ATTITUDE ERROR KINEMATICS: APPLICATIONS IN ESTIMATION
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abstract
Several attitude error representations are presented for describing the orientation error kinematics. Compact forms of attitude error kinematics are derived for each representation. The attitude error is initially defined as rotational error between the current and the reference orientation. The development of nonlinear kinematic models enables arbitrarily large relative rotations and rotation rates for several standard attitude representations. Two distinct approaches to attitude error kinematics are developed. In the first one the estimated angular velocity is defined in the true attitude axes frame while in the second one is defined in the estimated attitude axes frame. The first approach is of interest in simulation, where the true attitude is known, while the second approach is for real estimation/control applications. Two nonlinear kinematic models are derived that are valid for arbitrarily large rotations and rotation rates. The development of Multiplicative Kalman Filter (MKF) using the Gyro model has been revised. By utilizing several attitude error kinematics methodologies to describe the spacecraft rotation error, we introduce different compact and efficient forms of Multiplicative Kalman Filter (MKF). The results presented are expected to be broadly useful to nonlinear attitude estimation filtering formulations. A discussion of the benefits of the derived error kinematic models is included.
