MTi and MTx User Manual and Tech. Doc., © 2005, Xsens Technologies B.V.
MT0100P.E
9
2.3.1 Quaternion orientation output mode
A unit quaternion vector can be interpreted to represents a rotation about a unit vector
n
through an angle
α
.
A unit quaternion itself has unit magnitude, and can be written in the following vector format;
Quaternions are an efficient, non-singular description of 3D orientation and a quaternion is
unique up to sign:
An alternative representation of a quaternion is as a vector with a complex part, the real
component is the first one, q
0
.
The inverse (
q
SG
) is defined by the complex conjugate (
†
) of
q
GS
. The complex conjugate is
easily calculated;
As defined here
q
GS
rotates a vector in the sensor co-ordinate system (
S
) to the global
reference co-ordinate system (
G
).
Hence,
q
SG
rotates a vector in the global reference co-ordinate system (
G
) to the sensor co-
ordinate system (
S
), where
q
SG
is the complex conjugate of
q
GS
.
q = ¡ q
k q k= 1
q
G S
= (cos(
®
2
); nsi n(
®
2
))
q
G S
= (q
0
; q
1
; q
2
; q
3
)
x
G
= q
G S
x
S
q
y
G S
= q
G S
x
S
q
SG
q
y
G S
= (q
0
; ¡ q
1
; ¡ q
2
; ¡ q
3
) = q
SG
The output definition in quaternion output mode is:
q0
q1
q2
q3
TS
MTData
MID 50 (0x32)
All data elements in DATA field are FLOATS (4 bytes)
TS= time stamp (optional)
