50.4.1 Additive quaternion filtering

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Parents: Quaternion index ,  which orientation parametrisation to-choose?

Source: Markley 2014

Additive quaternion filtering

Additive quaternion error unknown_filename.2.png

Methods of enforcing the normalisation

  1. Renormalise the estimate by brute force unknown_filename.1.png

  2. Modify KF update equations to enforce a norm constraint using a Lagrange multiplier

[1] and [2] yield biased estimates of the quaternion

Methods that don’t enforce normalisation

  1. Define the rotation matrix to be unknown_filename.png
    • guarantees orthogonality
    • introduces unobservable DOF: the quaternion norm
  2. Use the above equation without the ||q||-2 factor –> no orthogonality