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Abstract: The paper considers gossip distributed estimation of a static distributedrandom field a.k.a., large scale unknown parameter vector observed bysparsely interconnected sensors, each of which only observes a small fractionof the field. We consider linear distributed estimators whose structurecombines the information \emph{flow} among sensors the \emph{consensus} termresulting from the local gossiping exchange among sensors when they are able tocommunicate and the information \emph{gathering} measured by the sensors the\emph{sensing} or \emph{innovations} term. This leads to mixed time scalealgorithms-one time scale associated with the consensus and the other with theinnovations. The paper establishes a distributed observability conditionglobal observability plus mean connectedness under which the distributedestimates are consistent and asymptotically normal. We introduce thedistributed notion equivalent to the centralized Fisher information rate,which is a bound on the mean square error reduction rate of any distributedestimator; we show that under the appropriate modeling and structural networkcommunication conditions gossip protocol the distributed gossip estimatorattains this distributed Fisher information rate, asymptotically achieving theperformance of the optimal centralized estimator. Finally, we study thebehavior of the distributed gossip estimator when the measurements fade noisevariance grows with time; in particular, we consider the maximum rate at whichthe noise variance can grow and still the distributed estimator beingconsistent, by showing that, as long as the centralized estimator isconsistent, the distributed estimator remains consistent.



Autor: Soummya Kar, Jose' M.F. Moura

Fuente: https://arxiv.org/







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