On the Extraction of Angular Velocity from Attitude Measurements

In this paper we research the extraction of the angular rate vector from attitude information without differentiation, in particular from quaternion measurements. We show that instead of using a Kalman filter of some kind, it is possible to obtain good rate estimates, suitable for spacecraft attitude control loop damping, using simple feedback loops, thereby eliminating the need for recurrent covariance computation performed when a Kalman filter is used. This considerably simplifies the computations required for rate estimation in gyro-less spacecraft. Some interesting qualities of the Kalman filter gain are explored, proven and utilized. We examine two kinds of feedback loops, one with varying gain that is proportional to the well known Q matrix, which is computed using the measured quaternion, and the other type of feedback loop is one with constant coefficients. The latter type includes two kinds; namely, a proportional feedback loop, and a proportional-integral feedback loop. The various schemes are examined through simulations and their performance is compared. It is shown that all schemes are adequate for extracting the angular velocity at an accuracy suitable for control loop damping