One of the main contributions of this article is related to the multirate asynchronous filtering approach for the SLAM problem based on PFs. Previous multirate filter contributions are mainly for linear systems. A Kalman filter is applied for linear quadratic regulator (LQG) control, while in a Kalman filter is developed using lifting techniques. In this article, significant improvements for robot pose estimation are obtained when introducing multirate techniques to FastSLAM. In particular, it is shown that multirate fusion aims to provide more accurate results in loop-closing problems in SLAM (localization and map building problems with closed paths). Additionally, in this article a pose estimation algorithm based on least squares (LS) fitting of line features is proposed. Since the complexity of LS fitting is linear to the number of features, this implies a low computational cost than other techniques. Therefore, methods based on PFs such as MCL and FastSLAM that require a large number of particles may benefit from this fact. In particular, this provides an accurate approximation of the posterior PDF for FastSLAM 2.0.