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Modelling and System Identification

Lecturer Prof. M. DiehlSemester WiSe 2026/27Language English Exam date not setSources msi Schoukens_sysid_2013 Open in graph ↗
2 of 23 lecture notes written · VL03 held, no note yet

Lecture plan

Lectures follow the script · status as of Sat 31 Oct 2026
VLDateSessionChaptersNote
01Introduction1.0–1.2Written
02Probability and Statistics in a Nutshell2.0–2.3.1Written
Linear algebra tutorial–
03Lecture2.3.2–2.4No note yet
Today · Sat 31 Oct
Statistics tutorial–
04Lecture2.4–3.1Planned
05Lecture3.2–4.2Planned
06Lecture4.3–4.4.1Planned
07Lecture4.5–4.5.3Planned
08Lecture4.5–4.7Planned
09Lecture5–5.2.2Planned
10Microexam 1 (08:15–09:00), then lecture5.3Planned
Show 20 later sessionsHide 20 later sessions
VLDateSessionChaptersNote
11No lecture (recording)5.4–5.5Planned
12No lecture (recording)6–6.1.2Planned
13No lecture (recording)6.2–6.4Planned
14Lecture7–8.2Planned
15Lecture8.2–8.5Planned
16Lecture8.6Planned
17Lecture8.7Planned
Microexam 2 (08:15–09:00)–
No lecture–
No lecture, no exercise sessions–
18Lecture: proof of the Cramér–Rao inequality5.4.1Planned
19Lecture–Planned
20Lecture–Planned
21Lecture–Planned
Summary Ch. 1–4–
Microexam 3 (08:30–09:15), then summary Ch. 5–
Summary Ch. 6–8–
22Lecture–Planned
23Lecture–Planned
Summary + Q&A–

Course info

from the course index note

Schedule#

  • Lectures: Mon 08:15–09:55 (101, HS 026) and Wed 08:15–09:55 (101, HS 036), 2026-10-19 to 2027-02-10. Recordings on the video portal.
  • My exercise group (Group 1): Wed 14:00–16:00, building 51, SR 00 031 (tutor N.N.)
  • Hand-in: before the Monday lecture at 08:15, either in the lecture or in the mailbox in front of room 00-075 (building 102, ground floor). Programming exercises go through GitHub Classroom. Groups of up to 3 students, one week per sheet.
  • Put all group members’ matriculation numbers on every hand-in. There’s no mandatory sheet in the first weeks; the linear algebra and statistics tutorials come first.
  • Coding workflow: accept the sheet on GitHub Classroom → clone (just clone-sheet nn <url>) → run pytest locally → push. The tests are rerun on the server.
  • Tutor contact: syscop.msi@gmail.com

People#

  • Lecturer: Prof. Moritz Diehl
  • Co-lecturers: Ashwin Karichannavar, Katrin Baumgärtner

Exam & Studienleistung#

  • Final exam: written, closed book, date TBD. Allowed: pencil, paper, calculator, 2 handwritten double-sided A4 formula sheets. The grade comes only from the exam.
  • Register for both “MSI Exam” and “MSI Studienleistung”.
  • Studienleistung: at least 50 % in each block:
    • Block 1: Sheets 1–3 + Microexam 1 (40 pts, need 20)
    • Block 2: Sheets 4–6 + Microexam 2 (40 pts, need 20)
    • Block 3: Sheets 7–10 + Microexam 3 (40 pts + 10 bonus, need 20)
  • Microexams: 45 min, 20 multiple-choice questions on that block’s lectures and exercises
    • MSI Microexam 1 (not published): Wed 2026-11-25, 08:15–09:00
    • MSI Microexam 2 (not published): Wed 2026-12-23, 08:15–09:00
    • MSI Microexam 3 (not published): Wed 2027-01-27, 08:30–09:15
  • Past exams (in exam/past_exams/pdfs/): 2014 (PDF not published), 2015 (PDF not published), 2018 (PDF not published), 2019 (PDF not published). Skip questions on Appendix C (not taught this year).

