mean.Q4: Mean Rotation
In heike/rotations: Tools for working with rotational data

Description Usage Arguments Details Value References See Also Examples

Compute the projected or geometric mean of a sample of rotations

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  ## S3 method for class 'Q4'
 mean(Qs, type = "projected",
    epsilon = 1e-05, maxIter = 2000)

`Qs`	A n-by-4 matrix where each row corresponds to a random rotation in unit quaternion
`type`	String indicating 'projeted' or 'geometric' type mean estimator
`epsilon`	Stopping rule for the geometric method
`maxIter`	The maximum number of iterations allowed before returning most recent estimate

This function takes a sample of n unit quaternions and approximates the mean rotation. If the projected mean is called for then the according to Tyler (1981) an estimate of the mean is the eigenvector corresponding to the largest eigen value of Q`Q/n. If the geometric mean is called then the quaternions are transformed into 3-by-3 matrices and the mean.SO3 function is called.

projected or geometric mean of the sample

Manton J (2004). "A globally convergent numerical algorithm for computing the centre of mass on compact Lie groups." In _8th Conference on Control, Automation, Robotics and Vision, (ICARCV) _, volume 3, pp. 2211-2216. IEEE.

Moakher M (2002). "Means and averaging in the group of rotations." _SIAM Journal on Matrix Analysis and Applications_, *24*(1), pp. 1-16.

Tyler DE (1981). "Asymptotic inference for eigenvectors." _The Annals of Statistics_, pp. 725-736.

mean.SO3