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tolgabirdal/averaging_quaternions

  • [Qavg]=avg_quaternion_mar...
    by Tolga Birdal
  • [Qavg]=wavg_quaternion_ma...
    by Tolga Birdal
  • test_avg_quat.m
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5.0 | 2 ratings Rate this file 13 Downloads (last 30 days) File Size: 1.33 KB File ID: #40098

tolgabirdal/averaging_quaternions

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30 Jan 2013 (Updated )

This function computes the average (mean) quaternion.

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Description

Since quaternions are not regular vectors, but rather representations of orientation, an average quaternion cannot just be obtained by taking a weighted mean. This function implements the work done by F. Landis Merkley to calculate the average quaternion. The algorithm is explained by F. Landis Markley at:
http://www.acsu.buffalo.edu/~johnc/ave_quat07.pdf
For this particular implementation, I would also like to reference Mandar Harshe:
http://www-sop.inria.fr/members/Mandar.Harshe/knee-joint/html/index.html
While being basic and straightforward, this algorithm is compared with rotqrmean from VoiceBox and found to produce quite similar results, yet it is more elegant, much simpler to implement and follow. (Though, there might be difference in signs)

Required Products MATLAB
MATLAB release MATLAB 7.9 (R2009b)
MATLAB Search Path
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Comments and Ratings (3)
02 Jun 2014 Mosong Cheng  
30 Jan 2014 sathish  
30 Sep 2013 Tolga Birdal

Note that on 2001 Claus Gramkow showed that the naive mean is in fact a fair approximation of rotations:
http://www.soest.hawaii.edu/wessel/courses/gg711/pdf/Gramkow_2001_JMIV.pdf

I think re-orthagonalization using SVD after a standard averaging would suffice most applications.

Updates
29 Oct 2014

Weighted average added.
Test function added.

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