Spatial discretization error in Kalman filtering for discrete-time infinite dimensional systems
Optimization and Control
2014-10-08 v2
Abstract
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. We then 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.
Cite
@article{arxiv.1406.7160,
title = {Spatial discretization error in Kalman filtering for discrete-time infinite dimensional systems},
author = {Atte Aalto},
journal= {arXiv preprint arXiv:1406.7160},
year = {2014}
}