Modeling and System Identification

Prof. Moritz Diehl, Katrin Baumgärtner, Naya Baslan, Jakob Harzer, Doga Can Öner


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.

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,

If you have any feedback or questions about course organization write to

Let's meet you fellow MSI students on Monday, November 16th at 10 a.m., and on Wednesday, November 18th at 8.30 a.m.

  • Zoom Meeting, Meeting ID: 852 9843 8501, Passcode: MSIQ&A2020

Lectures and Q&A sessions. Due to Corona regulations, we provide lecture recordings, which are discussed in a weekly Q&A session held via Zoom. The Q&A sessions take place on Wednesdays 9:00 to 10:00h and are meant to discuss questions about the lecture with Prof. Diehl. Please watch the corresponding lecture recordings beforehand, i.e. stick to the lecture schedule given below.

  • Wednesday, 9:00 to 10:00, Zoom Meeting, Meeting ID: 852 9843 8501, Passcode: MSIQ&A2020

Exercises. The exercise sheets include both pen-and-paper exercises as well as programming exercises using Matlab. Exercise sheets are uploaded to the course webpage on Tuesdays. 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. The pen-and-paper exercises should be uploaded to the Ilias course page as a PDF file. We will upload solution recordings to the Ilias course webpage.

There are three exercise sessions on Fridays, you may attend any of the three session! 

  • Friday, 10:00 to 11:00, via Ilias (BigBlueButton) (Naya Baslan, from 078-014)
  • Friday, 11:00 to 12:00, via Ilias (BigBlueButton) (Doga Can Öner,  from 078-014)
  • Friday, 13:00 to 14:00, via Ilias (BigBlueButton) (Jakob Harzer, from 101-026)

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

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

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 20 exercise points in each of the three blocks:

  • Block 1: Exercises 1 - 3 + Microexam 1,
  • Block 2: Exercises 4 - 6 + Microexam 2,
  • Block 3: Exercises 7 - 9 + Microexam 3.

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)

Q&A sessions and Microexams

Wednesday, November 04, 9:00-10:00 Intro session (from 036)
Wednesday, November 11, 9:00-10:00 Q&A session on lecture 1, statistics & linear algebra tutorial
Wednesday, November 18, 9:00-10:00 Q&A session on lecture 2 + 3
Wednesday, November 25, 9:00-10:00 Q&A session on lecture 4 + 5
Wednesday, December 02, 9:00-10:00 Microexam 1 on Chapter 1-4.2
Wednesday, December 09, 9:00-10:00 Q&A session on lecture 6 + 7 + 8
Wednesday, December 16, 9:00-10:00 Q&A session on lecture 9 + 10
Wednesday, January 13, 9:00-10:00 Microexam 2 on Chapter 4.2-5.4
Wednesday, January 20, 9:00-10:00 Q&A session on lecture 11 + 12 + 13
Wednesday, January 27, 9:00-10:00 Q&A session on lecture 14 + 15
Wednesday, February 03, 9:00-10:00 Microexam 3 on Chapter 6.3-7, 9-9.3
Wednesday, February 10, 9:00-10:00 Q&A session on lecture 16 + 17


 Lecture Schedule (Recordings)

date topic chapters
Friday, November 6 Lecture 1: Introduction + Resistance Estimation 1-1.2
Wednesday, November 11 Lecture 2: Resistance Estimation + Statistic Basics 1.2.2-2.3
Friday, November 13 Lecture 3: Random Variables + Statisitical Estimators 2.3-2.4
Wednesday, November 18 Lecture 4: Resistance Estimation Revisited 2.5-3.1
Friday, November 20 Lecture 5: Optimization Basics + Linear Least Squares 3.1-4.2
Wednesday, November 25 Lecture 6: WLS + Ill-posed Problems 4.3-4.4.1
Friday, November 27 Lecture 7: Statistical Analysis of WLS 4.5-4.7
Wednesday, December 02 ---  
Friday, December 04 Lecture 8: Maximum Likelihood Estimation 5-5.1.1
Wednesday, December 09 Lecture 9: MAP Estimation + Recursive LLS 5.2-5.3.2
Friday, December 11 Lecture 10: Cramer Rao Bound 5.3-5.4
Wednesday, December 16 Lecture 11: Practical Solution of NLS 5.5.-6.2.2
Friday, December 18 Lecture 12: Dynamic System Classes 6.2.3-6.5.2
Friday, January 15 Lecture 13: Output and Equation Errors 7.1-7.3
Wednesday, January 20 Lecture 14: State Space Models 7.4
Friday, January 22 Lecture 15: RLS + Kalman Filter 9.1-9.3
Wednesday, January 27 Lecture 16: Extended Kalman Filter 9.5
Friday, January 29 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.

Solution recordings can be found on the ilias course page.

exercise sheet  published on   due
Sheet 1: Linear Algebra Basics + Estimator Example (data) 10. November 18. November, 9 a.m.
Sheet 2: Statistics + Parameter Estimation 17. November 25. November, 9 a.m.
Sheet 3: Optimality Conditions + Linear Least Squares (data) 24. November 02. December, 9 a.m.
Sheet 4: Weighted Linear Least Squares (data) 01. December 09. December, 9 a.m.
Sheet 5: Ill-Posed Linear Least Squares + Regularization (data) 08. December 16. December, 9 a.m.
Sheet 6: ML and MAP Estimation (data) 15. December 13. January, 9 a.m.
Sheet 7: Recursive Least Squares (updated!) (data) 16. December 20. January, 9 a.m.
Sheet 8: Nonlinear Least Squares + Linear Kalman Filter (data 1, data 2) 19. January 27. January, 9 a.m.
Sheet 9 26. January 03. February, 9 a.m.



We recommend students to install MATLAB on their laptop. The university provides licences.

There is an online (in browser) version of MATLAB. This service is provided by MathWorks and can be accessed with a MathWorks account. We won't be able to provide support for the online version and the exercises may exceed its capabilities.

The Matlab exercises should be handed in via Matlab Grader. you'll get an invitation link on Wednesday, November 4th, please note that you can use your MathWorks account (which is needed to install Matlab) to register with Matlab Grader.

If you have never used Matlab before, check out this tutorial.


Supplementary Material accompanying the Q&A Sessions by the lecturer


  • Corona Modelling: new cases per day in Germany by Robert Koch Institut (we removed the public link to the table with personal corona predictions but sent it via email to all participants)
  • CO2 Modelling in the 1980s: The Guardian, Original Report from Exxon in 1982
  • Nov 11, 2020, Task 1: Recent CO2 Data from Mauna Loa (for group prediction task on Nov 11). Task 1: Look at the data and predict the CO2 Level on July 1st, 2021. Data: co2_trend_mlo.pdfco2_data_mlo.pdf
  • Nov 11, 2020, Task 2: An identification experiment was performed on an electric motor, which is initially at rest. The time scale is in seconds. The input voltage was modified in steps (0,1,2,0 Volt) and the resulting speed output (in rad/s) was observed to follow with some lag (electric-motor-identification-data.pdf). A second plot shows a second input signal that is applied to the electric motor in another experiment. Try to identify the system and predict which speed the motor will have at time 4s, along with a confidence interval (electric-motor-input-data-for-prediction-task.pdf). (Google sheet link removed here, but still available in Ilias).
  • Jan. 20, 2021: Simplest Corona Model (population based): photo of blackboard