. These exact results are to be preferred to approximate methods based on measurements of a few selected points. The unit quaternion representing the best rotation is the eigenvector associated with the most positive eigenvalue of a symmetric 4 X 4 matrix. The elements of this matrix are combinations of sums

. The filter represents rotations using quaternions rather than Euler angles, which eliminates the long-standing problem of singularities associated with attitude estimation. A process model for rigid body angular motions and angular rate measurements is defined. The process model converts angular rates

In this paper we present a solution to the problem of controlling relative attitude in a leader-follower spacecraft formation, with focus on the rotation path for the follower spacecraft. Mathematical models of relative attitude kinematics and dynamics are presented, and a nonlinear control law

, attitude, and gyro bias by combining a GNSS receiver with an inertial measurement unit including a magnetometer. Previous work by the authors on this topic was based on local navigation equations that ignored the Earth’s rotation and curvature. Moreover, the attitude was represented by an over

The need for a formal definition of a reorientation event in molecular dynamics simulations is recognised, and this is furnished through the quaternion formalism. Any rotation can be represented by a unit fourdimensional vector, and the general vector representing a molecule's orientation

the Quest algorithm produces a computed quaternion input for the filter. This preprocessing reduces the dimension of the state vector and makes the mea-surement equations linear. Real-time implementation and testing results of the quaternion-based Kalman filter are presented. Experimental results validate

uses the iterated extended Kalman filter as an estimator and as a screw representation of the 3--D transformation based on dual quaternions. Dual quaternions provide a means to represent both rotation and translation in a unified notation. The method has been implemented and tes...

the Quest algorithm produces a computed quaternion input for the filter. This preprocessing reduces the dimension of the state vector and makes the mea-surement equations linear. Real-time implementation and testing results of the quaternion-based Kalman filter are presented. Experimental results validate

it for several seconds in advance. For this purpose, we propose in this study a long-term prediction approach based on a combined trajectory classification and particle filter framework. As a measure for the similarity between trajectories, we introduce the quaternion-based rotationally invariant longest common

distinct schemes of parameterization are analyzed: The first scheme concerns the traditional axis-angle approach, while the second employs stereographic projection from unit quaternion sphere to the 3D real projective space. Performance measurements are taken and a comparison is made between the two