Error analysis for numerical formulation of particle filter

Xiaoying Han, Jinglai Li, Dongbin Xiu

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


As an approximation of the optimal stochastic filter, particle filter is a widely used tool for numerical prediction of complex systems when observation data are available. In this paper, we conduct an error analysis from a numerical analysis perspective. That is, we investigate the numerical error, which is defined as the difference between the numerical implementation of particle filter and its continuous counterpart, and demonstrate that the error consists of discretization errors for solving the dynamic equations numerically and sampling errors for generating the random particles. We then establish convergence of the numerical particle filter to the continuous optimal filter and provide bounds for the convergence rate. Remarkably, our analysis suggests that more frequent data assimilation may lead to larger numerical errors of the particle filter. Numerical examples are provided to verify the theoretical findings.
Original languageEnglish
Pages (from-to)1337-1354
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number5
Early online dateMay 2015
Publication statusPublished - Jul 2015


  • data assimilation
  • sequential Monte Carlo.
  • particle filter
  • Bayesian filer


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