论文标题
与发射时间未知的多材料和信号匹配
Multilateration and Signal Matching with Unknown Emission Times
论文作者
论文摘要
假设一个源在未知时间以$ 3 $维的空间中发出信号，至少〜$ 5 $传感器收到。在几乎所有情况下，发射时间和源位置都可以从传感器接收信号的时代的知识中唯一地解决。这样做的任务是多材料问题。但是，当有几个源自多个来源的排放事件时，必须首先匹配接收的信号以找到排放时间和源位置。在本文中，我们建议在接收时间之间使用代数关系以实现这种匹配。当信号实际上是从单个排放事件中回声时，就会发生特殊情况。在这种情况下，解决信号匹配问题允许人们重建反射壁的位置。我们表明，无论墙壁的位置如何，我们的匹配算法几乎适用于传感器的所有位置。 在本文的第一部分中，我们考虑了多层问题，该问题等同于GPS问题，并提供了适用于所有维度的简单代数解决方案。
Assume that a source emits a signal in $3$-dimensional space at an unknown time, which is received by at least~$5$ sensors. In almost all cases the emission time and source position can be worked out uniquely from the knowledge of the times when the sensors receive the signal. The task to do so is the multilateration problem. But when there are several emission events originating from several sources, the received signals must first be matched in order to find the emission times and source positions. In this paper, we propose to use algebraic relations between reception times to achieve this matching. A special case occurs when the signals are actually echoes from a single emission event. In this case, solving the signal matching problem allows one to reconstruct the positions of the reflecting walls. We show that, no matter where the walls are situated, our matching algorithm works correctly for almost all positions of the sensors. In the first section of this paper we consider the multilateration problem, which is equivalent to the GPS-problem, and give a simple algebraic solution that applies in all dimensions.
