I'm trying to combine IMU displacements with the time of flight sensor readings in order to navigate through the indoor environment with a non-linear Kalman filter variant. In the graphic below, I tried to give an example of the setup. S0, S1, S2, and S3 are the time of flight anchors that can measure the distance between them and the tracked device. Their locations are given in the parentheses next to their label as meters.

Example setup

I've read some papers related to this work. The thing that I could not understand is how can I project my IMU readings from the body frame to the navigation frame? The navigation frame is the arbitrary frame that I've chosen and the body frame changes with the orientation of the device. In the papers, they are using the 3D rotation matrix below to project their IMU vectors onto the navigation frame (c and s are cosine and sine functions, and the symbols are Euler angles). Aren't the Euler angles that I am going to get from a 6-axis IMU relative?

3D rotation matrix

  • $\begingroup$ You receive the distance between the device and the TOF anchors and you're using this information to calculate the position of the device. Is my understanding correct? $\endgroup$
    – csg
    Apr 16, 2022 at 0:39
  • $\begingroup$ @csg Yes, you are right. $\endgroup$ Apr 16, 2022 at 6:58
  • $\begingroup$ I suppose your navigation frame is a static frame but your body frame is fixed on the device and it moves with the device. Is this correct? $\endgroup$
    – csg
    Apr 17, 2022 at 1:43
  • $\begingroup$ @csg Yes, exactly like you said. $\endgroup$ Apr 17, 2022 at 7:16


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