Journal ArticleDOI
On sequential Monte Carlo sampling methods for Bayesian filtering
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TLDR
An overview of methods for sequential simulation from posterior distributions for discrete time dynamic models that are typically nonlinear and non-Gaussian, and how to incorporate local linearisation methods similar to those which have previously been employed in the deterministic filtering literature are shown.Abstract:
In this article, we present an overview of methods for sequential simulation from posterior distributions. These methods are of particular interest in Bayesian filtering for discrete time dynamic models that are typically nonlinear and non-Gaussian. A general importance sampling framework is developed that unifies many of the methods which have been proposed over the last few decades in several different scientific disciplines. Novel extensions to the existing methods are also proposed. We show in particular how to incorporate local linearisation methods similar to those which have previously been employed in the deterministic filtering literatures these lead to very effective importance distributions. Furthermore we describe a method which uses Rao-Blackwellisation in order to take advantage of the analytic structure present in some important classes of state-space models. In a final section we develop algorithms for prediction, smoothing and evaluation of the likelihood in dynamic models.read more
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References
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Journal ArticleDOI
Novel approach to nonlinear/non-Gaussian Bayesian state estimation
TL;DR: An algorithm, the bootstrap filter, is proposed for implementing recursive Bayesian filters, represented as a set of random samples, which are updated and propagated by the algorithm.
Book
Stochastic Processes and Filtering Theory
TL;DR: In this paper, a unified treatment of linear and nonlinear filtering theory for engineers is presented, with sufficient emphasis on applications to enable the reader to use the theory for engineering problems.
Journal Article
Optimal Filtering
TL;DR: This book helps to fill the void in the market and does that in a superb manner by covering the standard topics such as Kalman filtering, innovations processes, smoothing, and adaptive and nonlinear estimation.
Journal ArticleDOI
On optimal e ∞ to e ∞ filtering
TL;DR: Taking a model matching approach, suboptimal solutions are presented that stem from the resulting l ∞ -induced norm-minimization problem.
Journal ArticleDOI
Filtering via Simulation: Auxiliary Particle Filters
Michael K. Pitt,Neil Shephard +1 more
TL;DR: This article analyses the recently suggested particle approach to filtering time series and suggests that the algorithm is not robust to outliers for two reasons: the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution.