Credits: 5

Schedule: 09.01.2019 - 10.04.2019

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

The lecturer of the course is Prof. Simo Särkkä ( and the course assistant is M.Sc. Filip Tronarp (

Teaching Period (valid 01.08.2018-31.07.2020): 

III‐IV 2019-2020 (spring)

Learning Outcomes (valid 01.08.2018-31.07.2020): 

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

Content (valid 01.08.2018-31.07.2020): 

Statistical modeling and estimation of non‐linear and non‐Gaussian 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 non‐linear
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 01.08.2018-31.07.2020): 

Final exam, home exercises, and project work.

Elaboration of the evaluation criteria and methods, and acquainting students with the evaluation (applies in this implementation): 

The course is evaluated based on final exam, home exercises, and project work. The grade of the course is the maximum of the grades of the examination and project work. You need to pass both the examination and the project work to pass the course. To pass the course, you also need to do at least 1/2 of the home exercises. Furthermore if you do (at least) 3/4 of the exercises, your grade increases by one (1 -> 2, 2 -> 3, 3 -> 4, 4 -> 5).

Workload (valid 01.08.2018-31.07.2020): 

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

Study Material (valid 01.08.2018-31.07.2020): 

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

Details on the course materials (applies in this implementation): 

The course book can be found in the following link and is also available, e.g., in Amazon:

Additional materials (examples from the book, etc.) can be found on the book's homepage (tab "Resources"):

Course Homepage (valid 01.08.2018-31.07.2020):

Prerequisites (valid 01.08.2018-31.07.2020): 

Basics of Bayesian inference, multivariate calculus and matrix algebra. Basic knowledge or
ability to learn to use Matlab or Octave is needed for completing the exercises. "ELEC‐E8104 Stochastic
models and estimation" is recommended, as well as "BECS‐E2601 Bayesian data analysis".

Grading Scale (valid 01.08.2018-31.07.2020): 


Registration for Courses (valid 01.08.2018-31.07.2020): 

via Weboodi

Further Information (valid 01.08.2018-31.07.2020): 

language class 3: English

Details on the schedule (applies in this implementation): 

The exercises and lectures are on Wednesdays in AS4 (1023-1024) in Maarintie 8 (TUAS). The exercises are at 14:15-15:00 and the lectures are 15:15-17:00. The lecture/exercise schedule below is preliminary and might change during the course. Note that the first lecture is on January 9th and there is no exercise session on that day.

  • 9.1. Overview of Bayesian modeling of time-varying systems (no exercise session before this lecture)
  • 16.1. From linear regression to Kalman filter and beyond
  • 23.1. Bayesian optimal filtering equations and the Kalman filter
  • 30.1. Extended Kalman filter, and statistic linearization
  • 6.2. Unscented Kalman filter, Gaussian Filter, GHKF and CKF
  • 13.2. Particle filtering
  • 20.2. (no lecture, no exercise session)
  • 27.2. Rao-Blackwellized particle filtering & information on project work
  • 6.3. Bayesian optimal smoother, Rauch-Tung-Striebel smoothing
  • 13.3. Gaussian and particle smoothers
  • 20.3. Bayesian estimation of parameters in state space models
  • 27.3. Recap of the course topics and project work information
  • 3.3. Individual project work starts
  • 3.4. Project work deadline
  • 10.4. Examination


Registration and further information