User manual


 DocumentMT0100P.N
©XsensTechnologiesB.V. MTiandMTxUserManualandTechnicalDocumentation
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4.3.1 Quaternionorientationoutputmode
Aunitquaternionvectorcanbeinterpretedtorepresentsarotationaboutaunitvectornthroughanangleα.

((), ()
22
GS
qcossin)
α
α
(,,,)qqqqq=

qq=−
†
(, , , )
= n


Aunitquaternionitselfhasunitmagnitude,andcanbewritteninthefollowingvectorformat;

0123GS
1q =




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;

0123GS SG
qqqqqq
=−−−=
†
qq qq==xx x

Asdefined here

q
GS
rotatesavectorinthesensorco‐ordinatesystem(S)totheglobalreferenceco‐ordinate
system(G).

GS GS GS SGGS S


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
.



4.3.2 Euleranglesorientationoutputmode
Thedefinition used for'Euler‐angles'here is equivalentto'roll, pitch, yaw/heading' (also known asCardan).
TheEuler‐anglesareof XYZEarthfixedtype(subsequentrotationaroundglobalX,YandZaxis,alsoknownas
aerospacesequence).

Theoutputdefinitioninquaternionoutputmodeis:

MTData DATA = 
MID50(0x32)

All data elements in DATA field are FLOATS (4 bytes) , unless specified otherwise by modifying the
OutputSettingDataFormatfield.

q3q2q1q0