Observability Investigation for Rotational Calibration of (Global-pose aided) VIO under Straight Line Motion

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
with respect to 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 the existing observability
conclusion, our novel theoretical finding disseminates more precise principle
to the research community and provides explainable calibration guideline for
practitioners. Our analysis is validated by rigorous theory and experiments.