Multivariable feedback particle filter

Tao Yang, Richard S. Laugesen, Prashant G. Mehta, Sean P. Meyn

Research output: Contribution to journalArticlepeer-review


This paper presents the multivariable extension of the feedback particle filter (FPF) algorithm for the nonlinear filtering problem in continuous-time. The FPF is a control-oriented approach to particle filtering. The approach does not require importance sampling or resampling and offers significant variance improvements; in particular, the algorithm can be applied to systems that are not stable. This paper describes new representations and algorithms for the FPF in the general multivariable nonlinear non-Gaussian setting. Theory surrounding the FPF is improved: Exactness of the FPF is established in the general setting, as well as well-posedness of the associated boundary value problem to obtain the filter gain. A Galerkin finite-element algorithm is proposed for approximation of the gain. Its performance is illustrated in numerical experiments.

Original languageEnglish (US)
Pages (from-to)10-23
Number of pages14
StatePublished - Sep 1 2016


  • Estimation theory
  • Nonlinear filtering
  • Particle filtering

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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