Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems

Philippe Moireau; Dominique Chapelle

ESAIM: Control, Optimisation and Calculus of Variations (2011)

  • Volume: 17, Issue: 2, page 380-405
  • ISSN: 1292-8119

Abstract

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We propose a general reduced-order filtering strategy adapted to Unscented Kalman Filtering for any choice of sampling points distribution. This provides tractable filtering algorithms which can be used with large-dimensional systems when the uncertainty space is of reduced size, and these algorithms only invoke the original dynamical and observation operators, namely, they do not require tangent operator computations, which of course is of considerable benefit when nonlinear operators are considered. The algorithms are derived in discrete time as in the classical UKF formalism – well-adapted to time discretized dynamical equations – and then extended into consistent continuous-time versions. This reduced-order filtering approach can be used in particular for the estimation of parameters in large dynamical systems arising from the discretization of partial differential equations, when state estimation can be handled by an adequate Luenberger observer inspired from feedback control. In this case, we give an analysis of the joint state-parameter estimation procedure based on linearized error, and we illustrate the effectiveness of the approach using a test problem inspired from cardiac biomechanics.

How to cite

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Moireau, Philippe, and Chapelle, Dominique. "Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems." ESAIM: Control, Optimisation and Calculus of Variations 17.2 (2011): 380-405. <http://eudml.org/doc/272963>.

@article{Moireau2011,
abstract = {We propose a general reduced-order filtering strategy adapted to Unscented Kalman Filtering for any choice of sampling points distribution. This provides tractable filtering algorithms which can be used with large-dimensional systems when the uncertainty space is of reduced size, and these algorithms only invoke the original dynamical and observation operators, namely, they do not require tangent operator computations, which of course is of considerable benefit when nonlinear operators are considered. The algorithms are derived in discrete time as in the classical UKF formalism – well-adapted to time discretized dynamical equations – and then extended into consistent continuous-time versions. This reduced-order filtering approach can be used in particular for the estimation of parameters in large dynamical systems arising from the discretization of partial differential equations, when state estimation can be handled by an adequate Luenberger observer inspired from feedback control. In this case, we give an analysis of the joint state-parameter estimation procedure based on linearized error, and we illustrate the effectiveness of the approach using a test problem inspired from cardiac biomechanics.},
author = {Moireau, Philippe, Chapelle, Dominique},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {filtering; data assimilation; state and parameter estimation; identification in PDEs},
language = {eng},
number = {2},
pages = {380-405},
publisher = {EDP-Sciences},
title = {Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems},
url = {http://eudml.org/doc/272963},
volume = {17},
year = {2011},
}

TY - JOUR
AU - Moireau, Philippe
AU - Chapelle, Dominique
TI - Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2011
PB - EDP-Sciences
VL - 17
IS - 2
SP - 380
EP - 405
AB - We propose a general reduced-order filtering strategy adapted to Unscented Kalman Filtering for any choice of sampling points distribution. This provides tractable filtering algorithms which can be used with large-dimensional systems when the uncertainty space is of reduced size, and these algorithms only invoke the original dynamical and observation operators, namely, they do not require tangent operator computations, which of course is of considerable benefit when nonlinear operators are considered. The algorithms are derived in discrete time as in the classical UKF formalism – well-adapted to time discretized dynamical equations – and then extended into consistent continuous-time versions. This reduced-order filtering approach can be used in particular for the estimation of parameters in large dynamical systems arising from the discretization of partial differential equations, when state estimation can be handled by an adequate Luenberger observer inspired from feedback control. In this case, we give an analysis of the joint state-parameter estimation procedure based on linearized error, and we illustrate the effectiveness of the approach using a test problem inspired from cardiac biomechanics.
LA - eng
KW - filtering; data assimilation; state and parameter estimation; identification in PDEs
UR - http://eudml.org/doc/272963
ER -

References

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