In applications like environment monitoring and pollution control, physical quantities are modeled by spatio-temporal fields. It is of interest to learn the statistical distribution of such fields as a function of space, time or both. In this work, our aim is to learn the statistical distribution of a spatio-temporal field along a fixed one dimensional path, as a function of spatial location, in the absence of location information. Spatial field analysis, commonly done using static sensor networks is a well studied problem in literature. Recently, due to flexibility in setting the spatial sampling density and low hardware cost, owing to larger spatial coverage, mobile sensors are used for this purpose. The main challenge in using mobile sensors is their location uncertainty. Obtaining location information of samples requires additional hardware and cost. So, we consider the case when the spatio-temporal field along the fixed length path is sampled using a simple mobile sensing device that records field values while traversing the path without any location information. We ask whether it is possible to learn the statistical distribution of the field, as a function of spatial location, using samples from the location-unaware mobile sensor under some simple assumptions on the field. We answer this question in affirmative and provide a series of analytical and experimental results to support our claim.

翻译：在环境监测和污染控制等应用中，物理量通常由时空场建模。学习此类场随空间、时间或两者变化的统计分布具有重要意义。本文旨在无位置信息条件下，沿固定一维路径学习时空场随空间位置变化的统计分布。基于静态传感器网络的空间场分析是文献中研究充分的问题。近年来，由于移动传感器在空间采样密度设置上具有灵活性、硬件成本较低且覆盖范围更广，已被用于此目的。使用移动传感器的主要挑战在于其位置不确定性。获取样本位置信息需要额外的硬件和成本。因此，我们考虑以下场景：使用简单移动传感设备沿固定长度路径采样时空场，该设备在行进过程中仅记录场值而不采集位置信息。我们提出一个问题：在基于场的若干简单假设下，能否通过无位置感知移动传感器采集的样本学习到场随空间位置变化的统计分布？我们对这一问题给出肯定回答，并提供一系列分析与实验结果以支持该结论。