Spatial discretization error in Kalman filtering for discrete-time infinite dimensional systems

Atte Aalto

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arXiv · 1406.7160

Spatial discretization error in Kalman filtering for discrete-time infinite dimensional systems

Atte Aalto

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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.

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Atte Aalto. 2014-10-07. Spatial discretization error in Kalman filtering for discrete-time infinite dimensional systems. https://arxiv.org/abs/1406.7160

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