Accurate vision-aided inertial navigation depends on proper calibration of the relative pose of the camera and the inertial measurement unit (IMU). Calibration errors introduce bias in the overall motion estimate, degrading navigation performance -sometimes dramatically. However, existing camera-IMU calibration techniques are difficult, time-consuming and often require additional complex apparatus. In this paper, we formulate the camera-IMU relative pose calibration problem in a filtering framework, and propose a calibration algorithm which requires only a planar camera calibration target. The algorithm uses an unscented Kalman filter to estimate the pose of the IMU in a global reference frame and the 6-DoF transform between the camera and the IMU. Results from simulations and experiments with a low-cost solid-state IMU demonstrate the accuracy of the approach.