Spacecraft attitude estimation algorithm based on multiplicative quaternion and constrained filter

A multiplicative constrained attitude estimation algorithm is proposed by using unit quaternion to describe the attitude. A major advantage of using the quaternion is that the kinematics equation is linear in the quaternion and is also free of singularities, but the normalization constraint condition must be preserved accurately. First, the differences in the definition of estimation errors and state correction modes between the additive and multiplicative filter algorithms are compared, and the disadvantages in the physical conception and estimation accuracy of the unconstrained quaternion estimation algorithm are also analyzed in detail. Then, an attitude estimator for the attitude measurement model composed of vector observation and gyros is designed by using the multiplicative constrained filter algorithm. According to the state part constrained attitude estimation problem, the state and covariance propagation equations and the optimal gain matrix subject to state normality constraint are derived. Subsequently the constrained gain matrix is applied to the measurement update phase of the attitude estimation algorithm. Finally, the numerical simulation result demonstrates the superiority in estimation accuracy and convergence property of the proposed algorithm.