Robust distributed estimation using the embedded subgraphs algorithm

Véronique Delouille, Ramesh Neelamani, Richard G. Baraniuk

Research output: Contribution to journalArticlepeer-review

50 Scopus citations


We propose a new iterative, distributed approach for linear minimum mean-square-error (LMMSE) estimation in graphical models with cycles. The embedded subgraphs algorithm (ESA) decomposes a loopy graphical model into a number of linked embedded subgraphs and applies the classical parallel block Jacobi iteration comprising local LMMSE estimation in each subgraph (involving inversion of a small matrix) followed by an information exchange between neighboring nodes and subgraphs. Our primary application is sensor networks, where the model encodes the correlation structure of the sensor measurements, which are assumed to be Gaussian. The resulting LMMSE estimation problem involves a large matrix inverse, which must be solved in-network with distributed computation and minimal intersensor communication. By invoking the theory of asynchronous iterations, we prove that ESA is robust to temporary communication faults such as failing links and sleeping nodes, and enjoys guaranteed convergence under relatively mild conditions. Simulation studies demonstrate that ESA compares favorably with other recently proposed algorithms for distributed estimation. Simulations also indicate that energy consumption for iterative estimation increases substantially as more links fail or nodes sleep. Thus, somewhat surprisingly, sensor network energy conservation strategies such as low-powered transmission and aggressive sleep schedules could actually prove counterproductive. Our results can be replicated using MATLAB code from

Original languageEnglish (US)
Pages (from-to)2998-3010
Number of pages13
JournalIEEE Transactions on Signal Processing
Issue number8
StatePublished - Aug 2006


  • Asynchronous iterations
  • Distributed estimation
  • Graphical models
  • Matrix splitting
  • Sensor networks
  • Wiener filter

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing


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