This paper presents the tinySLAM algorithm, which enables a mobile robot to perform automatic localization and mapping, called SLAM. Indeed, it is one of the essential bricks to build an autonomous robot that can evolve in an unknown environment. Several methods and algorithms have been developed to solve this problem, using various techniques and sensors. TinySLAM is a SLAM algorithm based on the principle of IML (Incremental Maximum Likelihood). It uses data from a laser sensor to estimate the most probable position of the robot in a 2D map. We have worked extensively on improving the computation speed of this estimate. Results obtained allowed us to run two loops of position estimation in parallel, with different characteristics. The algorithm has a better chance to find a good estimate of the position. In previous work, we presented a first version of this algorithm. This paper talks about the advances made in improving the tinySLAM algorithm, until version 1.1.