This paper describes a robust method for local selflocalization using point-to-point and point-to-line matching with a Lorentzian estimator. A 2-D laser telemeter is used to obtain distance measurements around the mobile robot within a range. The goal is to find the rigid transformation (displacement and rotation) that match two consecutive laser scans despite noisy measurements (outliers). In order to obtain the transformation parameters the Newton-Levenberg-Marquardt optimization method is used. Experimental results compare this approach with a correlation method and a point-to-point correspondence based on least squares. The proposed method shows better results, particularly when there is noisy data.