The process of simultaneously building the map and locating a vehicle is known as Simultaneous Localization and Mapping (SLAM) and can be used for autonomous navigation. The estimation of vehicle states and landmarks plays an important role in SLAM. Most of the SLAM algorithms are based on extended Kalman filters (EKFs). However, EKF's are not the best choice for SLAM as they suffer from the assumption of Gaussian noise statistics and linearization errors, which can degrade the performance. H∞ filter is one of the alternative of Kalman filter. This paper investigates three SLAM algorithms: (i) EKF SLAM (ii) extended H∞(EH∞) SLAM and (iii) mixed extended H2/H∞(EH2/H∞) SLAM. A comparison of the three algorithms is given through numerical simulations.