Vision-aided Inertial Navigation Systems (V-INS) can provide precise state estimates for the 3D motion of a vehicle when no external references (e.g., GPS) are available. This is achieved by combining inertial measurements from an IMU with visual observations from a camera under the assumption that the rigid transformation between the two sensors is known. Errors in the IMU-camera calibration process causes biases that reduce the accuracy of the estimation process and can even lead to divergence. In this paper, we present a Kalman filter-based algorithm for precisely determining the unknown transformation between a camera and an IMU. Contrary to previous approaches, we explicitly account for the time correlations of the IMU measurements and provide a figure of merit (covariance) for the estimated transformation. The proposed method does not require any special hardware (such as spin table or 3D laser scanner) except a calibration target. Simulation and experimental results are presented that validate the proposed method and quantify its accuracy.