This paper addresses the localization and mapping problem for a robot moving through a (possibly) unknown environment where indistinguishable landmarks can be detected. A set theoretic approach to the problem is presented. Computationally efficient algorithms for measurement-to-feature matching, estimation of landmark positions, estimation of robot location and heading are derived, in terms of uncertainty regions, under the hypothesis that errors affecting all sensors measurements are unknown-but-bounded. The proposed technique is validated in both simulation and experimental setups.