## 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. 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.

Original language | English |
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Pages (from-to) | I51-I72 |

Journal | IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION |

Volume | 35 |

Issue number | 1 |

DOIs | |

Publication status | Published - 29 Mar 2018 |

MoE publication type | A1 Journal article-refereed |

## Keywords

- infinite dimensional systems
- Kalman filter
- optimal estimation
- reduced-order filtering
- Riccati equation
- spatial discretization