Mapping and Localization, which serve as the basis for autonomously navigating a mobile robot, have been extensively studied for more than 20 years. However there are still some problems unsolved, especially on mapping and localization by use of sonar. With wide beam, sonar acts as a range-only measurement equipment in some sense. Consequently，mapping and localization with sonar data are with more challenges. In this thesis, we study the problem of mapping and localization by use of sonar. The main contributions of this thesis include following issues:1) Considering that sonar can detect two types of target (point and line feature) in indoor environments, we propose a model called three measurements association model to associate sparse sonar data to specific features, and based on the model we use an iterative least square estimator to estimate the parameters of the features from associated sonar data and build a sonar feature map finally. Our approach avoids the problem caused by implementing data association from dense sonar data, satisfy the need of real-time application.2) Before implementation of robot localization based on the landmark or feature map, there is a common question that how many landmarks or features are enough to localize the robot. In this thesis, with some important results from observability analysis on the localization systems with rang-only measurement, we answer the question above. Furthermore, based on the results, we propose an approach for heading estimation using angle histogram and develop a MCL method based on optimal proposal distribution.3) SLAM problem attracts more and more attentions in mobile robot community. However, there is no affirmative answer on whether SLAM problem can be solved. With some important results from observability analysis on three types of SLAM systems and SLAM systems with rang-only measurements, we draw some conclusions that none of the SLAM systems we analyzed is completely observable. Furthermore, based on these results, we account for the estimation inconsistency in EKF-SLAM implementation and propose the conditions for implementing SLAM by adding known landmarks.4) For mapping dynamic environments, a Gaussian mixture model which can not only represent the position of the objects, but also the state of the objects is chosen in our approach. In addition, we deduced a factored formulation of Bayesian posterior for SLAM problem, base on which we develop an approach for SLAM in dynamic environments，with GMM to model the environment and particle filter to localize the mobile robot.
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