On the Convergence of Constrained Particle Filters

Nesrine Amor, Nidhal Carla Bouaynaya, Roman Shterenberg, Souad Chebbi

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

The power of particle filters in tracking the state of nonlinear and non-Gaussian systems stems not only from their simple numerical implementation but also from their optimality and convergence properties. In particle filtering, the posterior distribution of the state is approximated by a discrete mass of samples, called particles, that stochastically evolve in time according to the dynamics of the model and the observations. Particle filters have been shown to converge almost surely toward the optimal filter as the number of particles increases. However, when additional constraints are imposed, such that every particle must satisfy these constraints, the optimality properties and error bounds of the constrained particle filter remain unexplored. This letter derives performance limits and error bounds of the constrained particle filter. We show that the estimation error is bounded by the area of the state posterior density that does not include the constraining interval. In particular, the error is small if the target density is 'well localized' in the constraining interval.

Original languageEnglish (US)
Article number7906529
Pages (from-to)858-862
Number of pages5
JournalIEEE Signal Processing Letters
Volume24
Issue number6
DOIs
StatePublished - Jun 2017

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering
  • Applied Mathematics

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