M. Sarhan (USA)
The heat equation, continuous and discrete Finite element Galerkin methods, and Kalman filter
With zero mean white noise input and zero mean white noise-corrupted output, the heat equation as a state equation and an output function of time are presented. A continuous state space model for the input-output system is obtained by applying finite element Galerkin method. A Kalman filter is designed to estimate the state and the output of the corrupted continuous time approximated system. A discrete time Galerkin procedure is derived to obtain a discrete state space model. A discrete Kalman filter is designed to estimate the state and the output of the corrupted discrete time approximated system. The upper bound of the error estimate is derived in each of the two cases.
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