Interesting paper in PNAS, from July. I believe it is open access, so
anyone can read/download.   Aaron

http://www.pnas.org/content/110/30/12186.short

The supplemental information (SI) shows some of the equipment and more math.

I. Dokmanić, R. Parhizkar, A. Walther, Y. M. Lu, and M. Vetterli, “Acoustic
echoes reveal room shape,” Proceedings of the National Academy of Sciences,
vol. 101, no. 30, pp. 12186–12191, Jul. 2013.


Abstract

Imagine that you are blindfolded inside an unknown room. You snap your
fingers and listen to the room’s response. Can you hear the shape of the
room? Some people can do it naturally, but can we design computer
algorithms that hear rooms? We show how to compute the shape of a convex
polyhedral room from its response to a known sound, recorded by a few
microphones. Geometric relationships between the arrival times of echoes
enable us to “blindfoldedly” estimate the room geometry. This is achieved
by exploiting the properties of Euclidean distance matrices. Furthermore,
we show that under mild conditions, first-order echoes provide a unique
description of convex polyhedral rooms. Our algorithm starts from the
recorded impulse responses and proceeds by learning the correct assignment
of echoes to walls. In contrast to earlier methods, the proposed algorithm
reconstructs the full 3D geometry of the room from a single sound emission,
and with an arbitrary geometry of the microphone array. As long as the
microphones can hear the echoes, we can position them as we want. Besides
answering a basic question about the inverse problem of room acoustics, our
results find applications in areas such as architectural acoustics, indoor
localization, virtual reality, and audio forensics.
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