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Optimal Dirac Approximation by Exploiting Independencies

Eberhardt, Henning; Klumpp, Vesa; Hanebeck, Uwe D.

Abstract:
The sample-based recursive prediction of discrete-time nonlinear stochastic dynamic systems requires a regular reapproximation of the Dirac mixture densities characterizing the state estimate with an exponentially increasing number of components. For that purpose, a systematic approximation method is proposed that is deterministic and guaranteed to minimize a new type distance measure, the so called modified Cram\'{e}r-von Mises distance. A huge increase in approximation performance is achieved by exploiting structural independencies usually occurring between the random variables used as input to the system. The corresponding prediction step achieves optimal performance when no further assumptions can be made about the system function. In addition, the proposed approach shows a much better convergence compared to the prediction step of the particle filter and by far fewer Dirac components are required for achieving a given approximation quality. As a result, the new approximation method opens the way for the development of new fully deterministic and optimal stochastic state estimators for nonlinear dynamic systems.

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Volltext §
DOI: 10.5445/IR/1000035095
Zugehörige Institution(en) am KIT Institut für Anthropomatik (IFA)
Publikationstyp Proceedingsbeitrag
Jahr 2010
Sprache Englisch
Identifikator ISBN: 978-1-4244-7427-1
urn:nbn:de:swb:90-350952
KITopen-ID: 1000035095
Erschienen in Proceedings of the 2010 American Control Conference (ACC 2010), Baltimore, Maryland, USA, June 30-July 02, 2010
Verlag IEEE, Piscataway
Seiten 1392-1398
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