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The two main challenges offered by Simultaneous Localization and Mapping (SLAM) are that of observability and extending state estimation to exploration. This thesis explores and uses solutions to render the SLAM problem observable, by proposing the Reconfigurable Extended Kalman Filter (EKF) that addresses imposing observability, maintaining observability and choice of observability constraints. Additionally, Bayesian theory and Dempster-Shafer theory of evidential reasoning are analyzed, and Occupancy grid based maps based on Dempster-Shafer theory of evidential reasoning are created and analyzed in large environment for their potential use in exploration and obstacle avoidance. Tackling both issues with different algorithms yield better solutions to the challenges offered by robotic exploration, and this is demonstrated through simulation results in representative environments.ii To my amazing parents, who taught me the value of hard work, patience and perseverance.

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