I am working on a calibration algorithm where the motion is related to the observability of the parameters that I am calibrating.

Let's say we have a 6 dof trajectory and wants to quantify its motion to see how dynamically it has moved. (e.g, to see if it is covering a wide angle in rpy space.)

For example to quantify the SO(3) we can convert it into so(3) then apply PCA to decompose its covariance to see the scatterness along the principal axises. A widely spread motion will give more observability on the parameter calibration.

Is there any reference paper or document for this problem?

  • $\begingroup$ A 6dof motion trajectory is equal to an air vehicle. It can have a point in the 3d space and can rotate against each axis. For describing such motion a so called notation is useful. In case of flight maneuvers the Aresti Catalog is a well known example. $\endgroup$ – Manuel Rodriguez Feb 19 at 15:18
  • $\begingroup$ And we are preferring answers which can say something about quantifying motion trajectory for robotics applications. According to the amount of literature the topic is interesting and it make sense to go into the details. $\endgroup$ – Manuel Rodriguez Feb 21 at 9:40
  • $\begingroup$ added a bit more details. $\endgroup$ – C.O Park Feb 22 at 1:17

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