title: Parametric Bayesian filters for nonlinear stochastic dynamical systems: a survey.
abstract: Nonlinear stochastic dynamical systems are commonly used to model physical processes. For linear and Gaussian systems, the Kalman filter is optimal in minimum mean squared error sense. However, for nonlinear or non-Gaussian systems, the estimation of states or parameters is a challenging problem. Furthermore, it is often required to process data online. Therefore, apart from being accurate, the feasible estimation algorithm also needs to be fast. In this paper, we review Bayesian filters that possess the aforementioned properties. Each filter is presented in an easy way to implement algorithmic form. We focus on parametric methods, among which we distinguish three types of filters: filters based on analytical approximations (extended Kalman filter, iterated extended Kalman filter), filters based on statistical approximations (unscented Kalman filter, central difference filter, Gauss-Hermite filter), and filters based on the Gaussian sum approximation (Gaussian sum filter). We discuss each of these filters, and compare them with illustrative examples.
authors.forename: Pawe
authors.initials: P
authors.lastname: Stano
authors.forename: Zsófia
authors.initials: Z
authors.lastname: Lendek
authors.forename: Jelmer
authors.initials: J
authors.lastname: Braaksma
authors.forename: Robert
authors.initials: R
authors.lastname: Babuska
authors.forename: Cees
authors.initials: C
authors.lastname: de Keizer
authors.forename: Arnold J
authors.initials: AJ
authors.lastname: den Dekker
mesh_terms: D001499:Bayes Theorem; D003198:Computer Simulation; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D012815:Signal Processing, Computer-Assisted; D013269:Stochastic Processes