On Distributed Linear Estimation With Observation Model Uncertainties

TL;DR

This paper develops distributed linear estimation techniques for Gaussian sources in bandwidth-limited sensor networks with uncertain observation models, deriving MSE expressions and proposing optimal rate allocation strategies.

Contribution

It introduces novel rate allocation methods for minimizing MSE under bandwidth constraints in networks with uncertain observation noise.

Findings

Proposed methods achieve near-CRLB MSE with low noise and sufficient bandwidth.

Derived closed-form MSE expression for LMMSE estimator in the presence of model uncertainties.

Compared performance of different rate allocation strategies, showing advantages of the proposed methods.

Abstract

We consider distributed estimation of a Gaussian source in a heterogenous bandwidth constrained sensor network, where the source is corrupted by independent multiplicative and additive observation noises, with incomplete statistical knowledge of the multiplicative noise. For multi-bit quantizers, we derive the closed-form mean-square-error (MSE) expression for the linear minimum MSE (LMMSE) estimator at the FC. For both error-free and erroneous communication channels, we propose several rate allocation methods named as longest root to leaf path, greedy and integer relaxation to (i) minimize the MSE given a network bandwidth constraint, and (ii) minimize the required network bandwidth given a target MSE. We also derive the Bayesian Cramer-Rao lower bound (CRLB) and compare the MSE performance of our proposed methods against the CRLB. Our results corroborate that, for low power multiplicative observation noises and adequate network bandwidth, the gaps between the MSE of our proposed methods and the CRLB are negligible, while the performance of other methods like individual rate allocation and uniform is not satisfactory.