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 Bayesian basis of estimation in linear and nonlinear dynamic systems. The student understands the principles behind approximate filters and smoothers, and is able to use them in practice. The student knows how to estimate parameters online and offline in nonlinear systems.

Credits: 5

Schedule: 13.01.2021 - 14.04.2021

Teacher in charge (valid 01.08.2020-31.07.2022): Ville Kyrki, Simo Särkkä

Teacher in charge (applies in this implementation): Ville Kyrki, Simo Särkkä

Contact information for the course (valid 27.12.2020-21.12.2112):

Prof. Simo Särkkä (

Co-lecturers / assistants:
M.Sc. Zheng Zhao (

Please add "ELEC-E8106" to the subject when sending email concerning the course.

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:

    Statistical modeling and estimation in nonlinear and nonGaussian systems. Bayesian filtering and smoothing theory. Extended Kalman filtering and smoothing, sigma point and unscented filtering and smoothing, sequential Monte Carlo particle filtering and smoothing. Adaptive nonlinear filtering; ML, MAP, MCMC, and EM estimation of system parameters. Example applications from navigation, remote surveillance, and time series analysis.

Assessment Methods and Criteria
  • Valid 01.08.2020-31.07.2022:

    Final exam, home exercises, and project work.

  • Valid 01.08.2020-31.07.2022:

    Contact teaching 26 h (lectures and exercise sessions), independent studies and project work
    110 h, examination 3 h


Study Material
  • Valid 01.08.2020-31.07.2022:

    Särkkä: Bayesian Filtering and Smoothing (2013), handouts.

Substitutes for Courses
  • Valid 01.08.2020-31.07.2022:

    Substitutes ELEC-E8105 - Non-linear Filtering and Parameter Estimation

  • Valid 01.08.2020-31.07.2022:

    Basics of (Bayesian) statistics, multivariate calculus, and matrix algebra. Basic knowledge of Matlab, Octave, or Python is needed for completing the exercises and project work. "ELEC-E8740 Basics of sensor fusion" is recommended, and "CS-E5710 Bayesian Data Analysis" can be useful.

SDG: Sustainable Development Goals

    9 Industry, Innovation and Infrastructure