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Nonlinear Bayesian Estimation with Compactly Supported Wavelets

Hekler, Achim; Kiefel, Martin; Hanebeck, Uwe D.

Bayesian estimation for nonlinear systems is still a challenging problem, as in general the type of the true probability density changes and the complexity increases over time. Hence, approximations of the occurring equations and/or of the underlying probability density functions are inevitable. In this paper, we propose an approximation of the conditional densities by wavelet expansions. This kind of representation allows a sparse set of characterizing coefficients, especially for smooth or piecewise smooth density functions. Besides its good approximation properties, fast algorithms operating on sparse vectors are applicable and thus, a good trade-off between approximation quality and run-time can be achieved. Moreover, due to its highly generic nature, it can be applied to a large class of nonlinear systems with a high modeling accuracy. In particular, the noise acting upon the system can be modeled by an arbitrary probability distribution and can influence the system in any way.

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Volltext §
DOI: 10.5445/IR/1000035085
Zugehörige Institution(en) am KIT Institut für Anthropomatik (IFA)
Publikationstyp Proceedingsbeitrag
Jahr 2010
Sprache Englisch
Identifikator ISBN: 978-1-4244-7745-6
KITopen-ID: 1000035085
Erschienen in Proceedings of the 2010 IEEE Conference on Decision and Control (CDC 2010), Atlanta, Georgia, USA, 15-17 Dec. 2010
Verlag IEEE, Piscataway
Seiten 5701-5706
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