On Learning the Distribution of a Random Spatial Field in a Location-Unaware Mobile Sensing Setup

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.