On Tue, 23 Jun 2009 20:45:54 -0500, Michael Plante wrote:

>>On Sat, 20 Jun 2009 11:04:38 -0700, Rune Allnor wrote:
>>
>>> On 20 Jun, 19:50, Tim Wescott <t...@seemywebsite.com> wrote:
>>>
>>>> My choice of oddball integrals was intentional, as I want to go on to
>>>> calculating various moments for the probability distributions of the
>>>> surface of the hypersphere when 3D probability distributions are
> mapped
>>>> onto it. Â*Clearly if I map a tight Gaussian distribution onto the
>>>> hypersphere with a standard deviation that's much smaller than the
>>>> hypersphere radius the resulting probability distribution will be
> easy;
>>>> it's figuring out what happens as that probability distribution opens
>>>> up that's making my brain cramp.
>>>
>>> I'm a bit curious about what kind of problem leads you out in such
> kinds
>>> of calculations?
>>
>>Unscented transformations for quaternion PDFs used to represent angles
>>in
>
>>a (hopefully soon-to-be) unscented Kalman filter. The math needed to
>>represent body rotations is quite hairy; to date unit-length quaternions
>
>>seems to be the best approach, although getting this PDF stuff figured
>>out is proving to be interesting, at best.
>>
>>
> Search for the paper "Unscented Filtering in a Unit Quaternion Space for
> Spacecraft Attitude Estimation" ...it's on IEEE. This problem has been
> attacked before, and that paper seemed to be a good read. I have not
> tried implementing it, but I could probably trudge through it
> eventually.

Well, except for the "spacecraft" part that could just about be the title
of what I'm doing.

That may even be worthwhile to pay for.

--
www.wescottdesign.com