Elements of probability theory – random variables – Gaussian distribution – stochastic processes – characterizations and properties – Gauss-Markov processes – Brownian motion process – Gauss-Markov models – Optimal estimation for discrete-time systems – fundamental theorem of estimation – optimal prediction. Optimal filtering – Weiner approach – continuous time Kalman Filter – properties and implementation – steady-state Kalman Filter – discrete-time Kalman Filter – implementation – sub-optimal steady-state Kalman Filter – Extended Kalman Filter – practical applications. Optimal smoothing – Optimal fixed-interval smoothing – optimal fixed-point smoothing – optimal fixed-lag smoothing – stability – performance evaluation.

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