Sampling and Reconstruction of Spatial Fields using Mobile Sensors

TL;DR

This paper explores how mobile sensors can improve spatial field sampling and reconstruction by reducing aliasing and sensor density requirements, especially for time-invariant and time-varying fields, compared to static sensors.

Contribution

It introduces a novel mobile sensing framework with anti-aliasing filtering, analytically quantifies its advantages over static sampling, and extends the approach to dynamic fields with practical simulation results.

Findings

Mobile sensing with anti-aliasing filters suppresses spatial aliasing effectively.

Using mobile sensors can reduce the required sensor density for accurate field reconstruction.

The approach is effective for both static and time-varying spatial fields, demonstrated through simulations.

Abstract

Spatial sampling is traditionally studied in a static setting where static sensors scattered around space take measurements of the spatial field at their locations. In this paper we study the emerging paradigm of sampling and reconstructing spatial fields using sensors that move through space. We show that mobile sensing offers some unique advantages over static sensing in sensing time-invariant bandlimited spatial fields. Since a moving sensor encounters such a spatial field along its path as a time-domain signal, a time-domain anti-aliasing filter can be employed prior to sampling the signal received at the sensor. Such a filtering procedure, when used by a configuration of sensors moving at constant speeds along equispaced parallel lines, leads to a complete suppression of spatial aliasing in the direction of motion of the sensors. We analytically quantify the advantage of using such a sampling scheme over a static sampling scheme by computing the reduction in sampling noise due to the filter. We also analyze the effects of non-uniform sensor speeds on the reconstruction accuracy. Using simulation examples we demonstrate the advantages of mobile sampling over static sampling in practical problems. We extend our analysis to sampling and reconstruction schemes for monitoring time-varying bandlimited fields using mobile sensors. We demonstrate that in some situations we require a lower density of sensors when using a mobile sensing scheme instead of the conventional static sensing scheme. The exact advantage is quantified for a problem of sampling and reconstructing an audio field.