Angular Velocity Determination Directly from Star Tracker Measurements John L. Crassidis * Introduction Star trackers are increasingly used on modern day spacecraft. With the rapid advance- ment of imaging hardware and high-speed computer processors, current trackers are small and routinely achieve arc-second attitude accuracy. 1 Typical sampling rates for these track- ers range from 1 to 10 Hz. As computer processor technology advances these frequencies will increase, leading to filter designs that provide even more accurate results. The body angular velocity can be derived using a derivative approach in the attitude kinematics model. For example, if the attitude quaternion q and it’s derivative ˙ q (which is usually approximated by a finite-difference) are known, then the angular velocity ω can be computed from the kinematics equations, with ω =2Ξ T (q)˙ q, where Ξ(q) is a 4 × 3 matrix function of the quaternion (see Ref. [2] for more details). However, this approach requires knowledge of the attitude, which is determined from the star reference and body measure- ment vectors. In this note a new and simple approach to determine the angular velocity is shown that depends only on knowledge of the body vector measurements, which are obtained directly from the star tracker. Therefore, angular velocities can still be determined in the event of star pattern recognition anomalies, which may be used to control the spacecraft in the event of gyro failures. Angular Velocity Determination In this section a least-squares approach is used to determine the angular velocity from star tracker body measurements alone. Consider the following unit-vector measurement model * Assistant Professor, Department of Mechanical and Aerospace Engineering, University at Buffalo, State University of New York, Amherst, NY 14260-4400. Senior Member AIAA. J. L. Crassidis 1 of 12