Distributed nonlinear filtering of partially observed Markov chains over WSNs: Truncating the ADMM

Dionysios S. Kalogerias, Athina P. Petropulu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

In this work, we study stability of distributed non-linear filtering of Markov chains with finite state space, partially observed in conditionally Gaussian noise. We propose a filtering scheme, which relies on the distributed evaluation of the likelihood part of the centralized nonlinear filter and is based on a particular specialization of the Alternating Direction Method of Multipliers (ADMM) for fast average consensus. Assuming the same number of consensus steps between any two consecutive noisy measurements, our main contribution is summarized in the full characterization of a minimal number of iterations, such that the distributed filter remains uniformly stable with a prescribed accuracy level, within a finite operational horizon, T and across all sensors. Our main result shows that e-stability of the distributed filtering process depends only loglinearly on T and (roughly) the size of the network. If this loglinear bound is fulfilled, any additional consensus iterations will further incur a fully quantified exponential decay in the consensus error. Our bounds are universal, in the sense that they are independent of the structure of the HMM under consideration.

Original languageEnglish (US)
Title of host publicationConference Record of the 49th Asilomar Conference on Signals, Systems and Computers, ACSSC 2015
EditorsMichael B. Matthews
PublisherIEEE Computer Society
Pages299-303
Number of pages5
ISBN (Electronic)9781467385763
DOIs
StatePublished - Feb 26 2016
Event49th Asilomar Conference on Signals, Systems and Computers, ACSSC 2015 - Pacific Grove, United States
Duration: Nov 8 2015Nov 11 2015

Publication series

NameConference Record - Asilomar Conference on Signals, Systems and Computers
Volume2016-February
ISSN (Print)1058-6393

Other

Other49th Asilomar Conference on Signals, Systems and Computers, ACSSC 2015
Country/TerritoryUnited States
CityPacific Grove
Period11/8/1511/11/15

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Computer Networks and Communications

Keywords

  • ADMM
  • Average Consensus
  • Distributed State Estimation
  • Markov Chains
  • Nonlinear Filtering

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