Syllabus

Elements of probability theory - random variables-G aussian distribution-stochastic processes- characterizations and properties-Gauss-Markov proce sses-Brownian motion process-Gauss- Markov models - Optimal estimation for discrete-tim e 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 Filt er-Extended Kalman Filter-practical applications. Optimal smoothing - Optimal fixed-int erval smoothing optimal fixed-point smoothing-optimal fixed-lag smoothing-stability-per formance evaluation.