On Distributed Linear Estimation With Observation Model Uncertainties

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.

References in corpus (4)

• Optimal Identical Binary Quantizer Design for Distributed Estimation
• On Distributed Vector Estimation for Power and Bandwidth Constrained Wireless Sensor Networks
• On Quantizer Design for Distributed Bayesian Estimation in Sensor Networks
• Maximum Likelihood Estimation from Sign Measurements with Sensing Matrix Perturbation

Cited by in corpus (1)

• A Joint Model and Data Driven Method for Distributed Estimation