This chapter presents an overview of algorithms deeply rooted in a sensor-based approach to the SLAM problem that provide global convergence guarantees and allow for the use of partially observable landmarks. The presented algorithms address the more usual range-and-bearing SLAM problem, either in 2-D using a LiDAR or in 3-D using an RGB-D camera, as well as the range-only and bearing-only SLAM problems. For each of these formulations a nonlinear system is designed, for which state and output transformations are considered together with augmented dynamics, in such a way that the underlying system structure can be regarded as linear time-varying for observability analysis and filter design purposes. This naturally allows for the design of Kalman filters with, at least, globally asymptotically stable error dynamics, for which several experimental and simulated trials are presented to highlight the performance and consistency of the obtained filters.