This paper presents a navigation of an autonomous robot using simultaneous localization and mapping (SLAM) in outdoor environments. SLAM is a method in which localization and mapping are done simultaneously in an unknown environment without an access to a priori map. This paper introduces a probabilistic approach to a SLAM problem under Gaussian and non-Gaussian conditions and offers alternative solutions. First, an extended Kalman filter algorithm for the SLAM problem under Gaussian condition will be shown. Also, an alternative way of dealing with SLAM problem with assumption of non-Gaussian and called FastSLAM will be analyzed. FastSLAM is an algorithm that using Rao-Blackwellised method for particle filtering, estimates the path of robot while the landmarks positions which are mutually independent and with no correlation, can be estimated by EKF. This is done using a factorization that fits very well into SLAM problem based on a Bayesian network. In this paper, a real outdoor autonomous robot is presented and several experiments have been performed based on both methods. The experimental results are discussed and compared.