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.