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Bayesian semiparametric Wiener system identification
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.
University of Calif Berkeley, CA USA .
2013 (English)In: Automatica, ISSN 0005-1098, Vol. 49, no 7, 2053-2063 p.Article in journal (Refereed) Published
Abstract [en]

We present a novel method for Wiener system identification. The method relies on a semiparametric, i.e. a mixed parametric/nonparametric, model of a Wiener system. We use a state-space model for the linear dynamical system and a nonparametric Gaussian process model for the static nonlinearity. We avoid making strong assumptions, such as monotonicity, on the nonlinear mapping. Stochastic disturbances, entering both as measurement noise and as process noise, are handled in a systematic manner. The nonparametric nature of the Gaussian process allows us to handle a wide range of nonlinearities without making problem-specific parameterizations. We also consider sparsity-promoting priors, based on generalized hyperbolic distributions, to automatically infer the order of the underlying dynamical system. We derive an inference algorithm based on an efficient particle Markov chain Monte Carlo method, referred to as particle Gibbs with ancestor sampling. The method is profiled on two challenging identification problems with good results. Blind Wiener system identification is handled as a special case.

Place, publisher, year, edition, pages
Elsevier , 2013. Vol. 49, no 7, 2053-2063 p.
Keyword [en]
System identification, Wiener, Block-oriented models, Gaussian process, Semiparametric, Particle filter, Ancestor sampling, Particle Markov chain Monte Carlo
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-95954DOI: 10.1016/j.automatica.2013.03.021ISI: 000321233900011OAI: diva2:641716

Funding Agencies|project Calibrating Nonlinear Dynamical Models|621-2010-5876|Swedish Research Council||CADICS||Linnaeus Center||

Available from: 2013-08-19 Created: 2013-08-12 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.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1530
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
urn:nbn:se:liu:diva-97692 (URN)10.3384/diss.diva-97692 (DOI)978-91-7519-559-9 (print) (ISBN)
Public defence
2013-10-25, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Swedish Research Council
Available from: 2013-10-08 Created: 2013-09-19 Last updated: 2013-10-08Bibliographically approved

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