Fluctuations, stability and instability of a distributed particle filter with local exchange

Kari Heine, Nick Whiteley

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We study a distributed particle filter proposed by Bolić et al. (2005). This algorithm involves m groups of M particles, with interaction between groups occurring through a “local exchange” mechanism. We establish a central limit theorem in the regime where M is fixed and m→∞. A formula we obtain for the asymptotic variance can be interpreted in terms of colliding Markov chains, enabling analytic and numerical evaluations of how the asymptotic variance behaves over time, with comparison to a benchmark algorithm consisting of m independent particle filters. We prove that subject to regularity conditions, when m is fixed both algorithms converge time-uniformly at rate M^{−1/2}. Through use of our asymptotic variance formula we give counter-examples satisfying the same regularity conditions to show that when M is fixed neither algorithm, in general, converges time-uniformly at rate m^{−1/2}.
Original languageEnglish
Pages (from-to)2508-2541
Number of pages34
JournalStochastic Processes and their Applications
Issue number8
Early online date9 Dec 2016
Publication statusPublished - 1 Aug 2017


  • Hidden Markov model
  • Particle Filter
  • Central limit theorem
  • Asymptotic variance
  • Local exchange
  • Sequential Monte Carlo


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