  The process of simultaneously mapping the environment in three dimensional
(3D) space and localizing a moving vehicle's pose (orientation and position) is
termed Simultaneous Localization and Mapping (SLAM). SLAM is a core task in
robotics applications. In the SLAM problem, each of the vehicle's pose and the
environment are assumed to be completely unknown. This paper takes the
conventional SLAM design as a basis and proposes a novel approach that ensures
fast adaptation of the nonlinear observer for SLAM. Due to the fact that the
true SLAM problem is nonlinear and is modeled on the Lie group of
$\mathbb{SLAM}_{n}\left(3\right)$, the proposed observer for SLAM is nonlinear
and modeled on $\mathbb{SLAM}_{n}\left(3\right)$. The proposed observer
compensates for unknown bias attached to velocity measurements. The results of
the simulation illustrate the robustness of the proposed approach.
