Multiplicative extended Kalman filter (MEKF) has been widely applied in the vast majority of spacecraft attitude determination missions. For the arbitrary reference frame, the linear quaternion kinematics equation and the dynamical model of three-component attitude errors were formulated, and gyro-aided and gyro-free attitude determination schemes were designed. The typical basic equation of the MEKF was developed, including the detailed models for vector measurements, quaternion measurements and Euler angle measurements. The research can provide theory reference and technique support for spacecraft missions.