Performance of Linear Field Reconstruction Techniques with Noise and Uncertain Sensor Locations

TL;DR

This paper analyzes the performance of linear field reconstruction methods in noisy, uncertain sensor networks, providing analytical and asymptotic error expressions, and offering design guidelines for sensor deployment.

Contribution

It derives analytical and asymptotic mean square error expressions for various linear reconstruction techniques under noise and sensor uncertainty, guiding sensor network design.

Findings

Asymptotic MSE expressions match simulations for small sensor counts

Guidelines for sensor network design considering multiple parameters

Validation of asymptotic analysis through numerical simulations

Abstract

We consider a wireless sensor network, sampling a bandlimited field, described by a limited number of harmonics. Sensor nodes are irregularly deployed over the area of interest or subject to random motion; in addition sensors measurements are affected by noise. Our goal is to obtain a high quality reconstruction of the field, with the mean square error (MSE) of the estimate as performance metric. In particular, we analytically derive the performance of several reconstruction/estimation techniques based on linear filtering. For each technique, we obtain the MSE, as well as its asymptotic expression in the case where the field number of harmonics and the number of sensors grow to infinity, while their ratio is kept constant. Through numerical simulations, we show the validity of the asymptotic analysis, even for a small number of sensors. We provide some novel guidelines for the design of sensor networks when many parameters, such as field bandwidth, number of sensors, reconstruction quality, sensor motion characteristics, and noise level of the measures, have to be traded off.