For more than two decades, the issue of simultaneous localization and mapping (SLAM) has gained more attention from researchers and remains an influential topic in robotics. Currently, various algorithms of the mobile robot SLAM have been investigated. However, the probability-based mobile robot SLAM algorithm is often used in the unknown environment. In this paper, the authors proposed two main algorithms of localization. First is the linear Kalman Filter (KF) SLAM, which consists of five phases, such as (a) motionless robot with absolute measurement, (b) moving vehicle with absolute measurement, (c) motionless robot with relative measurement, (d) moving vehicle with relative measurement, and (e) moving vehicle with relative measurement while the robot location is not detected. The second localization algorithm is the SLAM with the Extended Kalman Filter (EKF). Finally, the proposed SLAM algorithms are tested by simulations to be efficient and viable. The simulation results show that the presented SLAM approaches can accurately locate the landmark and mobile robot.