Online extrinsic calibration is crucial for building "power-on-and-go" moving platforms, like robots and AR devices. However, blindly performing online calibration for unobservable parameter may lead to unpredictable results. In the literature, extensive studies have been conducted on the extrinsic calibration between IMU and camera, from theory to practice. It is well-known that the observability of extrinsic parameter can be guaranteed under sufficient motion excitation. Furthermore, the impacts of degenerate motions are also investigated. Despite these successful analyses, we identify an issue regarding the existing observability conclusion. This paper focuses on the observability investigation for straight line motion, which is a common-seen and fundamental degenerate motion in applications. We analytically prove that pure translational straight line motion can lead to the unobservability of the rotational extrinsic parameter between IMU and camera (at least one degree of freedom). By correcting observability conclusion, our novel theoretical finding disseminate more precise principle to the research community and provide explainable calibration guideline for practitioners. Our analysis is validated by rigorous theory and experiments.

Accurate global localization is crucial for autonomous navigation and planning. To this end, 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 adaptive 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.