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In this paper, we study in-depth the problem of online self-calibration forrobust and accurate visual-inertial state estimation. In particular, we firstperform a complete observability analysis for visual-inertial navigationsystems (VINS) with full calibration of sensing parameters, including IMU andcamera intrinsics and IMU-camera spatial-temporal extrinsic calibration, alongwith readout time of rolling shutter (RS) cameras (if used). We investigatedifferent inertial model variants containing IMU intrinsic parameters thatencompass most commonly used models for low-cost inertial sensors. Theobservability analysis results prove that VINS with full sensor calibration hasfour unobservable directions, corresponding to the system's global yaw andtranslation, while all sensor calibration parameters are observable givenfully-excited 6-axis motion. Moreover, we, for the first time, identifyprimitive degenerate motions for IMU and camera intrinsic calibration. Eachdegenerate motion profile will cause a set of calibration parameters to beunobservable and any combination of these degenerate motions are stilldegenerate. Extensive Monte-Carlo simulations and real-world experiments areperformed to validate both the observability analysis and identified degeneratemotions, showing that online self-calibration improves system accuracy androbustness to calibration inaccuracies. We compare the proposed onlineself-calibration on commonly-used IMUs against the state-of-art offlinecalibration toolbox Kalibr, and show that the proposed system achieves betterconsistency and repeatability. Based on our analysis and experimentalevaluations, we also provide practical guidelines for how to perform onlineIMU-camera sensor self-calibration.

Online Self-Calibration for Visual-Inertial Navigation Systems: Models, Analysis and Degeneracy