This paper presents the design, analysis, and experimental validation of a globally asymptotically stable (GAS) filter for simultaneous localization and mapping (SLAM) with application to unmanned aerial vehicles. The main contributions of this paper are the results of global convergence and stability for SLAM in tridimensional (3-D) environments. The SLAM problem is formulated in a sensor-based framework and modified in such a way that the structure may be regarded as linear time-varying for observability purposes, from which a Kalman filter with GAS error dynamics follows naturally. The proposed solution includes the estimation of both body-fixed linear velocity and rate gyro measurement biases. Experimental results from several runs, using an instrumented quadrotor equipped with a RGB-D camera, are included in the paper to illustrate the performance of the algorithm under realistic conditions.