  The simultaneous localization and mapping (SLAM) problem is considered in
three dimensions. The proposed algorithm, differential geometric SLAM
(DG-SLAM), employs methods from differential geometry to propagate the state
and map estimates. Unlike EKF SLAM, the proposed filter is provably
asymptotically stable under the assumption of no measurement noise or biases.
The robustness of the DG-SLAM algorithm is assessed in simulation with
measurement noise. The simulation demonstrates successful localization and
mapping.
