A system for controlling an aerospace vehicle using on-line inertia estimation may include an attitude sensor to measure an attitude of the aerospace vehicle. The system may also include a processor on board the aerospace vehicle. An inertia estimator operable on the processor may generate an on-line inertia estimate of the aerospace vehicle. A rate and attitude estimator operable on the processor may determine an angular position and angular velocity of the aerospace vehicle using the attitude measurement of the aerospace vehicle and the on-line inertia estimate for controlling movement and orientation of the aerospace vehicle without any rates of rotation of the aerospace vehicle being required.