论文标题
地面车辆可以听到房间的形状吗？
Can a Ground-Based Vehicle Hear the Shape of a Room?
论文作者
论文摘要
假设地面车辆在带墙壁或其他平面表面的房间内移动。车辆可以通过单个声音事件的回声重建墙壁的位置吗？我们假设车辆带有一些麦克风，并且扬声器也安装在车辆上，或者放置在房间的固定位置。我们证明，如果（1）没有从地板，天花板或倾斜墙收到回声，并且车辆至少携带三个非电击麦克风，或者如果（2）任何倾斜的壁可能出现，则扬声器固定在房间中并且有四个非电源型麦克风。 困难在于回声匹配问题：如何确定哪些回声来自同一墙。我们通过使用Cayley-Menger的决定因素来解决此问题。我们的证明使用计算交换代数中的方法。
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 non-collinear microphones, or if (2) walls of any inclination may occur, the loudspeaker is fixed in the room and there are four non-coplanar 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.
