Nonlinear Bayesian estimation: From Kalman filtering to a broader horizon

Huazhen Fang, Ning Tian, Yebin Wang, Mengchu Zhou, Mulugeta A. Haile

Research output: Contribution to journalReview articlepeer-review

144 Scopus citations


This article presents an up-to-date tutorial review of nonlinear Bayesian estimation. State estimation for nonlinear systems has been a challenge encountered in a wide range of engineering fields, attracting decades of research effort. To date, one of the most promising and popular approaches is to view and address the problem from a Bayesian probabilistic perspective, which enables estimation of the unknown state variables by tracking their probabilistic distribution or statistics U+0028 e.g., mean and covariance U+0029 conditioned on a system U+02BC s measurement data. This article offers a systematic introduction to the Bayesian state estimation framework and reviews various Kalman filtering U+0028 KF U+0029 techniques, progressively from the standard KF for linear systems to extended KF, unscented KF and ensemble KF for nonlinear systems. It also overviews other prominent or emerging Bayesian estimation methods including Gaussian filtering, Gaussian-sum filtering, particle filtering and moving horizon estimation and extends the discussion of state estimation to more complicated problems such as simultaneous state and parameter U+002F input estimation.

Original languageEnglish (US)
Article number8283968
Pages (from-to)401-417
Number of pages17
JournalIEEE/CAA Journal of Automatica Sinica
Issue number2
StatePublished - Mar 2018

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Artificial Intelligence
  • Information Systems
  • Control and Systems Engineering


  • Kalman filtering (KF)
  • Nonlinear Bayesian estimation
  • State estimation
  • Stochastic estimation


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