Simultaneous Localization and Mapping (SLAM) using for the mobile robot navigation has two main problems. First problem is the computational complexity due to the growing state vector with the added landmark in the environment. Second problem is data association which matches the observations and landmarks in the state vector. In this study, we compare Extended Kalman Filter (EKF) based SLAM which is well-developed and well-known algorithm, and Compressed Extended Kalman Filter (CEKF) based SLAM developed for decreasing of the computational complexity of the EKF based SLAM. We write two simulation program to investigate these techniques. Firts program is written for the comparison of EKF and CEKF based SLAM according to the computational complexity and covariance matrix error with the different numbers of landmarks. In the second program, EKF and CEKF based SLAM simulations are presented. For this simulation differential drive vehicle that moves in a 10m square trajectory and LMS 200 2-D laser range finder are modelled and landmarks are randomly scattered in that 10m square environment.