On the Effect of Correlated Measurements on the Performance of Distributed Estimation

TL;DR

This paper investigates how spatial correlation among sensor observations affects the accuracy of distributed estimation in wireless sensor networks, deriving formulas for outage probability and demonstrating the impact of correlation on estimation performance.

Contribution

It introduces a model for correlated sensor observations with distance-dependent correlation and provides a closed-form expression for outage probability considering these correlations.

Findings

Correlation reduces estimation error compared to uncorrelated observations.

Distance-based correlation significantly impacts outage probability.

Analytic results are validated through numerical simulations.

Abstract

We address the distributed estimation of an unknown scalar parameter in Wireless Sensor Networks (WSNs). Sensor nodes transmit their noisy observations over multiple access channel to a Fusion Center (FC) that reconstructs the source parameter. The received signal is corrupted by noise and channel fading, so that the FC objective is to minimize the Mean-Square Error (MSE) of the estimate. In this paper, we assume sensor node observations to be correlated with the source signal and correlated with each other as well. The correlation coefficient between two observations is exponentially decaying with the distance separation. The effect of the distance-based correlation on the estimation quality is demonstrated and compared with the case of unity correlated observations. Moreover, a closed-form expression for the outage probability is derived and its dependency on the correlation coefficients is investigated. Numerical simulations are provided to verify our analytic results.