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We propose a novel methodology for reliable localization of an autonomous mobile robot navigating in an unstructured environment using noisy absolute measurements from its exteroceptive sensors. A new deterministic filtering technique is introduced, which is based on the recursive computation of a bounding set that is guaranteed to contain the true state of the system, despite process and observation noise, and taking into explicit consideration uncertainties due to the linearization error. The proposed set-valued nonlinear filter relies on a two-step prediction-correction structure, with each step requiring the solution of a particular convex optimization problem. The method is illustrated by simulation on a localization problem for a nonholonomic rover, and it is compared with the standard extended Kalman filter approach.