This paper proposes a novel filter for sensor-based bearing-only simultaneous localization and mapping in three dimensions with globally exponentially stable (GES) error dynamics. A nonlinear system is designed, its output transformed, and its dynamics augmented so that the proposed formulation can be considered as linear time-varying for the purpose of observability analysis. This allows the establishment of observability results related to the original nonlinear system that naturally lead to the design of a Kalman filter with GES error dynamics. The performance of the proposed algorithm is assessed resorting to real experiments based on the Rawseeds dataset as well as further realistic simulations. (C) 2017 Elsevier B.V. All rights reserved.