Recently, mobile devices such as smart phones and quad-copters 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 IMU- camera calibration with uncertain measurements: boundary constraint, adaptive prediction, and angular velocity constraint. These algorithms incorporate a Bayesian filtering framework to estimate calibration parameters more efficiently. The experimental results on both simulation and real data demonstrated the superiority of the proposed algorithms.