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Title: Can a ground‐based vehicle hear the shape of a room?
Abstract Assume that a ground‐based vehicle moves in a room with walls or other planar surfaces. Can the vehicle reconstruct the positions of the walls from the echoes of a single sound event? We assume that the vehicle carries some microphones and that a loudspeaker is either also mounted on the vehicle or placed at a fixed location in the room. We prove that the reconstruction is almost always possible if (1) no echoes are received from floors, ceilings, or sloping walls and the vehicle carries at least three noncollinear microphones, or if (2) walls of any inclination may occur, the loudspeaker is fixed in the room and there are four noncoplanar microphones. The difficulty lies in the echo‐matching problem: How to determine which echoes come from the same wall. We solve this by using a Cayley–Menger determinant. Our proofs use methods from computational commutative algebra.  more » « less
Award ID(s):
1928930
PAR ID:
10529671
Author(s) / Creator(s):
;
Publisher / Repository:
Wiley
Date Published:
Journal Name:
Studies in Applied Mathematics
Volume:
151
Issue:
1
ISSN:
0022-2526
Page Range / eLocation ID:
352 to 368
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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