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Document MT1600P.2019.A
© Xsens Technologies B.V.
MTi Family Reference Manual
4.2.3 Orientation data
By default, the local earth-fixed reference coordinate system L
XYZ
is defined as a right-handed Cartesian
coordinate system with
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:
•
X positive to the East (E).
•
Y positive to the North (N).
•
Z positive when pointing up (U).
This coordinate system is known as ENU (East-North-Up) and is the standard in inertial navigation for
aviation and geodetic applications. Note that it is possible to change L
XYZ
using a different convention,
like NWU (North-West-Up) or NED (North-East-Down), by changing an alignment matrix or applying an
orientation reset.
The 3D orientation output is defined as the orientation between the body-fixed coordinate system, S
xyz
or O
xyz
, and the local earth-fixed co-ordinate system, L
XYZ
.
Orientation output modes
The output orientation can be presented in different equivalent representations:
•
Unit Quaternions;
•
Euler angles
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: roll, pitch, yaw (XYZ Earth fixed type) are output following the aerospace
sequence (Z-
Y’
-
X”)
;
•
Rotation Matrix (directional cosine matrix).
A positive rotation is always “right
-
handed”, i.e. defined according to the
right-hand rule (corkscrew rule),
see Figure 9. This means a positive rotation is defined as clockwise in the direction of the axis of rotation.
Figure 9: Right hand rule
to find more information on how quaternions, Euler angles and the rotation
matrix relate to each other.
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The default reference coordinate system L
XYZ
only applies to the MTi in Normal output mode. Refer to the Low
Level Communication Protocol Documentation for detailed orientation output specifications when using the ASCII
(NMEA) output mode.
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Please note that 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
). In practice, this means
roll and pitch is not defined as such when pitch is close to ±90 deg. This singularity is in
no way
present in the
quaternion or rotation matrix output mode.
