Please note! Course description is confirmed for two academic years, 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: 03.09.2024 - 04.12.2024

Teacher in charge (valid for whole curriculum period):

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

Contact information for the course (applies in this implementation):

CEFR level (valid for whole curriculum period):

Language of instruction and studies (applies in this implementation):

Teaching language: English. Languages of study attainment: English


  • valid for whole curriculum period:

    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 for whole curriculum period:

    Final exam, assignments.

  • valid for whole curriculum period:

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


Study Material
  • valid for whole curriculum period:

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

    Torsten Söderström: Discrete-Time Stochastic Systems - Estimation and Control.  Second edition, Springer-Verlag, London, UK, 2002. (375 pp) 

Substitutes for Courses


Further Information
  • valid for whole curriculum period:

    Teaching Language: English

    Teaching Period: 2024-2025 Autumn I - II
    2025-2026 Autumn I - II