  The design of a globally convergent position observer for feature points from
visual information is a challenging problem, especially for the case with only
inertial measurements and without assumptions of uniform observability, which
remained open for a long time. We give a solution to the problem in this paper
assuming that only the bearing of a feature point, and biased linear
acceleration and rotational velocity of a robot -- all in the body-fixed frame
-- are available. Further, in contrast to existing related results, we do not
need the value of the gravitational constant either. The proposed approach
builds upon the parameter estimation-based observer recently developed in
(Ortega et al., Syst. Control Lett., vol.85, 2015) and its extension to matrix
Lie groups in our previous work. Conditions on the robot trajectory under which
the observer converges are given, and these are strictly weaker than the
standard persistency of excitation and uniform complete observability
conditions. Finally, as an illustration, we apply the proposed design to the
visual inertial navigation problem.
