Please note! Course description is confirmed for two academic years (1.8.2018-31.7.2020), which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.


The student understands the main concepts in stochastics, mathematics and main concepts related to estimation and state estimation, the role of uncertainty in dynamic systems and is able to implement state estimation algorithms both in linear and nonlinear case. The student understands what duality between control and estimation means in control engineering and, from this point of view,  the main approaches of stochastic control.

Credits: 5

Schedule: 08.09.2020 - 08.12.2020

Teacher in charge (valid 01.08.2020-31.07.2022): Arto Visala

Teacher in charge (applies in this implementation): Arto Visala

Contact information for the course (valid 31.08.2020-21.12.2112):

Lecturer: DSc Arto Visala,, +358 50 5755936

Assistant: MSc Tabish Badar,, +358 50 5507847

CEFR level (applies in this implementation):

Language of instruction and studies (valid 01.08.2020-31.07.2022):

Teaching language: English

Languages of study attainment: English


  • Valid 01.08.2020-31.07.2022:

    Basics of statistics and stochastic processes. Basic concepts in estimation, ML, MAP, LS, MMSE; unbiased estimators. Linear estimation in static systems. Optimal state estimation in discrete linear dynamic systems, Kalman filter and information filter. Optimal State estimation in nonlinear dynamic systems, recursive functional relationship. Approximation of optimal nonlinear state estimation, particle filter, extended Kalman filters, 1st and 2nd order. Adaptive estimation. Duality of estimation and control. Main approaches in stochastic control.

Assessment Methods and Criteria
  • Valid 01.08.2020-31.07.2022:

    Final exam (66%), assignments (34%).

  • Applies in this implementation:

    In autumn 2020 evaluation consists of Exam (100%), in exam you can get extra points corresponding one grade by submitting in time valid Home assignments given in connection of exercises. It is possible to get the excellent grade without  Home assignments, but it is not easy.

  • Valid 01.08.2020-31.07.2022:

    Contact teaching, independent studies and work based-learning, examination

    Contact teaching: 12 X 2 +5 x 2 = 34 h
    Indepenedent work: 97 h


Study Material
  • Valid 01.08.2020-31.07.2022:

    Yaakov Bar-Shalom, et al: Estimation with applications to tracking and navigation (2001). Notes on duality and stochastic control.

Substitutes for Courses
  • Valid 01.08.2020-31.07.2022:

    Substituted (2015) AS-84.3128 Estimation and Sensor Fusion Methods

  • Valid 01.08.2020-31.07.2022:

    Basic knowledge of control engineering and robotics, basic probability theory and statistics.



Registration and further information