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Explicit Fractional Model Order Estimation Using Unscented and Ensemble Kalman Filters

[+] Author Affiliations
Michailas Romanovas, Lasse Klingbeil, Martin Traechtler

Hahn-Schickard-Gesellschaft, Institute of Microsystems and Information Technology (HSG-IMIT), Villingen-Schwenningen, Germany

Yiannos Manoli

University of Freiburg, Freiburg, Germany

Paper No. DETC2011-47835, pp. 275-284; 10 pages
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 3: 2011 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5480-8
  • Copyright © 2011 by ASME


The article presents an approach for combining methods of recursive Bayesian estimation with models of dynamical systems with varying differentiation order. The work addresses the problem of explicit fractional order estimation and tracking by constructing an efficient Unscented Kalman filter, where the model order is directly estimated within an augmented state along with the variables of interest. The feasibility of the estimation method is assessed using a benchmark problem based on a simplified fractional neuron firing rate model and time-dependent differentiation order. The proposed technique is compared to an implicit method based on Interacting Multiple Model filtering and a computationally efficient method using a modification of the Ensemble Kalman filter. The performance with respect to different parameters and filter settings is analyzed and a corresponding discussion is provided.

Copyright © 2011 by ASME
Topics: Kalman filters



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