Material#

Lectures Table#

Generated viewLecture planshown above

Topics & Concepts#

Generated viewTopics and conceptsshown below

Exercises & Studienleistung#

Lecture Plan (tentative)#

Lecture plan32 sessionsshown above with their notes and status

URLS#

Topics & concepts of this course

1 topic · 3 concepts
Resistance Estimation Example

The running example of MSI chapters 1–2, estimating a resistance from noisy voltage and current measurements with three plausible estimators that converge to three different values, and the noise-model analysis that shows which one is asymptotically unbiased.

Foundations used by this course

marked as used in MSI, or covered by its lectures
Analysis1 topic · 1 concept

Jacobian Matrix

Linear Algebra2 topics · 8 concepts

Determinant · Eigenvalue · Eigenvector · Invertible Matrix · Linear Map · Matrix Rank · Positive Semidefinite Matrix · System of Linear Equations

Probability and Statistics3 topics · 20 concepts

Asymptotically Unbiased Estimator · Bayes' Theorem · Conditional Probability · Consistent Estimator · Correlation · Covariance · Covariance Matrix · Estimator · Expected Value · Law of Large Numbers · Multivariate Normal Distribution · Normal Distribution · Probability Density Function · Random Variable · Sample Mean · Sample Variance · Statistical Independence · Unbiased Estimator · Uniform Distribution · Variance

