TY - JOUR

T1 - Information Flow Optimization for Estimation in Linear Models Using a Sensor Network

AU - Deshmukh, Aditya

AU - Liu, Jing

AU - Veeravalli, Venugopal V.

AU - Verma, Gunjan

N1 - Funding Information:
This work was supported by the U.S. Army Research Laboratory, University of Illinois at Urbana-Champaign through Cooperative Agreement under Grant W911NF-17-2-0196.
Publisher Copyright:
© 1994-2012 IEEE.

PY - 2023

Y1 - 2023

N2 - The problem considered is one of maximizing the information flow through a sensor network tasked with estimating, at a fusion center, an underlying parameter in a linear observation model. The sensor nodes take observations, quantize them, and send them to the fusion center through a network of relay nodes. The links in the network are assumed to satisfy certain capacity constraints in terms of the maximum number of bits that can be transmitted on the links. Furthermore, the relay nodes are assumed to satisfy flow conservation constraints, i.e., the number of bits flowing into a relay node is equal to the number of bits flowing out of it. It is shown that this flow optimization problem for estimation can be cast as a Network Utility Maximization (NUM) problem by suitably defining the utility functions at the sensors. The inference problem considered is one of parameter estimation with a linear observation model, which is studied in both Bayesian and non-Bayesian settings. Upper bounds on the mean-squared error (MSE) of optimal linear estimators are obtained in both settings, and these bounds are used to construct utility functions for the corresponding NUM problems. It is verified via simulations that the bit assignments at the sensors obtained through the solutions to the NUM problems, in both the Bayesian and non-Bayesian settings, yield considerably better estimation performance than the Max-Flow solution that simply assigns bits to the sensors in such a way as to maximize the total bits transmitted to the fusion center.

AB - The problem considered is one of maximizing the information flow through a sensor network tasked with estimating, at a fusion center, an underlying parameter in a linear observation model. The sensor nodes take observations, quantize them, and send them to the fusion center through a network of relay nodes. The links in the network are assumed to satisfy certain capacity constraints in terms of the maximum number of bits that can be transmitted on the links. Furthermore, the relay nodes are assumed to satisfy flow conservation constraints, i.e., the number of bits flowing into a relay node is equal to the number of bits flowing out of it. It is shown that this flow optimization problem for estimation can be cast as a Network Utility Maximization (NUM) problem by suitably defining the utility functions at the sensors. The inference problem considered is one of parameter estimation with a linear observation model, which is studied in both Bayesian and non-Bayesian settings. Upper bounds on the mean-squared error (MSE) of optimal linear estimators are obtained in both settings, and these bounds are used to construct utility functions for the corresponding NUM problems. It is verified via simulations that the bit assignments at the sensors obtained through the solutions to the NUM problems, in both the Bayesian and non-Bayesian settings, yield considerably better estimation performance than the Max-Flow solution that simply assigns bits to the sensors in such a way as to maximize the total bits transmitted to the fusion center.

KW - Flow optimization

KW - Internet of Things

KW - sensor networks

KW - statistical inference

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U2 - 10.1109/LSP.2023.3245540

DO - 10.1109/LSP.2023.3245540

M3 - Article

AN - SCOPUS:85149413408

SN - 1070-9908

VL - 30

SP - 170

EP - 174

JO - IEEE Signal Processing Letters

JF - IEEE Signal Processing Letters

ER -