A Large Deviations Result for Aggregation of Independent Noisy Observations

TL;DR

This paper analyzes the tradeoff in sensor networks between sensing quality and aggregation, demonstrating that larger scale aggregation is optimal at high noise levels, while moderate aggregation is better at lower noise levels.

Contribution

It provides a large deviations analysis of optimal aggregation strategies for independent noisy sensors under capacity constraints.

Findings

Larger scale aggregation outperforms smaller scale at high noise levels.

Moderate scale aggregation is optimal below a critical noise threshold.

The results inform sensor network design for different noise regimes.

Abstract

Sensing and aggregation of noisy observations should not be considered as separate issues. The quality of collective estimation involves a difficult tradeoff between sensing quality which increases by increasing the number of sensors, and aggregation quality which typically decreases if the number of sensors is too large. We examine a strategy for optimal aggregation for an ensemble of independent sensors with constrained system capacity. We show that in the large capacity limit larger scale aggregation always outperforms smaller scale aggregation at higher noise levels, while below a critical value of noise, there exist moderate scale aggregation levels at which optimal estimation is realized.