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: 11.01.2024 - 17.04.2024

Teacher in charge (valid for whole curriculum period):

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

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:

    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 for whole curriculum period:

    Final exam, home exercises, and project work.

  • valid for whole curriculum period:

    Contact teaching (lectures and exercise sessions), independent studies and project work, examination


Study Material
  • valid for whole curriculum period:

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

Substitutes for Courses


Further Information
  • valid for whole curriculum period:

    Teaching Language : English

    Teaching Period : 2022-2023 Spring III - IV
    2023-2024 Spring III - IV