This work deals with the Simultaneous Localisation and Mapping algorithm as it pertains to the deployment of mobile systems in unknown environments. Simultaneous Localisation and Mapping (SLAM) as defined here is the process of concurrently building up a map of the environment and using this map to obtain improved estimates of the location of the vehicle. In essence, the vehicle relies on its ability to extract useful navigation information from the data returned by its sensors. The vehicle typically starts at an unknown location with no a priori knowledge of landmark locations. From relative observations of landmarks, it simultaneously computes an estimate of vehicle and landmarks locations. While continuing in motion, the vehicle builds a complete map of landmarks and uses these to provide continuous estimates of the vehicle location. This work describes an algorithmic solution to this problem and presents the formulation of a novel approach to the mapping of terrain features that provides improved computational efficiency in the SLAM algorithm.