Handling the Inconsistency of Relative Map Filter

In \cite{martinelli_2004_open_challenges_in}, a version of Relative Map Filter (\RMF) is proposed to solve the simultaneous localization and map building (SLAM) problem. In the \RMF, the map states contain only quantities invariant under shift and rotation. The estimation of the map states and their correlations is carried out in an optimal way using the Kalman filter. However, the dependency among the map states is not taken into account, thus the resulting map states are inconsistent. This paper presents two methods to enforce the consistency of the relative map states. The idea is to maintain a geometrically consistent map by solving a set of constraints between the map states. Experimental results obtained by using the proposed methods on real platform data show better performance than those deduced from the original \RMF.