Reference : Spatial discretization error in Kalman filtering for discrete-time infinite dimension...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Spatial discretization error in Kalman filtering for discrete-time infinite dimensional systems
Aalto, Atte mailto [Aalto University > Department of Mathematics and Systems Analysis]
IMA Journal of Mathematical Control and Information
Oxford University Press
Yes (verified by ORBilu)
United Kingdom
[en] Kalman filter ; reduced-order filtering ; Riccati equation
[en] 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.

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