Concept index

this course and the foundations it uses · 32
A-posteriori Probability → Bayes' Theorem A-priori Probability → Bayes' Theorem Arithmetic Mean → Sample Mean Arithmetisches Mittel → Sample Mean Asymptotic Unbiasedness → Asymptotically Unbiased Estimator Asymptotically Unbiased → Asymptotically Unbiased Estimator Asymptotically Unbiased Estimator Asymptotisch erwartungstreuer Schätzer → Asymptotically Unbiased Estimator Asymptotische Erwartungstreue → Asymptotically Unbiased Estimator Average → Sample Mean Average of Ratios → Simple Approach EstimatorBayes Rule → Bayes' Theorem Bayes Theorem → Bayes' Theorem Bayes' Law → Bayes' Theorem Bayes' Rule → Bayes' Theorem Bayes' Theorem Bedingte Wahrscheinlichkeit → Conditional Probability Bessel's Correction → Sample Variance Bias → Estimator Biased → Unbiased Estimator Biased Estimator → Unbiased EstimatorCharacteristic Polynomial → Eigenvalue Charakteristisches Polynom → Eigenvalue Conditional Density → Conditional Probability Conditional PDF → Conditional Probability Conditional Probability Consistency → Consistent Estimator Consistent → Consistent Estimator Consistent Estimator Continuous Uniform Distribution → Uniform Distribution Correlation Correlation Coefficient → Correlation cov → Covariance Matrix Covariance Covariance Matrix Covariance Operator → Covariance MatrixDensity Function → Probability Density Function Dependent → Statistical Independence det → Determinant Determinant Determinante → Determinant Dichtefunktion → Probability Density FunctionEigenbasis → Eigenvector Eigenraum → Eigenvector Eigenspace → Eigenvector Eigenspectrum → Eigenvalue Eigenvalue Eigenvalues → Eigenvalue Eigenvector Eigenvectors → Eigenvector Eigenvektor → Eigenvector Eigenwert → Eigenvalue Empirical Mean → Sample Mean Empirical Variance → Sample Variance Empirische Varianz → Sample Variance Error in Variables → Error-in-Variables Estimator Error-in-Variables → Error-in-Variables Estimator Error-in-Variables Estimator Errors-in-Variables Estimator → Error-in-Variables Estimator Erwartungstreue → Unbiased Estimator Erwartungstreuer Schätzer → Unbiased Estimator Erwartungswert → Expected Value Estimate → Estimator Estimator EV Estimator → Error-in-Variables Estimator Expectation → Expected Value Expectation Operator → Expected Value Expectation Value → Expected Value Expected Value Experimental Mean → Sample MeanFunktionalmatrix → Jacobian MatrixGauss Distribution → Normal Distribution Gauß-Verteilung → Normal Distribution Gaussian → Normal Distribution Gaussian Distribution → Normal Distribution Gaussian Random Vector → Multivariate Normal Distribution Gesetz der großen Zahlen → Law of Large Numbers Gleichverteilung → Uniform DistributionHomomorphismus → Linear MapIndependence → Statistical Independence Independent Events → Statistical Independence Independent Random Variables → Statistical Independence Inverse Matrix → Invertible Matrix Invertible Matrix Invertierbare Matrix → Invertible MatrixJacobi Matrix → Jacobian Matrix Jacobi-Matrix → Jacobian Matrix Jacobian → Jacobian Matrix Jacobian Matrix Joint PDF → Probability Density Function Joint Probability → Conditional ProbabilityKonsistenter Schätzer → Consistent Estimator Konsistenz → Consistent Estimator Korrelation → Correlation Korrelationskoeffizient → Correlation Kovarianz → Covariance Kovarianzmatrix → Covariance MatrixLaw of Large Numbers Least Squares → Least Squares Estimator Least Squares Estimator LGS → System of Linear Equations Linear Equation System → System of Linear Equations Linear Function → Linear Map Linear Least Squares Estimator → Least Squares Estimator Linear Map Linear System → System of Linear Equations Linear Transformation → Linear Map Lineare Abbildung → Linear Map Lineares Gleichungssystem → System of Linear Equations LLN → Law of Large Numbers LLS → Least Squares Estimator LS Estimator → Least Squares EstimatorMarginal Distribution → Probability Density Function Matrix Rank Mean → Expected Value Mean Squared Deviation → Sample Variance Mean Value → Expected Value Mehrdimensionale Normalverteilung → Multivariate Normal Distribution Method of Least Squares → Least Squares Estimator Mittelwert → Sample Mean Multidimensional Gaussian → Multivariate Normal Distribution Multidimensional Normal Distribution → Multivariate Normal Distribution Multivariate Gaussian → Multivariate Normal Distribution Multivariate Normal Distribution Multivariate Normalverteilung → Multivariate Normal DistributionNonsingular Matrix → Invertible Matrix Normal Distribution Normally Distributed → Normal Distribution Normalverteilung → Normal DistributionPDF → Probability Density Function Point Estimator → Estimator Positiv definite Matrix → Positive Semidefinite Matrix Positiv semidefinite Matrix → Positive Semidefinite Matrix Positive Definite Matrix → Positive Semidefinite Matrix Positive Semi-Definite Matrix → Positive Semidefinite Matrix Positive Semidefinite Matrix Positive Semidefiniteness → Positive Semidefinite Matrix Probability Density → Probability Density Function Probability Density Function PSD Matrix → Positive Semidefinite MatrixR_EV → Error-in-Variables Estimator R_LS → Least Squares Estimator R_SA → Simple Approach Estimator Random Variable Random Variables → Random Variable Random Vector → Random Variable Rang → Matrix Rank Rang einer Matrix → Matrix Rank Rank → Matrix Rank Regular Matrix → Invertible Matrix Reguläre Matrix → Invertible MatrixSA Estimator → Simple Approach Estimator Sample Mean Sample Variance Satz von Bayes → Bayes' Theorem Schätzer → Estimator Schätzfunktion → Estimator Schätzwert → Estimator Simple Approach → Simple Approach Estimator Simple Approach Estimator Singular Matrix → Invertible Matrix Spectrum → Eigenvalue Standard Deviation → Variance Standard Normal Distribution → Normal Distribution Standardabweichung → Variance Statistical Estimator → Estimator Statistical Independence Stetige Gleichverteilung → Uniform Distribution Stichprobenmittel → Sample Mean Stichprobenvarianz → Sample Variance Stochastic Independence → Statistical Independence Stochastische Unabhängigkeit → Statistical Independence Streuung → Variance Strong Law of Large Numbers → Law of Large Numbers System of Linear EquationsUnabhängigkeit → Statistical Independence Unbiased → Unbiased Estimator Unbiased Estimator Unbiasedness → Unbiased Estimator Uncorrelated → Correlation Uniform Distribution Uniform PDF → Uniform Distribution Unkorreliert → Correlation Unverzerrter Schätzer → Unbiased EstimatorVariance Variance-Covariance Matrix → Covariance Matrix Varianz → VarianceWahrscheinlichkeitsdichte → Probability Density Function Weak Law of Large Numbers → Law of Large NumbersZufallsgröße → Random Variable Zufallsvariable → Random Variable Zufallsvektor → Random Variable

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