Convergence results in distributed Kalman filtering

Soummya Kar, Shuguang Cui, H. Vincent Poor, José M.F. Moura

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

3 Scopus citations

Abstract

The paper studies the convergence properties of the estimation error processes in distributed Kalman filtering for potentially unstable linear dynamical systems. In particular, it is shown that, in a weakly connected communication network, there exist (randomized) gossip based information dissemination schemes leading to a stochastically bounded estimation error at each sensor for any non-zero rate γ̄ of inter-sensor communication (the rate γ̄ is defined to be the average number of inter-sensor communications per signal evolution epoch). A gossip-based information exchange protocol, the M-GIKF, is presented, in which sensors exchange estimates and aggregate observations at a rate γ̄ > 0, leading to desired convergence properties. Under the assumption of global (centralized) detectability of the signal/observation model (necessary for a centralized estimator having access to all sensor observations at all times to yield bounded estimation error), it is shown that the distributed M-GIKF leads to a stochastically bounded estimation error at each sensor. The conditional estimation error covariance sequence at each sensor is shown to evolve as a random Riccati equation (RRE) with Markov modulated switching. The RRE is analyzed through a random dynamical system (RDS) formulation, and the asymptotic estimation error at each sensor is characterized in terms of an associated invariant measure μγ̄ of the RDS.

Original languageEnglish (US)
Title of host publication2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings
Pages2500-2503
Number of pages4
DOIs
StatePublished - Aug 18 2011
Event36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Prague, Czech Republic
Duration: May 22 2011May 27 2011

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Other

Other36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011
CountryCzech Republic
CityPrague
Period5/22/115/27/11

All Science Journal Classification (ASJC) codes

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

Keywords

  • Distributed Kalman filtering
  • Gossip algorithms
  • Invariant Measure
  • Random Dynamical Systems

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    Kar, S., Cui, S., Poor, H. V., & Moura, J. M. F. (2011). Convergence results in distributed Kalman filtering. In 2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings (pp. 2500-2503). [5946992] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). https://doi.org/10.1109/ICASSP.2011.5946992