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Localizing Multiple Events Using Times of Arrival: a Parallelized, Hierarchical Approach to the Association Problem

机译:使用到达时间本地化多个事件:关联问题的并行,分层方法

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A fundamental problem in localizing multiple events based on Times of Arrival (ToAs) at a number of sensors is that of associating ToAs with events. We consider this problem in the context of acoustic sensors monitoring events that are closely spaced in time. Due to the relatively low speed of propagation of sound, the order in which the events arrive at a sensor need not be the same as the order in which they occur, potentially creating fundamental ambiguities. We first explore such ambiguities in an idealized setting with two events and noiseless observations, showing that it is possible to localize both events with nine or more sensors (as long as degenerate sensor placement is avoided), but that we can construct examples with six sensors for which unambiguous space-time localization is not possible. We then show that these potential ambiguities are not a bottleneck in typical practical settings, proposing and evaluating an algorithm that successfully localizes multiple events using noisy observations. The algorithm employs parallelism and hierarchical processing to avoid the excessive complexity of naïvely trying all possible associations of events with ToAs. We use discretization of hypothesized event times to enable us to efficiently generate a set of candidate event locations, which contain noisy versions of true events as well as phantom events. We refine these estimates iteratively, discarding “obvious” phantoms, and then solve a linear programming formulation for matching true events to ToAs, while identifying outliers and misses. Simulation results indicate excellent performance that is comparable to a genie-based algorithm which is given the correct association between ToAs and events.
机译:基于到达时间(ToA)在多个传感器上定位多个事件的基本问题是将ToAs与事件相关联的问题。我们在声音传感器监视时间间隔紧密的事件的背景下考虑此问题。由于声音传播的速度相对较低,因此事件到达传感器的顺序不必与事件发生的顺序相同,从而可能产生根本的歧义。我们首先在具有两个事件和无噪声观测值的理想环境中探索此类歧义,表明可以使用九个或更多传感器定位两个事件(只要避免退化传感器放置),但是我们可以使用六个传感器构造示例为此,不可能进行明确的时空定位。然后,我们证明这些潜在的歧义在典型的实际环境中不是瓶颈,提出并评估了一种使用嘈杂的观测值成功定位多个事件的算法。该算法采用并行和分层处理,以避免过分幼稚地尝试将所有可能的事件与ToA关联的过于复杂。我们使用假设事件时间的离散化来使我们能够高效地生成一组候选事件位置,其中包含真实事件以及幻像事件的嘈杂版本。我们迭代地完善这些估计,丢弃“明显”的模型,然后求解线性规划公式,以将真实事件与ToA匹配,同时识别异常值和遗漏值。仿真结果表明,出色的性能可与基于Genie的算法相媲美,后者基于ToAs与事件之间具有正确的关联。

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