Calibration of an IMU-Camera Cluster Using Planar Mirror Reflection and Its Observability Analysis

This paper describes a novel and a low-cost calibration approach to estimate the relative transformation between an inertial measurement unit (IMU) and a camera, which are rigidly mounted together. The calibration is performed by fusing the measurements from the IMU-camera rig moving in front of a planar mirror. To construct the visual observations, we select a set of key features (KFs) attached to the visual inertial rig where the 3-D positions of the KFs are unknown. During calibration, the system is navigating in front of the planar mirror, while the vision sensor observes the reflections of the KFs in the mirror, and the inertial sensor measures the system's linear accelerations and rotational velocities over time. Our first contribution in this paper is studying the observability properties of IMU-camera calibration parameters. For this visual inertial calibration problem, we derive its time-varying nonlinear state-space model and study its observability properties using the Lie derivative rank condition test. We show that the calibration parameters and the 3-D position of the KFs are observable. As our second contribution, we propose an approach for estimating the calibration parameters along with the 3-D position of the KFs and the dynamics of the analyzed system. The estimation problem is then solved in the unscented Kalman filter framework. We illustrate the findings of our theoretical analysis using both simulations and experiments. The achieved performance indicates that our proposed method can conveniently be used in consumer products like visual inertial-based applications in smartphones for localization, 3-D reconstruction, and surveillance applications.