efficacy of $\mathcal{CIRFE}$.'
author:
- 'Anit Kumar Sahu, , Dusan Jakovetic,  and Soummya Kar,  [^1]'
bibliography:
- 'CentralBib.bib'
- 'dsprt.bib'
- 'glrt.bib'
title: '$\mathcal{CIRFE}$: A Distributed Random Fields Estimator'
---

Distributed Estimation, Consensus Algorithms, Distributed Inference, Random Fields, Stochastic Approximation

INTRODUCTION
============

In this paper, we are interested in distributed inference of the parameterized state of the large-scale cyber physical systems (CPS) like sensor networks monitoring a spatially distributed field, or CPSs where physical entities with sensing capabilities are deployed over large areas. Relevant applications include, minimum cost flow problems (see, for example [@ahuja1988network]), distributed model predictive control (see, for example [@mota2015distributed; @halvgaard2016distributed]), distributed localization (see, for example [@Khan-DILAND-TSP-2010]). An important example of the systems of interest is the smart grid–a large network of generators and loads instrumented with, for example, phasor measurement units (PMUs)[@kekatos2013distributed; @de2010synchronized]. Our goal is to reconstruct the physical field or state of the CPS that is represented by a vector parameter. The structure of the physical layer is reflected through the coupling among the observation sequences across different nodes. Suppose, for the purpose of illustration, corresponding to each field location, there is a low-power inexpensive sensor monitoring the location. The noisy sensor measurement at a 