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Course Catalog 2014-2015
ASE-5036 Optimal Estimation and Prediction Based on Models, 7 cr |
Additional information
Suitable for postgraduate studies
Person responsible
Robert Piche
Lessons
| Study type | P1 | P2 | P3 | P4 | Summer | Implementations | Lecture times and places |
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Requirements
Exam, homework and computer exercises, 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 for random vectors | Laws of total expectation and total variance |
| 2. | Kalman filter | Stationary Kalman filter, information filter, discretisation, robust filter | Bayesian Cramer-Rao bound |
| 3. | EKF, UKF, particle filter | GHKF, CKF, Rao-Blackwellized filter | Optimal importance distribution |
| 4. | RTS smoother | Extensions of RTS smoother for nonlinear systems | Particle smoother |
| 5. | Parameter estimation using EM and MCMC | Identification using particle-EM, Particle-MCMC |
Study material
| Type | Name | Author | ISBN | URL | Edition, availability, ... | Examination material | Language |
| Book | Bayesian Filtering and Smoothing | Simo Särkkä | 9781107619289 | Yes | English |
Prerequisites
| Course | Mandatory/Advisable | Description |
| ASE-2510 Johdatus systeemien analysointiin | Advisable | |
| ASE-5016 Advanced Methods of Data-driven Modelling and Analysis | Advisable |
Additional information about prerequisites
Prerequisites are courses given in Finnish. Thus for this course it is sufficient to know the background in modeling and probability from any suitable course.
Prerequisite relations (Requires logging in to POP)
Correspondence of content
| Course | Corresponds course | Description |
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More precise information per implementation
| Implementation | Description | Methods of instruction | Implementation |
| Lectures and exercises for the course. | Lectures Excercises Practical works |
Contact teaching: 40 % Distance learning: 0 % Self-directed learning: 60 % |