In applications involving large scale systems such as discretized partial differential equations, it is often of interest to use data to estimate state variables associated with a subregion of the spatial domain. In this paper we derive an extension of the classical Kalman filter in which data injection is confined to a subspace of the system states.
A state estimation problem for linearized magnetohydrodynamic(MHD) flow is considered. The ideal MHD equations governing the flow of plasma in a twodimensional channel are linearized about an equilibrium flow. Pseudospectral collocation methods are used to spatially discretize the linear partial differential equations and obtain a state-space model of the linearized dynamics. Three different discrete-time Kalman filtering algorithms are used to estimate the state variables, and their performance is analyzed.
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