Recently, mobile devices such as smart phones and pads are being equipped with inertial measurement units (IMUs) because of advances in micro-electro-mechanical systems technology. This has increased the importance of IMU–camera fusion for vision-based applications. However, ultralow-cost IMUs take much less accurate measurements than low-cost and high-cost IMUs. This uncertainty degrades the accuracy and reliability of IMU–camera calibration, which is the most important step for IMU–camera fusion technology. In this paper, we propose three effective algorithms for robust and accurate IMU–camera calibration with uncertain measurements: boundary constraint, adaptive propagation, and angular velocity constraint. These algorithms incorporate a Bayesian filtering framework to estimate calibration parameters more efficiently. The simulation and experimental results both demonstrated the superiority of the proposed algorithms.