Document MT0605P.E
© Xsens Technologies B.V.
MTi User Manual
44
4.11 Reset of output or reference co-ordinate systems
In some situations it may occur that the MT sensor axes are not exactly aligned with the axes of the
object of which the orientation has to be recorded. It may be desired to output the orientation and/or
calibrated inertial data in different sensor-fixed f
rame (S’ instead of S) or a different earth-fixed local
frame (L’ instead of L). The transformations are defined by the rotation matrices
L’L
R and
SS’
R resulting
in the following equations affecting the rotation matrix
LS
R, the SDI data (
S
∆
q and
S
∆
v), the calibrated
data (
S
s), and the sensor fusion algorithm output (
L
x):
𝑅
𝐿
′
𝑆
′
=
𝑅 ∙ 𝑅
𝐿𝑆
∙
𝑅
𝑆𝑆
′
𝐿
′
𝐿
∆𝑞
𝑆
′
= ( 𝑞
𝑆𝑆
′
)
∗
∆𝑞
𝑆
∆𝑞
𝑆𝑆
′
∆𝑣
𝑆
′
= ( 𝑅
𝑆𝑆
′
)
𝑇
∆𝑣
𝑠
𝑠
𝑆
′
= ( 𝑅
𝑆𝑆
′
)
𝑇
∙ 𝑠
𝑆
𝑥 =
𝑅
𝐿
′
𝐿
∙ 𝑥
𝐿
𝐿′
Five methods are available to facilitate in obtaining the output in the desired coordinate frames, which
are:
1.
An inclination reset that levels the sensor by defining the S’ frame.
2.
A heading reset that defines the L’ frame by setting the x-axis of L’ frame while maintaining the
z-axis along the vertical (also known as "bore sighting").
3. A combined inclination/heading reset, referred to as alignment reset.
4.
Setting an arbitrary alignment rotation matrix to rotate S to the chosen frame S’ :
SS’
R.
5. Setting an arbitrary alignment rotation matrix to rotate L to the chos
en frame L’ :
L’L
R.
The different orientation resets are explained using Figure 10, showing a side and top view of each of
the resets, with the standard orientation output
LS
R.
Orientation resets
The orientation reset functions aim to facilitate in aligning the sensor object it is strapped to, by
defining the L’ frame (heading reset) and the S’ frame (inclination reset) resulting in
L’S’
R, defined in the
equations above. The orientation reset is separated in an inclination reset (leveling) and a heading
reset (bore sighting). After a full orientation reset, the orientation of the L’ and S’ frames are equal, and
the coordinate axes are defined by:
• the L’ and S’ z-axis is the vertical (up, along gravity)
• the L’ and S’ x-axis equals the S x-axis, but projected on the horizontal plane
• the L’ and S’ y-axis is chosen as to obtain a right handed coordinate frame.
The coordinate rotation matrices
L’L
R and
SS’
R are calculated by:
𝑅
𝐿
′
𝐿
= ( 𝑋
𝐿
𝐿′
, 𝑌
𝐿
𝐿′
, 𝑍
𝐿
𝐿′
)
𝑅
𝑆𝑆
′
= ( 𝑅
𝐿𝑆
)
𝑇
∙
𝑅 = ( 𝑅
𝐿𝑆
)
𝑇
∙
𝐿𝑆′
( 𝑅
𝐿′𝐿
)
𝑇
𝑋
𝐿
𝐿′
= ⟨𝑅𝑛 ∙ 𝑅
𝐿𝑆
∙ (1 0 0)
𝑇
⟩
𝑍
𝐿
𝐿′
= (0 0 1)
𝑇
𝑌
𝐿
𝐿′
= ⟨ 𝑍
𝐿
𝐿′
× 𝑋
𝐿
𝐿′
⟩
