Observability Analysis of IMU Intrinsic Parameters in Stereo Visual–Inertial Odometry

In this article, we present self-calibrated visual-inertial odometry (VIO) that estimates inertial measurement unit (IMU) intrinsic parameters (scale factor and misalignment) using a stereo camera without any calibration boards. Most of the visual-inertial navigation algorithms assume that the visual and inertial sensors are well-calibrated before operating. However, this could degrade the navigation performance due to unmodeled errors. Specifically, we employ an extended Kalman filter (EKF)-based pose estimator in which the filter state is augmented by the IMU intrinsic parameter to model the egomotion more precisely. Since raw IMU readings are transformed by the intrinsic parameter, these are key factors that determine the performance of the egomotion tracking. The main contribution of this article is an analytic observability analysis of the self-calibrated VIO that is a nonlinear time-varying system. We inspect the rank of the observability matrix formed by Lie derivatives of the nonlinear system. Our theoretical result reveals that the IMU intrinsic parameter is fully observable when all six axes of an IMU are excited. This is further confirmed by our simulation experiments by examining state uncertainties. Moreover, the real-world experiment using a publicly available and author-collected data set reveals that the pose tracking performance is improved by modeling IMU intrinsic parameters.