[uf-new] Microformat for expressing uncertainty?

[Charlie]

I have some information I'd like to serve via a RESTful web service, and
after a bunch of reading I think it would be really cool to make a
machine-readable web service and a human-readable web site that are one and
the same, using XHTML + Microformats.

Not surprisingly, there does not appear to be a microformat that fully
captures the information I want to serve. hAtom might be usable for the
timestamped-item nature of it (I haven't looked it over yet) and geo is a
start, but I will have to build upon geo.

I could go and write my own, and describe it using XMDP. In fact, I probably
will.

But before going off and doing that, I wanted to share my need with the
microformats community and ask if anyone else has needs along these lines.
If there is interest, maybe we could design a new microformat. If not, maybe
somebody can at least help or give advice?

Essentially, I want to publish geographic point locations that have
associated uncertainty information. geo has no notion of uncertainty. It
doesn't even have altitude, but I noticed there is a proposed extension to
add altitude, so maybe I can use that.

There are, of course, many ways one might wish to express uncertainty. You
could attach an "uncertainty" property to the latitude value and another to
the longitude value, to represent absolute floor and ceiling values. Or you
could attach a specific "floor" and "ceiling" property to each. Or you could
attach similar values to define a 1-sigma probability region.

So far, that makes for a pretty simple idea for a microformat - adding
uncertainty to any kind of numerical value. Unfortunately, my needs are a
little more complex than that.

For a geospatial point (lat, lon, alt), I want to define an uncertainty
region. This means I can't treat each numerical value separately. What I
actually have for each point is a covariance matrix - a 3x3 symmetric matrix
(it has 6 unique values, but is commonly displayed as a 3x3 square with nine
elements).

The eigenvectors of this matrix give the axes of an ellipsoid in space, and
the eigenvalues give unit lengths for their respective eigenvectors. The
one-sigma probability region for a point is centered at the latitude,
longitude and altitude given for that point, with the orientations of the
axes given by the eigenvectors and the half-axis-lengths given by the
eigenvalues. Also, given the covariance matrix, a user can construct a
probability region to any sigma (or % confidence, to put it another way) by
choosing a scaling factor to apply to the eigenvalues.

So in other words, we're talking about uncertainty in more than one
dimension, as expressed by a covariance matrix.

Does anyone know of work along these lines in the microformats world? Would
it be better to try to generalize this concept to apply uncertainty to a
range of other microformats? Or would it be better to stick to the case of
geographic locations?

In the geographic case, I've figured out how to construct KML that draws the
error region I described above in Google Earth as a translucent bubble, so
that is already one cool application of it.

Thanks for reading. I would love to hear people's thoughts on how to design
such a format!

Charlie
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