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.

--
http://www.wescottdesign.com