Generalizing random-vector SLAM with random finite sets

The simultaneous localization and mapping (SLAM) problem in mobile robotics has traditionally been formulated using random vectors. Alternatively, random finite sets(RFSs) can be used in the formulation, which incorporates non-heursitic-based data association and detection statistics within an estimator that provides both spatial and cardinality estimates of landmarks. This paper mathematically shows that the two formulations are actually closely related, and that RFS SLAM can be viewed as a generalization of vector-based SLAM. Under a set of ideal detection conditions, the two methods are equivalent. This is validated by using simulations and real experimental data, by comparing principled realizations of the two formulations.