Angular Velocity Determination Directly from Star Tracker Measurements

Introduction Star trackers are increasingly used on modern day spacecraft. With the rapid advancement of imaging hardware and high-speed computer processors, current trackers are small and routinely achieve arc-second attitude accuracy. Typical sampling rates for these trackers 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 q̇ (which is usually approximated by a finite-difference) are known, then the angular velocity ω can be computed from the kinematics equations, with ω = 2 Ξ (q) q̇, 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 measurement 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.