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On Bandlimited Field Estimation from Samples Recorded by a Location-Unaware Mobile Sensor

机译：基于位置未知移动传感器记录的样本的带域有限域估计

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摘要

Sampling of physical fields with mobile sensor is an emerging area. In this context, this work introduces and addresses some aspects of a fundamental question: can a spatial field be estimated from samples taken at unknown sampling locations? In a field (signal) sampling setup, unknown sampling locations, sample quantization, unknown bandwidth of the field, and presence of measurement-noise present difficulties in the process of field estimation. In this work, except for quantization, the other three issues will be tackled together in a mobile-sampling framework. Spatially bandlimited fields are considered. It is assumed that measurement-noise affected field samples are collected on spatial locations obtained from an unknown renewal process. That is, the samples are obtained on locations obtained from a renewal process, but the sampling locations and the renewal process distribution are unknown. In this challenging unknown sampling location setup, it is shown that the mean-squared error in field estimation decreases as O(1) where n is the average number of samples collected by the mobile sensor. The average number of samples collected is determined by the inter-sample spacing distribution in the renewal process. An algorithm to ascertain spatial field's bandwidth is detailed, which works with high probability as the average number of samples n increases. This algorithm works in the same setup, i.e., in the presence of measurement-noise and unknown sampling locations.
机译：移动传感器对物理场的采样是一个新兴领域。在这种情况下，这项工作引入并解决了一个基本问题的某些方面：能否从未知采样位置采集的样本估算空间场？在现场（信号）采样设置中，未知的采样位置，样本量化，未知的现场带宽以及测量噪声的存在在现场估计过程中都带来了困难。在这项工作中，除了量化之外，其他三个问题将在移动采样框架中一起解决。考虑空间上受限的字段。假定在从未知更新过程获得的空间位置上收集了受测量噪声影响的现场样本。即，在从更新过程获得的位置上获取样本，但是采样位置和更新过程分布是未知的。在这种具有挑战性的未知采样位置设置中，显示出场估计中的均方误差降低为O（1 / n），其中n是移动传感器收集的样本的平均数量。收集的样本的平均数量由更新过程中的样本间间隔分布确定。详细介绍了一种确定空间场带宽的算法，随着平均样本数n的增加，该算法很有可能起作用。该算法以相同的设置工作，即在存在测量噪声和未知采样位置的情况下。

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