**Prof. Moritz Diehl, Katrin Baumgärtner**

Modeling and System Identification (MSI) is concerned with the search for mathematical models for real-life systems. The course is based on statistics, optimization and simulation methods for differential equations. The exercises will be based on pen-and-paper exercises and computer exercises with MATLAB. You can get a **Matlab Student license** via the University, please check here

Course language is English and all course communication is via this course homepage.

If you have any questions regarding the exercises/lectures, please send an **email to the tutors**, syscop.msi@gmail.com

If you have any feedback or questions about course organization write to katrin.baumgaertner@imtek.uni-freiburg.de

**Lectures. **The lectures will take place on Mondays, 8:00 - 10:00 a.m, Building 101, HS 036, and Wednesdays, 9:00-10:00, Building 101, HS 026. It is possible to attend both in person and remotely via Zoom

- https://uni-freiburg.zoom.us/j/62699713471?pwd=Y1RQajRrT21DNFVJelRuQjVvK1AwUT09
- Passcode: MSIWS2021

If you cannot attend, you may watch the lecture recordings, see below.

**Exercises. **The exercise sheets include both pen-and-paper exercises as well as programming exercises using Matlab. Exercise sheets can be handed in during the Q&A session on Mondays or might be uploaded to the course ILIAS page. You have one week to work on the sheet and you might work in groups of at most three students. Programming exercises should be handed in via Matlab Grader.

There are three exercise sessions.

- Wednesdays, 12:00-13:00, in-person, room: SR 00 014 (G.-Köhler-Allee 078)
- Wednesdays, 12:00-13:00, online, via BigBlueButton (available via Ilias)
- Wednesdays, 16:00-17:00, online, via BigBlueButton (available via Ilias)

During the exercise session, the exercise solutions are discussed. Afterwards there is room for questions on the current exercise sheet.

Please join the **ILIAS course**: https://ilias.uni-freiburg.de/goto.php?target=crs_2368593_rcodeaeYdrEHFgD&client_id=unifreiburg

**Written material.** The lecture closely follows the script, which can be found below:

- Lecture Notes on Modelling and System Identification (unrevised, from start of semester)
- Additional Section 4.5.3 on Cramer Rao Lower Bound for Linear Estimators: PDF
- Additional Section 5.4.1 on the Proof of the Cramer Rao Inequality: PDF
- REVISED VERSION of the lecture notes: PDF

Please note that we do *not *cover Chapter 8 and Chapter 9.4. Additional material that covers some of the lecture contents:

- A script by Johan Schoukens (Vrije Universiteit Brussel, Belgium), which can be found here.
- The textbook
*Ljung, L. (1999). System Identification: Theory for the User. Prentice Hall*. This book is available in the faculty library.

#### Final Evaluation and Microexams

Please make sure you register for both the *MSI Exam* and the *MSI Studienleistung*!

The final grade of the course is based solely on a final written exam at the end of the semester. The final exam is a closed book exam, only pencil, paper, and a calculator, and two handwritten double-sided A4 sheets of self-chosen formulae are allowed.

Each exercise sheet gives a maximum of 10 points. Three online microexams written during some of the lecture slots give a maximum of 10 exercise points each. In order to pass the exercises accompanying the course (*Studienleistung*), one has to obtain at least 50% of the maximum exercise points in each of the three blocks:

- Block 1: Exercises 1 - 3 + Microexam 1 (total 40 points)
- Block 2: Exercises 4 - 6 + Microexam 2 (total 40 points)
- Block 3: Exercises 7 - 10 + Microexam 3 (total 40 points + 10 bonus points)

To prepare for the written exam, check out the exams from previous semesters: 2018, 2015, 2014. (Please note that these exams contain questions on Chapter 8 of the MSI script, which is *not* covered in this year's lecture)

#### Lectures and Microexams

Monday, October 18, 8:00-10:00 | Intro session | QR |

Wednesday, October 20, 9:00-10:00 | Lecture | QR |

Monday, October 25, 8:00-10:00 | Lecture | QR |

Wednesday, October 27, 9:00-10:00 | Lecture | QR |

Wednesday, November 10, 9:00-10:00 | Guest Lecture: Andrea Ghezzi slides code | |

