The final exam for clearing OPTIMAL ESTIMATION AND FILTERING consists of an ORAL exam focused on the topics discussed in the classroom. Two (up to three) general topics are assigned to the student as a written task, each within a fixed time window (20  minutes approx.) and then discussed with the teacher at the end of the scheduled time. Examples of assigned written tasks are:

• Error covariance and Cramer-Rao lower bound

• Kullback-Leibner distance, Fisher matrix and Identifibility conditions

• Deterministic Weighted Least Squares (WLS) estimators

• Maximum Likelihood (ML) estimators and Invariance Principle

• ML estimators for linear statistical models

• Bayesian estimation, Maximum Expected Risk and Minimum Error Variance (MEV) estimators 

• Gaussian Statistical models and MEV estimators

• Orthogonality in L2 spaces, Projection Theorem and related results

• Comparative study of deterministic and Bayesian estimators

• Regularization of WLS estimators

• Kalman Filter (KF) and Kalman Predictor (KP)

• Stability analysis and convergence of the steady-state Kalman filter (SSKF) and Kalman Predictor (SSKP) 

• Extended Kalman filter (EKF) and Predictor (EKP)

The lessons are entirely contained in the Notes available in this page and collected in chapters, with Summary,  Notation and Appendix sections. The Appendices, Sections and Paragraphs with the footnote ``This section is not required for the final exam''  are supplementary and can be omitted by the student.