未知環境におけるエコーを用いた経路追跡：対称性の問題とその打破
Path Tracking using Echoes in an Unknown Environment: the Issue of Symmetries and How to Break Them
未知の平面構造環境で音響エコーから車両経路を再構成する際、環境の対称性による解の曖昧さを、スピーカーを車両ではなく環境の固定位置に置くことで解消できることを数学的に示し、3次元以上では常に、2次元では稀な例外を除き可能であることを証明した。
著者: Mireille Boutin, Gregor Kemper
分類: math.MG, cs.RO
原文アブストラクト
This paper deals with the problem of reconstructing the path of a vehicle in an unknown environment consisting of planar structures using sound. Many systems in the literature do this by using a loudspeaker and microphones mounted on a vehicle. Symmetries in the environment lead to solution ambiguities for such systems. We propose to resolve this issue by placing the loudspeaker at a fixed location in the environment rather than on the vehicle. The question of whether this will remove ambiguities regardless of the environment geometry leads to a question about breaking symmetries that can be phrased in purely mathematical terms. We solve this question in the affirmative if the geometry is in dimension three or bigger, and give counterexamples in dimension two. Excluding the rare situations where the counterexamples arise, we also give an affirmative answer in dimension two. Our results lead to a simple path reconstruction algorithm for a vehicle carrying four microphones navigating within an environment in which a loudspeaker at a fixed position emits short bursts of sounds. This algorithm could be combined with other methods from the literature to construct a path tracking system for vehicles navigating within a potentially symmetric environment.