Monday, November 8, 8:00-10:00 | Lecture | QR |

Wednesday, November 10, 9:00-10:00 | Lecture | QR |

Monday, November 15, 8:00-10:00 | Lecture | QR |

Wednesday, November 17, 9:00-10:00 | Microexam 1 on Chapter 1-4.2 (online) | |

Monday, November 22, 8:00-10:00 | Lecture | QR |

Wednesday, November 24, 9:00-10:00 | Lecture | QR |

Monday, November 29, 8:00-10:00 | Lecture | QR |

Wednesday, December 01, 9:00-10:00 | Lecture | QR |

Monday, December 6, 8:00-10:00 | Lecture | QR |

Wednesday, December 8, 9:00-10:00 | Lecture | QR |

Monday, December 13, 8:00-10:00 | Lecture | QR |

Wednesday, December 15, 9:00-10:00 | Lecture | QR |

Monday, December 20, 8:00-10:00 | Lecture | QR |

Wednesday, December 22, 9:00-10:00 | Microexam 2 on Chapter 4.2-5.4 (online) | |

Monday, January 10, 8:00-10:00 | Lecture | QR |

Wednesday, January 12, 9:00-10:00 | Lecture | QR |

Monday, January 17, 8:00-10:00 | Lecture | QR |

Wednesday, January 19, 9:00-10:00 | Lecture | QR |

Monday, January 24, 8:00-10:00 | Lecture | QR |

Wednesday, January 26, 9:00-10:00 | Microexam 3 on Chapter 6.3-7 (online) | |

Monday, January 31, 8:00-10:00 |
Lecture + Guest Lecture on Rotor Kite Identification by Daniel Unterweger (online) |
QR |

Wednesday, February 2, 9:00-10:00 | Lecture | QR |

Monday, February 7, 8:00-10:00 | Lecture | QR |

Wednesday, February 9, 9:00-10:00 | Summary Session |

**Lecture Recordings**

date |
topic |
chapters |

October 18 - October 22 | Lecture 1: Introduction + Resistance Estimation | 1-1.2 |

October 25 - October 29 | Lecture 2: Resistance Estimation + Statistic Basics | 1.2.2-2.3 |

October 25 - October 29 | Lecture 3: Random Variables + Statisitical Estimators | 2.3-2.4 |

November 8 - November 12 | Lecture 4: Resistance Estimation Revisited | 2.5-3.1 |

November 8 - November 15 | Lecture 5: Optimization Basics + Linear Least Squares | 3.1-4.2 |

November 22 - November 26 | Lecture 6: WLS + Ill-posed Problems | 4.3-4.4.1 |

November 29 - December 3 | Lecture 7: Statistical Analysis of WLS | 4.5-4.7 |

November 29 - December 3 | Lecture 8: Maximum Likelihood Estimation | 5-5.1.1 |

December 6 - December 10 | Lecture 9: MAP Estimation + Recursive LLS | 5.2-5.3.2 |

December 6 - December 10 | Lecture 10: Cramer Rao Bound | 5.3-5.4 |

December 13 - December 17 | Lecture 11: Practical Solution of NLS (Part 1, Part 2) | 5.5.-6.2.2 |

January 10 - January 14 | Lecture 12: Dynamic System Classes (old) | 6.2.3-6.5.2 |

January 10 | Lecture: Dynamic systems (new) (Part1, Part2) | |

January 14 | Lecture: ODEs and numerical integration | |

January 17 - January 21 | Lecture 13: Output and Equation Errors | 7.1-7.3 |

January 24 - January 28 | Lecture 14: State Space Models | 7.4 |

January 31 - February 4 | Lecture 15: RLS + Kalman Filter | 9.1-9.3 |

February 7 - February 11 | Lecture 16: Extended Kalman Filter | 9.5 |

February 7 - February 11 | Lecture 17: Moving Horizon Estimation | 9.6 |

#### Exercises and Tutorials

In the first week, there is no exercise sheet, but if you don't feel too confident about your linear algebra and statisitics skills, you might want to check out these tutorials that cover the basics needed for the MSI course.

You can get a Matlab Student license via the University, please check here

Sheet | Material | Deadline |

Sheet 1: Linear Algebra Basics + Estimator Example | data | November 2 |

Sheet 2: Statistics + Parameter Estimation | November 8 | |

Sheet 3: Optimality Conditions and Linear Least Squares | data | November 15 |

Sheet 4: Weighted Linear Least-Squares | data | November 29 |

Sheet 5: Ill-Posed Linear Least-Squares & Regularization | data | December 6 |

Sheet 6: Maximum Likelihood and MAP Estimation | data | December 13 |

Sheet 7: Recursive Least Squares | data | January 10 |

Sheet 8: Nonlinear Least Squares | data | January 17 |

Sheet 9: Kalman Filter | data | February 7 |

(Bonus) Sheet 10: Extended Kalman Filter | data | February 14 |

Check In for exercise sessions: