This paper proposes the design, analysis, and validation of a globally exponentially stable (GES) filter for tridimensional (3-D) range-only simultaneous localization and mapping. For observability analysis purposes, a nonlinear sensor-based dynamical system is formulated resorting only to exact linear and angular kinematics and a state augmentation is exploited that allows the proposed formulation to be considered as linear time-varying without linearizing the original nonlinear system. Constructive observability results can then be established, leading naturally to the design of a Kalman Filter with GES error dynamics. These results also provide valuable insight on the motion planning of the vehicle. Experimental results demonstrate the good performance of the algorithm and help validate the theoretical results presented. For completeness and to illustrate the necessity of a proper trajectory, simulation data are included as well.