  A geometric nonlinear observer algorithm for Simultaneous Localization and
Mapping (SLAM) developed on the Lie group of \mathbb{SLAM}_{n}\left(3\right) is
proposed. The presented novel solution estimates the vehicle's pose (i.e.
attitude and position) with respect to landmarks simultaneously positioning the
reference features in the global frame. The proposed estimator on manifold is
characterized by predefined measures of transient and steady-state performance.
Dynamically reducing boundaries guide the error function of the system to
reduce asymptotically to the origin from its starting position within a large
given set. The proposed observer has the ability to use the available velocity
and feature measurements directly. Also, it compensates for unknown constant
bias attached to velocity measurements. Unit-qauternion of the proposed
observer is presented. Numerical results reveal effectiveness of the proposed
observer. Keywords: Nonlinear filter algorithm, Nonlinear observer for
Simultaneous Localization and Mapping, Nonlinear estimator, nonlinear SLAM
observer on manifold, nonlinear SLAM filter on matrix Lie Group, observer
design, asymptotic stability, systematic convergence, Prescribed performance
function, pose estimation, attitude filter, position filter, feature filter,
landmark filter, gradient based SLAM observer, gradient based observer for
SLAM, adaptive estimate, SLAM observer, observer SLAM framework, equivariant
observer, inertial vision unit, visual, SLAM filter, SE(3), SO(3).
