Shu, Full 4-d quaternion
discrete Fourier transform based watermarking for color images, Journal of Digital Signal Processing, vol.
The rest of this paper is organized as follows: Section II illustrates the basics of quaternion
Euler angles, quaternions
, and transformation matrices.
this group is isomorphic to a semidirect product Q X C9 of the quaternion
group Q and the cyclic group C9 of order 9).
However, there is one controversy regarding the nomenclature in a quaternion
with a real part equal to zero--that is a quaternion
as Q = ix + jy + kz, also known as pure quaternion
--can be thought of as a vector.
principal component analysis (QPCA) and feature point extraction, Lang et al.
where x, y, z and w denote elements of a quaternion
of the classical (real) quaternion
algebra H = H(-1,-1/R) Denote by [Iso.
Even though quaternion
representation of orientation is more reliable, for simplicity purposes in further hybrid tracking experiments Euler angles are used instead of quaternions
rel] are relative quaternion
and angular rates written in LVLH frame.
Reference  discussed how to transfer an attitude-tracking problem with a time-variable boundary condition into a fixed-boundary problem by means of line-of-sight coordinates, rotational quaternion
, and relative error feedback signals.
2 [Angstrom], and quaternion
and torsion steps of 5 were applied.
The sensors provided real-time kinematic data (sample frequency 60Hz) including acceleration and speed of rotation as well as quaternion
cubature Kalman filtering for spacecraft attitude estimation.
Let D be a non-trivial quaternion
division algebra over a non-archimedean localization field k.