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Techniques for efficient covariance propagation in the Extended/Unscented Kalman Filter based on model reduction
Norwegian University of Science and Technology, Faculty of Information Technology, Mathematics and Electrical Engineering, Department of Engineering Cybernetics.
2013 (English)MasteroppgaveStudent thesis
Abstract [en]

Physical processes gives engineers and researchers challenging task, such as modeling, simulation and control. One of the most important steps in these procedures are the ability to predict the systems behavior, which due to the size and complexity of the models often are computationally expensive. A too high computational cost may lead to delays in necessary information, interruptions in production systems, loss of nances, or even worse, loss of lives. Thus, nding more ecient way of predicting the behavior of physical processes are of particular interest. This thesis presents a new approach of improving the eciency in the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) through the use of techniques from model reduction. By reducing the main bulk of complexity, given by the covariance propagation in the EKF and the calculation of the sigma points in the UKF, while the full model is used for state propagation and the unscented transformation, respectively, the computational effort is reduced. A one and two dimensional heat conduction model with 400 and 1452 states are introduced. The reduced order model is obtained by applying the Galerkin projection based on a Proper Orthogonal Decomposition (POD) reduced-order basis or balanced truncation by empirical Gramians. The physical processes are simulated for several possible scenarios of errors one may encounter, to see how the estimation result is affected. The time complexity in the new approach is shown to be similar to the existing reduced approaches of state estimation, while only using the reduced model in the bulk of complexity. It also show a signicantly improvement over the original algorithms, given that the subspace conguration in the reduced model not exceeds a certain percentage of the full space. The derived EKF show great promise for a wide range of subspace congurations, except for in the case of induced model errors. The derived UKF has in general shown great promise for subspace congurations larger than one sixteenth of the full space, and for all subspace congurations in the case of model errors, independent of the magnitude of the error. The new approach show great promise for improving the eciency in the EKF and UKF through model reduction, without losing too much information in the process

Place, publisher, year, edition, pages
Institutt for teknisk kybernetikk , 2013. , 118 p.
URN: urn:nbn:no:ntnu:diva-21985Local ID: ntnudaim:8789OAI: diva2:646723
Available from: 2013-09-09 Created: 2013-09-09 Last updated: 2013-09-09Bibliographically approved

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