Simultaneous Localization and Mapping (SLAM) for the mobile robot navigation has two main problems. The first problem is the computational complexity due to the growing state vector with the added landmark in the environment. The second problem is the data association which matches the observations and landmarks in the state vector. In this study, we compare the Extended Kalman Filter-(EKF)-based SLAM which is well-developed and well-known algorithm, and the Compressed Extended Kalman Filter-(CEKF)-based SLAM developed for decreasing the computational complexity of the EKF-based SLAM. We describe two simulation programs to investigate these techniques. The first program is written for the comparison of EKF- and CEKF-based SLAMs according to the computational complexity and covariance matrix error with the different numbers of landmarks. In the second program, EKF- and CEKF-based SLAM with the ICNN and JCBB data association algorithms simulations are presented. For this simulation, the 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.