  This paper deals with the simultaneous estimation of the attitude, position
and linear velocity for vision-aided inertial navigation systems. We propose a
nonlinear observer on $SO(3)\times \mathbb{R}^{15}$ relying on body-frame
acceleration, angular velocity and (stereo or monocular) bearing measurements
of some landmarks that are constant and known in the inertial frame. Unlike the
existing local Kalman-type observers, our proposed nonlinear observer
guarantees almost global asymptotic stability and local exponential stability.
A detailed uniform observability analysis has been conducted and sufficient
conditions are derived. Moreover, a hybrid version of the proposed observer is
provided to handle the intermittent nature of the measurements in practical
applications. Simulation and experimental results are provided to illustrate
the effectiveness of the proposed state observer.
