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Reset of reference co-ordinate systems

In some situations it may be 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 retrieve the orientation and/or calibrated inertial data in different sensor-fixed frame (S’ instead of S) or a different earth-fixed local frame (L’ instead of L). The transformations are defined by the rotation matrices L’LR and SS’R resulting in the following equations affecting the rotation matrix LSR, the SDI data (S∆q and S∆v), the calibrated data (Ss), and the sensor fusion algorithm output (Lx):

  

 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’
  5. Setting an arbitrary alignment rotation matrix to rotate L to the chosen frame L’ : L’L

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 LSR.

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’LR and SS’R are calculated by:

 After an inclination and/or heading reset, the equation for L’S’R is applied (see above). It should be noted that the inclination reset (SS’R) will not work if the sensor x-axis is aligned along the z-axis of the object, since the sensor x-axis is used to describe the direction of the object x-axis. Furthermore, after a heading reset, the yaw may not be exactly zero, especially when the x-axis is close to the vertical. This is caused by the definition of yaw in Euler angles, which becomes unstable when the pitch approaches 90 deg.

 

In the figure above, the different alignments and resets define the S’ and/or L’ frame. (a): the default orientation output of S with respect to L: LSR; (b): after inclination reset, method 1: LS’R (c): after heading reset, method 2: L’SR, (d): after alignment reset, method 3: L’S’R. All of these are also possible to set with arbitrary alignments.

NWU and NED reference coordinate frames

The default reference coordinate frame in the MTi is ENU-frame, described in section 5.2.3, the MTi supports two other reference coordinate systems that can be selected. These are NWU and NED. 

NWU is the reference coordinate system that used to be the default up to the third generation MTi and MTi-G. In order to configure the MTi to provide data in the NWU local frame, apply the following rotation matrix in RotLocal.

 NED is a reference coordinate system often used in aerospace applications. NED is also a reference coordinate system available in the third generation MTi and MTi-G. In order to configure the MTi in NED, apply the following rotation matrix in RotLocal:

  

Arbitrary alignment

If the measured kinematics is required in a frame S’ and/or a frame L’ with known orientations with respect to standard sensor coordinate frames S and L, the alignment matrices can be set with an arbitrary but known orientation. This can be useful if for mechanical reasons the MT can only be fastened in some specific orientation. The alignment matrices L’LR or SS’R are applied to the output data according to the equations above. Refer to the MT Manager User Manual on how to use these alignment matrices.

The different orientation resets can be summarized as follows

  • Inclination reset: Applying SS’R only
  • Heading reset: Applying L’LR only
  • Alignment reset: Applying both L’LR, and SS’R

 NOTE: when applying SS’R and retrieving dq/dv only will result in double applying of SS’R when reprocessing orientation in XDA. To prevent this, set the MTi directly to orientation output. 

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