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This paper describes a deterministic approach for sensor-based localization and navigation of a mobile robot equipped with ultrasonic sensors using interval analysis. For localization, the map is 2-D and assumed to be known. It is shown that robot localization is achieved without the need for an interval model of the robot; instead, the physical limitations of the robot are used to predict and track the robot's position. In classical methods of robot localization such as Kalman filters, the data-association step is extremely complex and usually based on linearization. The interval analysis method proposed in this paper bypasses the data-association step and directly deals with the nonlinear problem in a global way.