This paper proposes a localization system for a mobile robot based on odometric data and RGB-D (Red, Green, Blue image and Depth map) measurements relative to a landmark, available from sensors installed on board. The localization system is composed of two cascaded estimators: i) a kinematic optimal attitude estimator; and ii) a position estimator designed in body-frame, based on an underlying LPV (Linear Parameter Varying) model, that avoids the need of approximations or linearization. Both underlying models are observable, even considering the presence of angular and linear slippages and the resulting estimators present globally asymptotically stable estimation error dynamics. Experiments to assess the performance of the proposed estimators were carried out resorting to a wheeled differential drive mobile robot in a laboratory instrumented with a Qualysis Motion Tracking System, used for ground-truth validation. An effective real-time localization system is obtained, featuring convergence to zero of the estimated errors, regardless the initial estimate and without requiring the landmark to be always visible, thus validating the system global stability. The results obtained paved the way to the integration of the proposed localization solution in a docking system for the same robot. The docking problem is solved with a smooth, time-invariant, globally asymptotically stable feedback control law, which allows for a very human-like closed-loop steering that drives the robot to a certain goal with a desired attitude and tunable curvature. Simulation and experimental results with the aforementioned robot are also presented, that illustrate the performance of the docking solution based on the proposed localization methods central to this work.