autumn 2020
TEK-3017 Applied Optimal Estimation in Engineering Systems - 10 ECTS

Application deadline

Applicants from Nordic countries: 1 June for the autumn semester and 1 December for the spring semester. Exchange students and Fulbright students: 1 October for the spring semester and 15 April for the autumn semester.

Type of course

The course is a technical specialization course and can be taken as a singular course.

Admission requirements

Kode 9371

Course overlap

If you pass the examination in this course, you will get an reduction in credits (as stated below), if you previously have passed the following courses:

TEK-8017 Applied Optimal Estimation in Engineering Systems 7 stp

Course content

The course will contain the main parts:

  • Introduction to linear systems with observers
  • Optimal estimation for linear systems
  • Linear systems with white system and measurement noise
  • Approximation of continuous-time linear stochastic systems
  • The Bayesian approach to parameter estimation
  • Kalman filter (KF) and Extended Kalman filter (EKF)
  • KF and EKF in navigation systems

Objectives of the course


The student ...

  • has advanced knowledge in understanding of linear systems in 1) various engineering applications, 2) fundamental concepts and methods on detection and estimation theory for signal processing, and 3) fundamental concepts and methods on linear systems in the presence of stochastic disturbances,
  • has in-depth knowledge in the core methods of this scientific field; Kalman filter (KF) and extended Kalman filter (EFK) methodologies, and its extensions to linear dynamics for stochastic parameter estimation and prediction problems,
  • can apply the knowledge in KF and EFK methodologies on developing data driven navigation systems.


The student can ...

  • make critical assessment of the uncertainties in measurements and data in navigation systems,
  • utilize parameter estimation to analyse multivariable system dynamics under stochastic random processes with noisy measurements
  • analyse the future behavior in the state variables of dynamic systems on the basis of past incomplete noisy measurements from one or more sensors (i.e. the sensor fusion approach),
  • utilize models and estimation algorithms, for both discrete-time and continuous-time dynamic systems, subject to one or more stochastic inputs and including noisy measurements from one or more sensors, including the associated algorithms in navigation systems,
  • carry out a R&D project related to navigation systems under guidance.


The student can ...

  • apply knowledge of KF and EFK methodologies in other fields to carry out advanced work tasks and projects,
  • formulate and solve problems, such as detection of event occurrences, extracting relevant information about the event, parameter estimation, system state estimation, and sensor fusion,
  • communicate relevant problems, analysis and conclusions in the field of navigation systems to experts and non-experts,
  • participate in brainstorming and innovation processes related to the subject.

Language of instruction and examination


Teaching methods

30 hours lectures , Case studies and group-work.


Report and oral exam.

The report counts 60 % and the oral exam counts 40 % in the final grading.

Both parts of the examination (the report and oral examination) must be passed to get the final grade. These two parts will be evaluated independent of each other.

Letter grading A - E, F - fail

Re-submit report and re-sit exam oral will be held the following semester. If the student has failed either parts of the course (the report or oral exam) he or she can re-submit/re-sit the failed part

  • About the course
  • Campus: Tromsø |
  • ECTS: 10
  • Course code: TEK-3017