Augmented Reality (AR) is an important branch of the Virtual Reality (VR) and is attracting much attention of the researchers all over the world in recent years. Its application is expanding from indoor environments to outdoor systems. One of the key technologies in AR system is attitude measurement. However, traditional attitude measurement devices can not be applied in outdoor AR systems due to their limited working ranges and errors caused by environmental interferences. An attitude measurement system based on the measurements of the gravity field and the magnetic field of the earth with the characteristics of large working range, small size and low power consumption is presented. Algorithms for its calibration are studied. The proposed system can not only be applied in AR applications, but also in various applications such as unmanned vehicles, dead reckoning systems, and oil drilling.The error sources of the proposed attitude measurement system are first analyzed in detail. Then an error model based on physical principles is studied. Finally a calibration method based on ellipsoid fitting and invariant of the geomagnetic dip angle at a specific location is presented. During the calibration procedure, a set of measurements of three-axis accelerometers and magnetometers are recorded at various attitudes. Then the hard iron offsets, the stretch matrix and the hanger matrix of the soft iron are solved by fitting an ellipsoid to the measured data of the magnetometers, and the aligner matrix of the soft iron are determined using the fact that the dip angle is constant at the current location. The proposed calibration method can be performed even when no heading reference is provided.A method to remove outliers from the measurements of the magnetometer based on random sampling consensus (RANSAC) and orthogonal distance is presented, which greatly improves the accuracy and stability of the calibration method for magnetometers.A calibration method for three-axis accelerometers with absolute tilt reference is provided and the attitude selection method for accelerometer calibration is discussed. The calibration method for the offset of the accelerometers without reference is also proposed.An adaptive Kalman filter based on the magnitude of the measurements is presented to keep the heading stable when there is a sudden magnetic disturbance in the horizontal plane, and a hybrid attitude measurement system is designed.Two attitude measurement systems are implemented respectively, one is based on two-axis accelerometers and the other is based on three-axis accelerometers and three gyroscopes. Experimental results show the effectiveness of the proposed algorithms.