weighted.mean.SO3: Weighted Mean Rotation

In heike/rotations: Tools for working with rotational data

Description

Compute the weighted geometric or projected mean of a sample of rotations

Usage

  ## S3 method for class 'SO3'
 weighted.mean(Rs, w, type = "projected",
    epsilon = 1e-05, maxIter = 2000, ...)

Arguments

Rs	A n-by-9 matrix where each row corresponds to a random rotation in matrix form
w	a numerical vector of weights the same length as the number of rows in Rs giving the weights to use for elements of Rs
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
...	only used for consistency with mean.default

Details

This function takes a sample of 3-by-3 rotations (in the form of a n-by-9 matrix where n>1 is the sample size) and returns the weighted projected arithmetic mean denoted S_P or geometric mean S_G according to the type option. For a sample of n random rotations Ri in SO(3), i=1,2,…,n, the mean-type estimator is defined as

argmin d(bar(R),S)

where bar(R)=∑ R_i/n and the distance metric d is the Riemannian or Euclidean. For more on the projected mean see Moakher (2002) and for the geometric mean see Manton (2004).

Value

weighted projected mean of the sample

References

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.

See Also

median.SO3 mean.SO3

Examples

Rs<-ruars(20,rvmises,kappa=0.01)
wt<-abs(1/angle(Rs))
weighted.mean(Rs,wt)

heike/rotations documentation built on May 17, 2019, 3:24 p.m.