  In this paper we address the inconsistency of the EKF-based SLAM algorithm
that stems from non-observability of the origin and orientation of the global
reference frame. We prove on the non-linear two-dimensional problem with point
landmarks observed that this type of inconsistency is remedied using the
Invariant EKF, a recently introduced variant ot the EKF meant to account for
the symmetries of the state space. Extensive Monte-Carlo runs illustrate the
theoretical results.
