—This paper presents an alternative formulation for the Bayesian feature-based simultaneous localisation and mapping (SLAM) problem, using a random finite set approach. For a feature based map, SLAM requires the joint estimation of the vehicle location and the map. The map itself involves the joint estimation of both the number of features and their states (typically in a 2D Euclidean space), as an a priori unknown map is completely unknown in both landmark location and number. In most feature based SLAM algorithms, so-called ‘feature management’ algorithms as well as data association hypotheses along with extended Kalman filters are used to generate the joint posterior estimate. This paper, however, presents a recursive filtering algorithm which jointly propagates both the estimate of the number of landmarks, their corresponding states, and the vehicle pose state, without the need for explicit feature management and data association algorithms. Using a finite set-valued join...