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 -