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# Transforming MTi data from local frame (L) to sensor frame (S)

The MTi has two reference frames: The sensor-fixed frame S (xyz as printed on the side of the MTi) and the local Earth-fixed frame L (by default East-North-Up). For a more detailed description of these frames, we refer to chapter 4.2 of the MTi Family Reference Manual.

The free acceleration  and velocity  estimates of the MTi are both outputted in the local Earth-fixed frame. The MTi does not support an output of these quantities in the sensor-fixed frame but users can easily convert them to the sensor-fixed frame by applying a rotation. The orientation estimate  describes the rotation from the sensor-fixed frame S to the local Earth-fixed frame L which is denoted by the superscript LS. The actual representation of the orientation depends on your settings. The MTi device family supports the output of the orientation as Euler angles , unit quaternions , or direction cosine matrices (DCM) . To convert the estimates between frames, we use the rotation matrix of the orientation . For the case that we use DCM matrices as orientation output the computation becomes trivial and explains also why DCM matrices are often referred to as rotation matrices:

The rotation from the local Earth-fixed frame L to the sensor-fixed frame S is then defined by

where we use the property of rotation matrices being orthogonal. Finally, we can rotate our estimates of velocity and free acceleration to the sensor frame:

Note that the estimates of velocity, free acceleration and orientation are all time-dependent and therefore, when applying the above conversion, it is important to always use estimates that were outputted by the MTi at the same time instance. The conversion is trivial if the MTi is configured to output the RotationMatrix directly. If this is undesired (e.g. due to bandwidth limitations) then the Xsens Device API also allows to translate between the different orientation output modes. For more details regarding the relationship between the three orientation output modes, we refer to this article