  Simultaneous Localization and Mapping (SLAM) is a process of concurrent
estimation of the vehicle's pose and feature locations with respect to a frame
of reference. This paper proposes a computationally cheap geometric nonlinear
SLAM filter algorithm structured to mimic the nonlinear motion dynamics of the
true SLAM problem posed on the matrix Lie group of
$\mathbb{SLAM}_{n}\left(3\right)$. The nonlinear filter on manifold is proposed
in continuous form and it utilizes available measurements obtained from group
velocity vectors, feature measurements and an inertial measurement unit (IMU).
The unknown bias attached to velocity measurements is successfully handled by
the proposed estimator. Simulation results illustrate the robustness of the
proposed filter in discrete form demonstrating its utility for the
six-degrees-of-freedom (6 DoF) pose estimation as well as feature estimation in
three-dimensional (3D) space. In addition, the quaternion representation of the
nonlinear filter for SLAM is provided. Keywords: Simultaneous Localization and
Mapping, Nonlinear observer algorithm for SLAM, inertial measurement unit,
inertial vision system, pose, position, attitude, landmark, estimation, IMU,
SE(3), SO(3), unmanned aerial vehicle, rigid-body, noise, nonlinear observer
for SLAM, Gaussian filter, Kalman filtering, navigation.
