A low-cost inertial measurement unit (IMU) and a rolling shutter camera form a conventional device configuration for localization of a mobile platform due to their complementary properties and low costs. This paper proposes a new calibration method that jointly estimates calibration and noise parameters of the low-cost IMU and the rolling shutter camera for effective sensor fusion in which accurate sensor calibration is very critical. Based on the graybox system identification, the proposed method estimates unknown noise density so that we can minimize calibration error and its covariance by using the unscented Kalman filter. Then, we refine the estimated calibration parameters with the estimated noise density in batch manner. Experimental results on synthetic and real data demonstrate the accuracy and stability of the proposed method and show that the proposed method provides consistent results even with unknown noise density of the IMU. Furthermore, a real experiment using a commercial smartphone validates the performance of the proposed calibration method in off-the-shelf devices.