TY - JOUR
T1 - Spatial discretization error in Kalman filtering for discrete-time infinite dimensional systems
AU - Aalto, Atte
N1 - Funding Information:
This work was supported by the Finnish Graduate School in Engineering Mechanics.
Publisher Copyright:
© 2016 The authors. All rights reserved.
PY - 2018/3/29
Y1 - 2018/3/29
N2 - We derive a reduced-order state estimator for discrete-time infinite dimensional linear systems with finite dimensional Gaussian input and output noise. This state estimator is the optimal one-step estimate that takes values in a fixed finite dimensional subspace of the system's state space-consider, for example, a finite element space. The structure of the obtained state estimator is like the Kalman filter, but with an additional optimal embedding operator mapping from the reduced space to the original state space. We derive a Riccati difference equation for the error covariance and use sensitivity analysis to obtain a bound for the error of the state estimate due to the state space discretization.
AB - We derive a reduced-order state estimator for discrete-time infinite dimensional linear systems with finite dimensional Gaussian input and output noise. This state estimator is the optimal one-step estimate that takes values in a fixed finite dimensional subspace of the system's state space-consider, for example, a finite element space. The structure of the obtained state estimator is like the Kalman filter, but with an additional optimal embedding operator mapping from the reduced space to the original state space. We derive a Riccati difference equation for the error covariance and use sensitivity analysis to obtain a bound for the error of the state estimate due to the state space discretization.
KW - infinite dimensional systems
KW - Kalman filter
KW - optimal estimation
KW - reduced-order filtering
KW - Riccati equation
KW - spatial discretization
UR - http://www.scopus.com/inward/record.url?scp=85057255908&partnerID=8YFLogxK
U2 - 10.1093/imamci/dnx015
DO - 10.1093/imamci/dnx015
M3 - Article
AN - SCOPUS:85057255908
VL - 35
SP - I51-I72
JO - IMA Journal of Mathematical Control and Information
JF - IMA Journal of Mathematical Control and Information
SN - 0265-0754
IS - 1
ER -