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Re: Averaging quaternions [message #38629 is a reply to message #38628]

Fri, 19 March 2004 06:53

John Lansberry
Messages: 3
Registered: March 2004

Junior Member

"Craig Markwardt" <craigmnet@REMOVEcow.physics.wisc.edu> wrote in message
news:on65d167y8.fsf@cow.physics.wisc.edu...
>
> GrahamWilsonCA@yahoo.ca (Graham) writes:
>
>> Does anyone know if it is possible to take an average of regularly
>> sampled quaternions to get a mean orientation (i.e. a mean rotation
>> matrix)? I seem to recall there being a trick involved but beyond
>> re-normalizing the resuling (averaged) quaternion, I cannot remember
>> what it is.
>
> I am sure I will be scolded by somebody, but I believe that you can
> average the quaternion components, and then normalize as you say.
> This is assumes that you are noise dominated.
>
Averaging components is a bad idea no matter what, since the result is never
a "quaternion." The OP doesn't imply anything about "noise."

> Also, there is one trick that I can think of, which is that
> quaternions are degenerate. For each unique rotation, there are two
> possible quaternions whose components have opposite signs. This is
> because a positive rotation about axis V is identical to a negative
> rotation about axis -V.
>
> If your system is capable of both signs indiscriminately, then you
> must make the sign conventions uniform. For example, by always making
> one component positive.

You are correct that q and -q represent the same rotation - that's not
"degenerate", it's just not "unique." Typically, the "scalar" part of the
quaternion, cos(theta/2), is chosen to be the component that's always
positive.

John

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[Message index]

		Re: Averaging quaternions By: Arnold Neumaier on Fri, 19 March 2004 08:24
		Re: Averaging quaternions By: John Lansberry on Fri, 19 March 2004 07:22
		Re: Averaging quaternions By: John Lansberry on Fri, 19 March 2004 07:14
		Re: Averaging quaternions By: John Lansberry on Fri, 19 March 2004 06:53
		Re: Averaging quaternions By: One Usenet Poster on Thu, 18 March 2004 20:17
		Re: Averaging quaternions By: Craig Markwardt on Thu, 18 March 2004 15:39
		Re: Averaging quaternions By: GrahamWilsonCA on Mon, 29 March 2004 12:45

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