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In this paper, an approach for fitting a circle to 2-D data which represent only a small part of the curve is described. This approach deals with the particular case where data is specified in terms of its Cartesian coordinates and the errors in both coordinates are not independent. Besides, an associated uncertainty ellipse which describes the measurement error and the variance matrix associated to the estimated parameters are obtained. This method is particularly well designed to fit a circle to a set of measured range readings provided by a 2-D laser range finder when these range readings are specified in terms of its Cartesian coordinates. Therefore, it has been successfully applied to acquire circle-shaped landmarks in a mobile robotics navigation task.