicle and a backstepping image-based controller that generates attitude, and thrust setpoints to the quadrotor autopilot. Both observer and controller share the same feedback information: spherical visual features. Therefore no further image elaboration is needed for the estimation. This, along with the fact that only simple computations on low- and constant-dimension arrays are involved, makes the proposed solution computationally cheap. Real-hardware experiments on a quadrotor are carried out to verify the validity of the proposed control system.