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Nonlinear Multidimensional Bayesian Estimation with Fourier Densities

Brunn, Dietrich; Sawo, Felix; Hanebeck, Uwe D.


Efficiently implementing nonlinear Bayesian estimators is still an unsolved problem, especially for the multidimensional case. A trade-off between estimation quality and demand on computational resources has to be found. Using multidimensional Fourier series as representation for probability density functions, so called Fourier densities, is proposed. To ensure non-negativity, the approximation is performed indirectly via Psi-densities, of which the absolute square represent the Fourier density. It is shown that PSI-densities can be determined using the efficient fast Fourier transform algorithm and their coefficients have an ordering with respect to the Hellinger metric. Furthermore, the multidimensional Bayesian estimator based on Fourier Densities is derived in closed form. That allows an efficient realization of the Bayesian estimator where the demands on computational resources are adjustable.

Volltext §
DOI: 10.5445/IR/1000013887
DOI: 10.1109/cdc.2006.377378
Zitationen: 9
Cover der Publikation
Zugehörige Institution(en) am KIT Fakultät für Informatik – Institut für Anthropomatik (IFA)
Publikationstyp Proceedingsbeitrag
Publikationsjahr 2006
Sprache Englisch
Identifikator ISBN: 1-4244-0171-2
KITopen-ID: 1000013887
Erschienen in Proceedings / 45th IEEE Conference on Decision and Control, 2006, 13 - 15 Dec. 2006, San Diego, CA, USA
Verlag IEEE Service Center
Seiten 1303 - 1308
Nachgewiesen in Dimensions
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