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Efficient Nonlinear Measurement Updating based on Gaussian Mixture Approximation of Conditional Densities

Huber, Marco F.; Brunn, Dietrich; Hanebeck, Uwe D.

Abstract:
Filtering or measurement updating for nonlinear stochastic dynamic systems requires approximate calculations, since an exact solution is impossible to obtain in general. We propose a Gaussian mixture approximation of the conditional density, which allows performing measurement updating in closed form. The conditional density is a probabilistic representation of the nonlinear system and depends on the random variable of the measurement given the system state. Unlike the likelihood, the conditional density is independent of actual measurements, which permits determining its approximation off-line. By treating the approximation task as an optimization problem, we use progressive processing to achieve high quality results. Once having calculated the conditional density, the likelihood can be determined on-line, which, in turn, offers an efficient approximate filter step. As result, a Gaussian mixture representation of the posterior density is obtained. The exponential growth of Gaussian mixture components resulting from repeated filtering is avoided implicitly by the prediction step using the proposed techniques.


Zugehörige Institution(en) am KIT Institut für Anthropomatik (IFA)
Publikationstyp Proceedingsbeitrag
Jahr 2007
Sprache Englisch
Identifikator ISBN: 1-4244-0988-8
URN: urn:nbn:de:swb:90-348296
KITopen ID: 1000034829
Erschienen in Proceedings of the 2007 American Control Conference (ACC 2007), New York, New York, USA, July, 2007
Verlag IEEE, Piscataway
Seiten 4425-4430
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