  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 (e.g., mean and covariance)
conditioned on the system's measurement data. This article offers a systematic
introduction of the Bayesian state estimation framework and reviews various
Kalman filtering (KF) 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 the Gaussian filtering, Gaussian-sum filtering, particle filtering
and moving horizon estimation and extends the discussion of state estimation
forward to more complicated problems such as simultaneous state and
parameter/input estimation.
