Techniques for efficient covariance propagation in the Extended/Unscented Kalman Filter based on model reduction
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
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.
IdentifiersURN: urn:nbn:no:ntnu:diva-21985Local ID: ntnudaim:8789OAI: oai:DiVA.org:ntnu-21985DiVA: diva2:646723
Imsland, Lars, Professor