Angular-Rate Estimation Using Quaternion Measurements

In most spacecraft (SC) there is a need to know the SC angular rate. Precise angular rate is required for attitude determination, and a coarse rate is needed for attitude control damping. Classically, angular rate information is obtained from gyro measurements. These days, there is a tendency to build smaller, lighter and cheaper SC, therefore the inclination now is to do away with gyros and use other means and methods to determine the angular rate. The latter is also needed even in gyro equipped satellites when performing high rate maneuvers whose angular-rate is out of range of the on board gyros or in case of gyro failure. There are several ways to obtain the angular rate in a gyro-less SC. When the attitude is known, one can differentiate the attitude in whatever parameters it is given and use the kinematics equation that connects the derivative of the attitude with the satellite angular-rate and compute the latter. Since SC usually utilize vector measurements for attitude determination, the differentiation of the attitude introduces a considerable noise component in the computed angular-rate vector.