>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 ar
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 b
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 suc
kinds
>> of calculations?
>
>Unscented transformations for quaternion PDFs used to represent angles i

>a (hopefully soon-to-be) unscented Kalman filter. The math needed to
>represent body rotations is quite hairy; to date unit-length quaternion

>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 fo
Spacecraft Attitude Estimation" ...it's on IEEE. This problem has bee
attacked before, and that paper seemed to be a good read. I have not trie
implementing it, but I could probably trudge through it eventually.