User manual


 DocumentMT0100P.N
©XsensTechnologiesB.V. MTiandMTxUserManualandTechnicalDocumentation
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14
• φ=roll
8
=rotationaroundX
G
,definedfrom[‐180°…180°]
• θ=pitch
9
=rotationaroundY
G
,definedfrom[‐90°…90°]
• ψ=yaw
10
=rotationaroundZ
G
,definedfrom[‐180°…180°]

NOTE:DuetothedefinitionofEuleranglesthereisamathematicalsingularitywhenthesensor‐fixedX‐axisis
pointingup ordownintheearth‐fixed referenceframe(i.e. pitch approaches±90°).Thissingularityis in no
waypresentinthequaternionorrotationmatrixoutputmode.

TheEuler‐anglescanbeinterpretedintermsofthecomponentsoftherotationmatrix,R
GS
,orintermsofthe
unitquaternion,q
GS
;

11
32 2 3 0 1
22
33 0 3
11
31 1 3 0 2
11
12 03
21
22
11 0 1
22
tan tan
221
sin ( ) sin (2 2 )
22
tan tan
221
GS
GS
GS
R
qq qq
Rqq
R
qq qq
qq qq
R
Rqq
φ
θ
ψ
−−
−−
−−
⎛⎞ ⎛
+
==
⎜⎟ ⎜
⎞
⎟
+
−
⎝⎠ ⎝
=− =− −
⎛⎞
⎛⎞
+
==
⎜⎟
⎜⎟
⎠
+
−
⎝⎠
⎝⎠


Here,thearctangent(tan
‐1
)isthefourquadrantinversetangentfunction.

NOTE:thattheoutputisindegreesandnotradians.



 


8
“roll”isalsoknownas:“bank”
9
“pitch”isalsoknownas:“elevation”or“tilt”
10
“yaw”isalsoknownas:“heading”,“pan”or“azimuth”
TheoutputdefinitioninEuler‐angleoutputmodeis:

MTData DATA = 
MID50(0x32)
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All data elements in DATA field are FLOATS (4 bytes) , unless specified otherwise by modifying the
OutputSettingDataFormatfield.

yawpitchroll