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Distributed Recursive Estimation under Heavy-Tail Communication Noise

Authors:Dusan Jakovetic, Manojlo Vukovic, Dragana Bajovic, Anit Kumar Sahu, Soummya Kar

Distributed Recursive Estimation under Heavy-Tail Communication Noise


We consider distributed recursive estimation of an unknown vector parameter
in the presence of impulsive communication noise. That is, we assume that interagent communication is subject to an additive communication noise that may have heavy-tails or is contaminated with outliers. To combat this effect, within the class of consensus+innovations distributed estimators, we introduce for the first time a nonlinearity in the consensus update. We allow for a general class of nonlinearities that subsumes, e.g., the sign function or componentwise saturation function. For the general nonlinear estimator and a general class of additive communication noises—that may have infinite moments of order higher than one—we establish almost sure convergence to the parameter. We further prove asymptotic normality and evaluate the corresponding asymptotic covariance. These results reveal interesting tradeoffs between the negative effect of “loss of information” due to incorporation of the nonlinearity and the positive effect of communication noise reduction. We also demonstrate and quantify benefits of introducing the nonlinearity in high-noise (low signal-to-noise ratio) and heavy-tail communication noise regimes.

Publication type:

Title of the journal:

SIAM Journal on Control and Optimization.

Year of Publication2023
Number, date or frequency of the Journal:Vol.61 Issue 3

Key Facts

  • Project Coordinator: Dr. Sotiris Ioannidis
  • Institution: Foundation for Research and Technology Hellas (FORTH)
  • E-mail: 
  • Start: 01.01.2021
  • Duration: 36 months
  • Participating Organisations: 17
  • Number of countries: 12

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This project has received funding from the European Union’s Horizon 2020 Research and Innovation program under grant agreement No 957337. The website reflects only the view of the author(s) and the Commission is not responsible for any use that may be made of the information it contains.