# 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

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topMoireau, 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/197333>.

@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; filtering},

language = {eng},

month = {5},

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/197333},

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

DA - 2011/5//

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; filtering

UR - http://eudml.org/doc/197333

ER -

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