Basics on probability theory: probability spaces, random vectors, distributions, distribution functions and probability densities, expectations and conditional expectations. Hilbert spaces of random vectors. Projection theorems. Convergence of random vectors. Limit theorems: Weak and Strong Laws. 

Bayesian versus deterministic approach to model estimation. Statistical models and statistical inference from data.

Optimality criteria: unbiasedness, consistency, efficiency. Cramer-Rao  lower-bound for error covariance. Kullback-Leibler pseudo-distance. 

Optimal deterministic estimation: weighted least squares (WLS) estimators, maximum likelihood (ML) estimators. Invariance principle for ML estimators. Recursive WLS estimators. 

Optimal  Bayesian estimation:  minimum error variance (MEV) estimators. Linear MEV estimators. 

Recursive optimal linear MEV: Kalman filter. Steady-state Kalman filter. Extended Kalman filter.