  Accurate global localization is crucial for autonomous navigation and
planning. To this end, various GPS-aided Visual-Inertial Odometry (GPS-VIO)
fusion algorithms are proposed in the literature. This paper presents a novel
GPS-VIO system that is able to significantly benefit from the online
calibration of the rotational extrinsic parameter between the GPS reference
frame and the VIO reference frame. The behind reason is this parameter is
observable. This paper provides novel proof through nonlinear observability
analysis. We also evaluate the proposed algorithm extensively on diverse
platforms, including flying UAV and driving vehicle. The experimental results
support the observability analysis and show increased localization accuracy in
comparison to state-of-the-art (SOTA) tightly-coupled algorithms.
