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Filtering and System Identification by Vincent Verdult, Michel Verhaegen

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5

Kalman filtering

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After studying this chapter you will be able to

•  use an observer to estimate the state vector of a linear time-invariant system;

•  use a Kalman filter to estimate the state vector of a linear system using knowledge of the system matrices, the system input and output measurements, and the covariance matrices of the disturbances in these measurements;

•  describe the difference among the predicted, filtered, and smoothed state estimates;

•  formulate the Kalman-filter problem as a stochastic and a weighted least-squares problem;

•  solve the stochastic least-squares problem by application of the completion-of-squares argument; ...

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