  A robust nonlinear stochastic observer for simultaneous localization and
mapping (SLAM) is proposed using the available uncertain measurements of
angular velocity, translational velocity, and features. The proposed observer
is posed on the Lie Group of $\mathbb{SLAM}_{n}\left(3\right)$ to mimic the
true stochastic SLAM dynamics. The proposed approach considers the velocity
measurements to be attached with an unknown bias and an unknown Gaussian noise.
The proposed SLAM observer ensures that the closed loop error signals are
semi-globally uniformly ultimately bounded. Simulation results demonstrates the
efficiency and robustness of the proposed approach, revealing its ability to
localize the unknown vehicle, as well as mapping the unknown environment given
measurements obtained from low-cost units.
