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A non-degenerate Rao-Blackwellised particle filter for estimating static parameters in dynamical models
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Division of Signals and Systems, Chalmers University.
2012 (English)In: Proceedings of the 16th IFAC Symposium on System Identification, 2012Conference paper, Oral presentation only (Refereed)
Abstract [en]

The particle filter (PF) has emerged as a powerful tool for solving nonlinear and/or non-Gaussian filtering problems. When some of the states enter the model linearly, this can be exploited by using particles only for the "nonlinear" states and employing conditional Kalman filters for the "linear" states; this leads to the Rao-Blackwellised particle filter (RBPF). However, it is well known that the PF fails when the state of the model contains some static parameter. This is true also for the RBPF, even if the static states are marginalised analytically by a Kalman filter. The reason is that the posterior density of the static states is computed conditioned on the nonlinear particle trajectories, which are bound to degenerate over time. To circumvent this problem, we propose a method for targeting the posterior parameter density, conditioned on just the current nonlinear state. This results in an RBPF-like method, capable of recursive identification of nonlinear dynamical models with affine parameter dependencies.

Place, publisher, year, edition, pages
2012.
Keyword [en]
Particle Filtering/Monte Carlo Methods; Nonlinear System Identification; Recursive Identification
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:liu:diva-81271DOI: 10.3182/20120711-3-BE-2027.00184OAI: oai:DiVA.org:liu-81271DiVA: diva2:551267
Conference
16th IFAC Symposium on System Identification, Brussels, Belgium, July 11-13, 2012.
Projects
CADICSCNDM
Funder
Swedish Research Council
Available from: 2012-09-10 Created: 2012-09-10 Last updated: 2013-10-08
In thesis
1. Particle filters and Markov chains for learning of dynamical systems
Open this publication in new window or tab >>Particle filters and Markov chains for learning of dynamical systems
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC) methods provide computational tools for systematic inference and learning in complex dynamical systems, such as nonlinear and non-Gaussian state-space models. This thesis builds upon several methodological advances within these classes of Monte Carlo methods.Particular emphasis is placed on the combination of SMC and MCMC in so called particle MCMC algorithms. These algorithms rely on SMC for generating samples from the often highly autocorrelated state-trajectory. A specific particle MCMC algorithm, referred to as particle Gibbs with ancestor sampling (PGAS), is suggested. By making use of backward sampling ideas, albeit implemented in a forward-only fashion, PGAS enjoys good mixing even when using seemingly few particles in the underlying SMC sampler. This results in a computationally competitive particle MCMC algorithm. As illustrated in this thesis, PGAS is a useful tool for both Bayesian and frequentistic parameter inference as well as for state smoothing. The PGAS sampler is successfully applied to the classical problem of Wiener system identification, and it is also used for inference in the challenging class of non-Markovian latent variable models.Many nonlinear models encountered in practice contain some tractable substructure. As a second problem considered in this thesis, we develop Monte Carlo methods capable of exploiting such substructures to obtain more accurate estimators than what is provided otherwise. For the filtering problem, this can be done by using the well known Rao-Blackwellized particle filter (RBPF). The RBPF is analysed in terms of asymptotic variance, resulting in an expression for the performance gain offered by Rao-Blackwellization. Furthermore, a Rao-Blackwellized particle smoother is derived, capable of addressing the smoothing problem in so called mixed linear/nonlinear state-space models. The idea of Rao-Blackwellization is also used to develop an online algorithm for Bayesian parameter inference in nonlinear state-space models with affine parameter dependencies.

Place, publisher, year, edition, pages
Linköping University Electronic Press, 2013. 42 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1530
Keyword
Bayesian learning, System identification, Sequential Monte Carlo, Markov chain Monte Carlo, Particle MCMC, Particle filters, Particle smoothers
National Category
Control Engineering Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-97692 (URN)10.3384/diss.diva-97692 (DOI)978-91-7519-559-9 (ISBN)
Public defence
2013-10-25, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Projects
CNDMCADICS
Funder
Swedish Research Council
Available from: 2013-10-08 Created: 2013-09-19 Last updated: 2013-10-08Bibliographically approved

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Lindsten, FredrikSchön, Thomas B.

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