In this paper, we describe an attitude estimation algorithm based on the direction cosine matrix (DCM) attitude representation and analyze its performance. This algorithm is appropriate for the implementation of a low-cost attitude and heading reference system (AHRS) which is composed of micro electrical mechanical system (MEMS) inertial measurement unit (IMU) and magnetometer triad. To reduce the computational burden, we estimate only six elements of the nine elements of the DCM. Kalman filtering is used to fuse the angular rate, specific force and magnetometer triad measurements. The DCM model has an advantage over other attitude representations because it has linear measurement equations of accelerometer and magnetometer triads. For the DCM orthogonalization, we recommend a low computational burden algorithm within the integration filter. Finally experimental data is used to verify the efficiency of the algorithm.