Angular momentum vector drift model and its parameter identification for high-speed rotational sphere

Abstract

Rotational sphere with high angular speed is able to maintain a fixed angular momentum vector in inertial space when it is freely supported without disturbing torque. This property allows the sphere being widely used as a star-in-bottle for two-degree angular reference. Angular momentum vector’s drift model is the key to guarantee the high precision. In this paper, we deduced the drift pattern based on general 20-coefficients model for the specific orientation of the sphere in servo platform with consideration of case-rotation-dwell auto-compensating device. Our model comprehensively considered sphere’s drift error, apparent motion of the earth, platform’s alignment error, case assembly error and misalignment angle between case rotating axis and sphere‘s angular momentum axis. We further deduced the kinematic equation of the platform and constructed Kalman filter to identify the sphere’s drift coefficients. Simulation results show that all the drift coefficients can be identified and the residual is less than 1.3″/day. 14 days’ real experimental result shows that residual is less than 10″/day and all the coefficients converged within 0.0001°/h. Both simulation and experiment on the estimation precision confirm that our model is accurate and efficient.