ASE-5037 Model-Based Estimation, 5-7 cr
Additional information
Suitable for postgraduate studies
Person responsible
Robert Piche
-->Requirements
(Exam and/or term project) and homework. Requirement for full 7 credits is participation in exercises, passing the exam, and writing a term project paper. Requirement for 5 credits: either (exercises and exam) or (exercises and term project).
Completion parts must belong to the same implementation
Learning Outcomes
The student can apply modern algorithms of Bayesian filtering and smoothing. Student is capable of (grade (3/5)) 1. using the basic concepts and formulas of probability and Bayesian statistical inference. 2. presenting a time-series estimation problem in a state-space form and understanding its statistical assumptions and limitations. 3. implementing the Kalman filter and the most common approximations of the nonlinear Bayesian filter and smoother. 4. understanding the approximations and limitations of different non-linear filters. 5. estimating static parameters of the state space model. Grade (1/5): the goal 4 and at least two other goals achieved
Content
| Content | Core content | Complementary knowledge | Specialist knowledge |
| 1. | Multivariate probability basics and the multivariate Gaussian distribution. | Chebyshev inequality | Laws of total expectation and total variance |
| 2. | Kalman filter | Stationary Kalman filter; information filter; missing measurement | discretisation of stochastic differential equation; Joseph formula |
| 3. | EKF, UKF | EKF2, GHKF | |
| 4. | Bootstrap particle filter | importance sampling; SIR | stratified resampling, RB particle filter |
| 5. | RTS smoother | extended RTS smoother; particle smoother | fixed-lag smoother; fixed-point smoother |
| 6. | state-space model parameter estimation using MCMC | estimation using EM |
Study material
| Type | Name | Author | ISBN | URL | Additional information | Examination material |
| Book | Bayesian Filtering and Smoothing | Simo Särkkä | 9781107619289 | The pdf is freely available online | Yes |
Prerequisites
| Course | Mandatory/Advisable | Description |
| ASE-2510 Johdatus systeemien analysointiin | Advisable |
Additional information about prerequisites
Knowledge of dynamic system modeling and probability from any suitable course is sufficient.
Correspondence of content
There is no equivalence with any other courses