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On Nonlinear Transformations of Stochastic Variables and its Application to Nonlinear Filtering
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-1971-4295
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2007 (English)Report (Other academic)
Abstract [en]

A class of nonlinear transformation-based filters (NLTF) for state estimation is proposed. The nonlinear transformations that can be used include first (TT1) and second (TT2) order Taylor expansions, the unscented transformation (UT), and the Monte Carlo transformation (MCT) approximation. The unscented Kalman filter (UKF) is by construction a special case, but also nonstandard implementations of the Kalman filter (KF) and the extended Kalman filter (EKF) are included, where there are no explicit Riccati equations. The theoretical properties of these mappings are important for the performance of the NLTF. TT 2 does by definition take care of the bias and covariance of the second order term that is neglected in the TT 1 based EKF. The UT computes this bias term accurately, but the covariance is correct only for scalar state vectors. This result is demonstrated with a simple example and a general theorem, which explicitly shows the difference between TT 1, TT 2, UT, and MCT.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2007. , 16 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 2828
Keyword [en]
Kalman filter, Extended Kalman filter, Nonlinear filtering, Nonlinear transformation, Unscented transform
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-56145ISRN: LiTH-ISY-R-2828OAI: oai:DiVA.org:liu-56145DiVA: diva2:316955
Available from: 2010-04-30 Created: 2010-04-30 Last updated: 2015-09-22Bibliographically approved

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Hendeby, GustafGustafsson, Fredrik

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
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  • de-DE
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