On Sat, 20 Jun 2009 11:37:27 -0700, Rune Allnor wrote:

> On 20 Jun, 20:14, Tim Wescott <t...@seemywebsite.com> 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 expected value is a 4-vector pointing in some desired direction and
> the PDF represents the probability distribution of actual directions?

Yup. Given a PDF I'd _like_ to be able to solve for the expected value
of the four vector elements, as well as their cross-correlation. I'd
like this to be in a form that's tractable enough that I can code it into
an algorithm without either making people's heads explode when they read
it and without making the processor bog down.

But for now I'll just settle with being able to get the element means and
variances out of the thing for a variety of variances of the Gaussians,
or a clear indication that if I insist on using Gaussians the math is
going to be hopelessly intractable.

--
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