AHRS Quaternions and Rotations
Quaternions
Quaternion은 사원수 또는 쿼터니언이라고 부르며, 복소수를 확장해 만든 수 체계입니다.
i2=j2=k2=ijk=−1q=xi+yj+zk+wq=[xyzw]T
Norm
q=x2+y2+z2+w2
Conjugate quaternion
qˉ=−xi−yj−zk+w
pq=qˉpˉ
Pure quaternion
q=[xyz0]T
Identity quaternion
I=[0001]T
Inverse quaternion
q−1=∣∣q∣∣2qˉ(q−1=qˉif ||q|| = 1)
Hamilton product
pq=L(p)q=R(q)p=pwpz−py−px−pzpwpx−pypy−pxpw−pzpxpypzpwqxqyqzqw=qw−qzqy−qxqzqw−qx−qy−qyqxqw−qzqxqyqzqw