The problem considered here is state estimation in the presence of bounded process and measurement noise. A new nonlinear state estimator, based on interval analysis and the notion of set inversion, is applied to robot localization and tracking. This estimator evaluates a set guaranteed to contain all values of the state that are consistent with the available observations, given the noise bounds and some possibility very large set containing the initial value of the state. Three situations are considered to illustrate the properties of the estimator.