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Spacecraft Angular Velocity Estimation Algorithm Based on Orientation Quaternion Measurements
# 12, December 2016
DOI: 10.7463/1216.0852496
author: M.V. Li^{1,*}
 ^{1} S.P. Korolev Rocket and Space Corporation «Energia», Korolev, Russia 
The spacecraft (SC) mission involves providing the appropriate orientation and stabilization of the associated axes in space. One of the main sources of information for the attitude control system is the angular rate sensor blocks. One way to improve a reliability of the system is to provide a back up of the control algorithms in case of failure of these blocks. To solve the problem of estimation of SP angular velocity vector in the inertial system of coordinates with a lack of information from the angular rate sensors is supposed the use of orientation data from the star sensors; in this case at each clock of the onboard digital computer. The equations in quaternions are used to describe the kinematics of rotary motion. Their approximate solution is used to estimate the angular velocity vector. Methods of modal control and multidimensional decomposition of a control object are used to solve the problem of observation and identification of the angular rates. These methods enabled us to synthesize the SP angular velocity vector estimation algorithm and obtain the equations, which relate the error quaternion with the calculated estimate of the angular velocity. Mathematical modeling was carried out to test the algorithm. Cases of different initial conditions were simulated. Time between orientation quaternion measurements and angular velocity of the model was varied. The algorithm was compared with a more accurate algorithm, built on more complete equations. Graphs of difference in angular velocity estimation depending on the number of iterations are presented. The difference in angular velocity estimation is calculated from results of the synthesized algorithm and the algorithm for more accurate equations. Graphs of error distribution for angular velocity estimation with initial conditions being changed are also presented, and standard deviations of estimation errors are calculated. The synthesized algorithm is inferior in accuracy assessment to the algorithm based on other equations, but wins in the simplicity of relations, which is important for using in the onboard computer. References Raushenbakh B.V., Tokar' E.N. Upravlenie orientatsiej kosmicheskikh apparatov [Attitude control of space vehicles]. Moscow: Nauka Publ., 1974. 598 p. (in Russ.).
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