Uniform ϵ-stability of distributed nonlinear filtering over DNAs: Gaussian-finite HMMs

Dionysios S. Kalogerias, Athina P. Petropulu

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we study stability of distributed filtering of Markov chains with finite state space, partially observed in conditionally Gaussian noise. We consider a nonlinear filtering scheme over a distributed network of agents, which relies on the distributed evaluation of the likelihood part of the respective centralized estimator. Distributed evaluation of likelihoods is based on a particular specialization of the alternating direction method of multipliers for fast average consensus. Assuming the same number of consensus steps between any two consecutive noisy measurements for each sensor in the network, we fully characterize a minimal number of such steps, so that the distributed filter remains uniformly stable with a prescribed accuracy level, in (0,1], within a finite operational horizon, T, and across all sensors. Stability is in the sense of the ℓ1-norm between the centralized and distributed versions of the posterior at each sensor, and at each time within T. Roughly speaking, our main result shows that uniform ϵ -stability of the distributed filtering process depends loglinearly on T and the size of the network, and logarithmically on 1. If this total loglinear bound is fulfilled, any additional consensus iterations will incur a fully quantified further exponential decay in the consensus error. Our bounds are universal, in the sense that they are independent of the particular structure of the Gaussian Hidden Markov Model under consideration.

Original languageEnglish (US)
Article number7581064
Pages (from-to)461-476
Number of pages16
JournalIEEE Transactions on Signal and Information Processing over Networks
Volume2
Issue number4
DOIs
StatePublished - Jan 1 2016

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Signal Processing
  • Computer Networks and Communications

Keywords

  • ADMM
  • Gaussian HMMs
  • Markov chains
  • average consensus
  • distributed estimation
  • nonlinear filtering

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