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Newton-based maximum likelihood estimation in nonlinear state space models
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-9424-1272
Uppsala University.
University of Newcastle, Australia.
2015 (English)In: Proceedings of the 17th IFAC Symposium on System Identification, 2015, 398-403 p.Conference paper, Published paper (Refereed)
Abstract [en]

Maximum likelihood (ML) estimation using Newton’s method in nonlinear state space models (SSMs) is a challenging problem due to the analytical intractability of the log- likelihood and its gradient and Hessian. We estimate the gradient and Hessian using Fisher’s identity in combination with a smoothing algorithm. We explore two approximations of the log-likelihood and of the solution of the smoothing problem. The first is a linearization approximation which is computationally cheap, but the accuracy typically varies between models. The second is a sampling approximation which is asymptotically valid for any SSM but is more computationally costly. We demonstrate our approach for ML parameter estimation on simulated data from two different SSMs with encouraging results. 

Place, publisher, year, edition, pages
2015. 398-403 p.
Keyword [en]
Maximum likelihood, parameter estimation, nonlinear state space models, Fisher’s identity, extended Kalman filters, particle methods, Newton optimization.
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-123208OAI: oai:DiVA.org:liu-123208DiVA: diva2:877583
Conference
17th IFAC Symposium on System Identification, Beijing, China, October 19-21, 2015
Projects
CADICSThe project Probabilistic modeling of dynamical systems (Contract number: 621- 2013-5524)
Funder
Swedish Research Council
Available from: 2015-12-07 Created: 2015-12-07 Last updated: 2016-05-04

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Kok, ManonDahlin, Johan

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf