Some results on SLAM and the closing the loop problem

This paper addresses the closing loop problem as the challenge of using all the information from the observation gathered when closing the loop in order to optimally adjust the whole map (assuming a correct data association). The proposed approach is an approximation, which allows the calculation of the gain without keeping track of all the correlations (i.e. with a complexity independent of the number of the map elements). Furthermore, the paper presents an explicit mathematical demonstration showing that the correlations computed by the EKF-based SLAM are overestimated. More precisely, it is shown that these correlations decrease exponentially with respect to the heading error of the robot. The approach is empirically demonstrated by means of meaningful simulations. The results are then discussed and conclusions are pointed out in the last section.