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

摘要

We derive a reduced-order state estimator for discrete-time infinitedimensional linear systems with finite dimensional Gaussian input and outputnoise. This state estimator is the optimal one-step estimate that takes valuesin a fixed finite dimensional subspace of the system's state space ---consider, for example, a Finite Element space. We then derive a Riccatidifference equation for the error covariance and use sensitivity analysis toobtain a bound for the error of the state estimate due to the state spacediscretization.