Symmetries in observer design: review of some recent results and   applications to EKF-based SLAM
  In this paper, we first review the theory of symmetry-preserving observers and we mention some recent results. Then, we apply the theory to Extended Kalman Filter-based Simultaneous Localization and Mapping (EKF SLAM). It allows to derive a new (symmetry-preserving) Extended Kalman Filter for the non-linear SLAM problem that possesses convergence properties. We also prove a special choice of the gains ensures global exponential convergence. 
Silvere Bonnabel
math.OC cs.RO cs.SY