User's Manual

Document MV0319P.N
© Xsens Technologies B.V.
MVN User Manual
107
From the same recording, Figure 64 shows that when the subject has moved, they have approached a
ferromagnetic material. This is known because the Mag Field Norm increases, in particular for the right
foot, as it increases above 1.5. If this value increases further and remains high for longer than a few 30
seconds (usually less than 2 can be dealt with in the algorithms used in MVN Studio) then this area
should be avoided, in particular during calibrations, but if possible, also during measurements.
19.3 MVN kinematics and output
19.3.1 Quaternion orientation representation
A unit quaternion vector can be interpreted to represent a rotation about a unit vector n through an angle
.
   
 
22
cos , sin
GB
q

 n
A unit quaternion itself has unit magnitude, and can be written in the following vector format:
 
0 1 2 3
, , , ,q q q q q
1q 
Quaternions are an efficient, non-singular description of 3D orientation and a quaternion is unique up to
sign:
qq
An alternative representation of a quaternion is as a vector with a complex part, the real component is
the first element .
The inverse
BG
q
is defined by the complex conjugate
*
of :
 
*
0 1 2 3
, , ,
GB BG
q q q q q q    
As defined here,
GB
q
rotates a vector
B
x
in the body co-ordinate system (B) to the global reference co-
ordinate system (G).
*G GB B GB GB B BG
q q q q     x x x
Where

represents a quaternion multiplication:
 
0
1 2 1 2 1 2, 1 2 2 1 1 2
0 0 0
q q = q q v v q v q v v v        
with:
 
 
1 2 3
1 2 3
1 1 , 1 , 1
2 2 , 2 , 2
v q q q
v q q q


and both

and

represent the standard dot and cross product, respectively. Be aware that the order
of multiplication is important. Quaternion multiplication is not commutative, meaning:
1 2 2 1q q q q  
19.3.2 Conversions
Quaternion to rotation matrix:

0
q
GB
q