  Motivated by the goal of achieving robust, drift-free pose estimation in
long-term autonomous navigation, in this work we propose a methodology to fuse
global positional information with visual and inertial measurements in a
tightly-coupled nonlinear-optimization-based estimator. Differently from
previous works, which are loosely-coupled, the use of a tightly-coupled
approach allows exploiting the correlations amongst all the measurements. A
sliding window of the most recent system states is estimated by minimizing a
cost function that includes visual re-projection errors, relative inertial
errors, and global positional residuals. We use IMU preintegration to formulate
the inertial residuals and leverage the outcome of such algorithm to
efficiently compute the global position residuals. The experimental results
show that the proposed method achieves accurate and globally consistent
estimates, with negligible increase of the optimization computational cost. Our
method consistently outperforms the loosely-coupled fusion approach. The mean
position error is reduced up to 50% with respect to the loosely-coupled
approach in outdoor Unmanned Aerial Vehicle (UAV) flights, where the global
position information is given by noisy GPS measurements. To the best of our
knowledge, this is the first work where global positional measurements are
tightly fused in an optimization-based visual-inertial odometry algorithm,
leveraging the IMU preintegration method to define the global positional
factors.
