- Basics on probability theory.

- Basics on estimation theory. Optimality criteria: centering, consistency, efficiency. Rao-Cramer lower-bound for covariance.

- Optimal estimation: least square estimates (WLS), maximal likelihood estimates (ML) and Bayesian estimates (B).

- Kalman filtering and prediction (KF and KP). Steady state Kalman filter (SSKF) and asympotitc optimality.

- Parametric identification. Identification with test inputs/control inputs. Identification for input-output and state space models. Mixed ML-KF techniques of identification

- Autoregressive models: AR, MA, ARMA and ARMAX models.


Notes on Filtering and System Identification:

1^ Module (probability spaces and random variables)

2^ Module (random vectors, orthogonality of random variable, types of convergence)

3^ Module (conditional probabilities and expectations, Bayes formulas)

4^ Module (Introduction to estimation theory, deterministic and stochastic estimates, stochastic estimates with minimum error variance)

5^ Module (Comparison criteria for optimal estimates: centering, efficiency, consistency; Cramer-Rao lower bound; weighted least squares and maximum likelihood estimators, optimal estimation of parameters and random variables)

6^ Module (Kalman filter; steady state Kalman filter; extended Kalman filter)

7^ Module (System identification: parametric identifiability and persistently exicitation)


EXAM STRUCTURE: The exam consists of an oral part on the topics covered in the course (see the syllabus) and the discussion of a project (see list of available projects below). Oral part and discussion of the project are done during the same exam session.

PROJECT DESCRIPTION: Each project is focused on specific theoretical topics or practical applications of theoretical results, studied and pioneered in scientific papers.

PROJECT REPORTS: A detailed written report must be produced on the assigned paper, proving a complete understanding of the technical solutions and simulations given in the paper and using detailed technical discussions and motivations.

PROJECT ASSIGNMENT: Each project is assigned to a maximum number of 3 students (different reports for each student). A project assignment request must be sent via e-mail to enclosing the name of the student(s) and his/her/their student number(s). The teacher will assign a project to the student(s) and a notification for the assignment with the project's identification number is sent immediately after.

DEADLINES: There is no deadline for assignment requests.


1) Extended Kalman filtering and weighted least squares dynamic identification of robot (paper) assigned to (#1843827, #1851121, #1858800)

2) Conditional Particle Filters for Simultaneous Mobile Robot Localization and People-Tracking (paper) assigned to #1495927, #1351445

3) System identification application using Hammerstein model (paper) assigned to # 1838538, (#1874590, #1707133)

4) Methods for the Nonlinear Transformation of Means and Covariances in Filters and Estimators (paper) assigned to #1637910, #1651036, #1858800

5) Localization of Mobile Robot using Particle Filter (paper) assigned to (#1684483, #1695082), (# 1596825, #1637371)

6) Unscented Kalman Filter (paper) assigned to # 1557024, #1611468, #1595304

7) Recursive Least Squares Estimation (paper) assigned to #1696842, #1420745

8) Subspace identification (paper) assigned to (# 1699966, #1694755, #1700819)

9) Overview of Maximum likelihood estimators (paper) (not assignable)

10) System Identification in Computer Vision (paper) assigned to #1659325, (#1693370, #1697872)

11) Nonlinear Identification Methods for Modeling Biomedical Systems (paper) assigned to (#1832994, #1695426), #1857850

12) Stochastic Stability of the Discrete-Time Extended Kalman Filter (paper) (not assignable)

13) Autoregressive Moving Avarage models I (paper) (not assignable)

14) Autoregressive Moving Avarage models II (paper) (not assignable)

15) Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking (paper) assigned to #1874590

16) Monte Carlo Particle Filter (paper) assigned to (#1848061, #1848003)

17) Particle Filters (paper) assigned to (# 1472014, #1580288), #1702840

18)Prediction Error Estimation Methods (paper) assigned to #1806661, (#1876166, #1722271)

19) Unscented Kalman Filtering for spacecraft attitude state and parameter estimation (paper) assigned to (#1710064, #1705326, #1700528)

20) Particle filter for UAV trajectory prediction under uncertainties (paper) assigned to (#1699272, #1709036), (#1872807, # 1852470)


Friday from 3 to 6 p.m. (Via Ariosto 25, room A207)