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Bounding Linearization Errors with Sets of Densities in Approximate Kalman Filtering

Noack, Benjamin; Klumpp, Vesa; Petkov, Nikolay; Hanebeck, Uwe D.

Abstract:
Applying the Kalman filtering scheme to linearized system dynamics and observation models does in general not yield optimal state estimates. More precisely, inconsistent state estimates and covariance matrices are caused by neglected linearization errors. This paper introduces a concept for systematically predicting and updating bounds for the linearization errors within the Kalman filtering framework. To achieve this, an uncertain quantity is not characterized by a single probability density anymore, but rather by a set of densities and accordingly, the linear estimation framework is generalized in order to process sets of probability densities. By means of this generalization, the Kalman filter may then not only be applied to stochastic quantities, but also to unknown but bounded quantities. In order to improve the reliability of Kalman filtering results, the last-mentioned quantities are utilized to bound the typically neglected nonlinear parts of a linearized mapping.

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Volltext §
DOI: 10.5445/IR/1000035094
Zugehörige Institution(en) am KIT Institut für Anthropomatik (IFA)
Publikationstyp Proceedingsbeitrag
Jahr 2010
Sprache Englisch
Identifikator ISBN: 978-0-9824438-1-1
urn:nbn:de:swb:90-350942
KITopen-ID: 1000035094
Erschienen in Proceedings of the 13th International Conference on Information Fusion (Fusion 2010), Edinburgh, United Kingdom, 26-29 July 2010
Verlag IEEE, Piscataway
Seiten 8 S.
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