TEK4050 – Stochastic Systems
Course description
Course content
In this course, you learn about mathematical descriptions of stochastic?systems, and how we can use information about the system, mathematical models as well as measurements, to estimate the state of the system. We concentrate primarily on linear systems in the time domain, for which the Kalman filter is the optimal estimator. We present equations, properties and applications of the discrete and continuous Kalman filter. As part of the course, you will also complete a project assignment, in which you will implement and test a Kalman filter on a computer.
Learning outcome
After completing the course, you will
- have a basic knowledge of state space systems driven by stochastic white noise
- be able to model, simulate and analyze such systems
- have basic knowledge of the properties and applications of the Kalman filter
- know how to design and analyze both optimal and suboptimal Kalman filters for linear stochastic systems
- know how to use the Kalman filter for nonlinear problems
Admission to the course
Students admitted at UiO must apply for courses in Studentweb. Students enrolled in other Master's Degree Programmes can, on application, be admitted to the course if this is cleared by their own study programme.
Nordic citizens and applicants residing in the Nordic countries may apply to take this course as a single course student.
If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures for international applicants.
Recommended previous knowledge
The course builds on knowledge equivalent to what is taught in MAT1110 – Calculus and Linear Algebra, MAT1120 – Linear Algebra, MAT-INF1310 – Ordinary differential equations (discontinued), MAT2310 – Optimal control theory (discontinued), STK1100 – Probability and Statistical Modelling and INF-MAT3350 – Numerical linear algebra (discontinued).
Overlapping courses
- 10 credits overlap with UNIK4500 – Stochastic systems (continued).
Teaching
3 hours of lectures per week throughout the semester.
You must hand in one mandatory term project which must be approved before you can sit the final?exam. In addition, you are encouraged to complete voluntary exercises.
The course lectures are given at the Department of Technology Systems in Kjeller Research Park. See the schedule for the student bus from Campus Blindern.
Examination
- A final oral exam counts 100% towards the final grade.
- The students must hand in one mandatory term project which must be approved before they can sit the final exam.
- In case of a high number of students, the exam may be written instead. This will be announced in the beginning of the semester.
It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for the following course:
Examination support material
No examination support material is allowed.
Language of examination
Courses taught in English will only offer the exam paper in English. You may write your examination paper in Norwegian, Swedish, Danish or English.
Grading scale
Grades are awarded on a scale from A to F, where A is the best grade and F?is a fail. Read more about the grading system.
Resit an examination
Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.
Re-scheduled examinations are not offered to students who withdraw during, or did not pass, the original examination.
More about examinations at UiO
- Use of sources and citations
- How to use AI as a student
- Special exam arrangements due to individual needs
- Withdrawal from an exam
- Illness at exams / postponed exams
- Explanation of grades and appeals
- Resitting an exam
- Cheating/attempted cheating
You will find further guides and resources at the web page on examinations at UiO.