Chair for Computer Aided Medical Procedures & Augmented Reality
Lehrstuhl für Informatikanwendungen in der Medizin & Augmented Reality

Kalman Filtering for Quaternions

How do we represent motion (angular velocities) of quaternions in our state vector?

How does a Quaternion with only 5DOF look like in 3D? Whats the "closest" Quaternion from that set of quaternions to a given quaternion?

  • this is something like the projection of the estimated quaternion to the subspace of the measured set of quaternions.
  • note that we do have only unit quaternions

How do we get from Euler angles to Quaternions?

  • the required formula can be found in Paul Heckbert (editor), Graphic Gems IV, Academic Press, 1994, ISBN: 0123361559
  • this of course depend heavily on the order of rotations
    • Q: how is the order of rotation in the trackers we use?

How does Error Propagation in Quaternions work? How do we compute the covariances?

  • Daniel Choukroun, Novel Methods for Attitude Determination Uisng Vector Observations, Ph.D. Thesis, 2003, Aerospace Engineering, Technion has a lot of stuff, including error covariance matrix of the queternion estimation error.
    • cites results from M.D. Shuster, S.D. Oh., Three Axis Attitude Determination From Vector Observations. Journal of Guidance, Control and Navigation, 4(1):70--77, January-February 1981.

Other Literature

Edit | Attach | Refresh | Diffs | More | Revision r1.5 - 23 Mar 2005 - 12:32 - NikolasDoerfler

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