ASE-7536 Model-Based Estimation, 5-7 cr
Additional information
Requirement for 7 credits is solution of homework problems, passing the exam, and writing a term project paper. Requirement for 5 credits: either (exercises and exam) or (exercises and term project).
Suitable for postgraduate studies.
Person responsible
Robert Piche
Lessons
| Implementation | Period | Person responsible | Requirements |
| ASE-7536 2018-01 | 3 - 4 |
Robert Piche |
Students are required to solve 2/3 of the homework exercises. In this implementation only the 5 credit version of the course (exercises and exam) is offered. There is no term project. |
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 model-based 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. implementing computations and interpret results for 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, treatment of missing measurement | discretisations of stochastic differential equation; Joseph formula |
| 3. | EKF, UKF, bootstrap particle filter | EKF2, GHKF, importance sampling, SIR | stratified resampling, RB particle filter |
| 4. | Bayesian fixed-interval filtering, RTS smoother | RTS extensions; particle smoother | fixed-lag smoothing; fixed-point smoothing |
| 5. | State-space model parameter estimation using MCMC | State space model parameter 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 | Yes |
Prerequisites
| Course | Mandatory/Advisable | Description |
| MAT-02506 Probability Calculus | Mandatory |
Correspondence of content
| Course | Corresponds course | Description |
|
ASE-5030 Optimal Estimation and Prediction Based on Models, 7 cr + ASE-5036 Optimal Estimation and Prediction Based on Models, 7 cr + ASE-7536 Model-Based Estimation, 5-7 cr | MAT-61706 Bayesian Filtering and Smoothing, 5 cr | |
| ASE-7536 Model-Based Estimation, 5-7 cr | ASE-5037 Model-Based Estimation, 5-7 cr |