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Course Catalog 2012-2013
ASE-5036 Optimal Estimation and Prediction Based on Models, 7 cr |
Additional information
Suitable for postgraduate studies
Person responsible
Risto Ritala
Lessons
| Study type | P1 | P2 | P3 | P4 | Summer | Implementations | Lecture times and places |
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Requirements
Exam. Homework exercises and computer exercises.
Learning outcomes
This course presents the methods to describe state information of a stochastic system and methods to update this information based on uncertain measurement data. Static and dynamic (both discrete and continuous time) systems. Student is capable of (grade (3/5) 1. To form the state estimate and estimate uncertainty for a system described with linear Gaussian model based on uncertain/incomplete data about state. 2. To present the principle of updating state information recursively for a Markov process; the principle of Bayes filter. 3. To construct a Kalman filer for linear Gaussian discrete time system. 4. To construct a Kalman filter for continuous time linear-Gaussian system, the state being measured at irregular intervals. 5. To construct dynamic validation algorithm for a linear static base function model (e.g. the calibration curve of a sensor). Grade (1/5): at least four of the goals achieved.
Content
| Content | Core content | Complementary knowledge | Specialist knowledge |
| 1. | Gaussian distribution and conditional distributions derived from it. | Mutual information and Kullback-Leibler distance. | Fisher Information and Cramer-Rao inequality. |
| 2. | Markov property and the resulting principle of updating state information recursively. Bayes filter. | Bias, uncertainty, consistency and efficiency of an estimate. | Kramers-Moyal equation |
| 3. | Kalman filter for linear-Gaussian system. | Fokker-Planck equation. | |
| 4. | Solution of a linear stochastic differential equation; the dynamics of the state information. | Optimizing reference measurements. | |
| 5. | Kalman filtering of parameters of static linear (base function) model; dynamic model validation. | Extended Kalman filter. Particle filter. |
Study material
| Type | Name | Author | ISBN | URL | Edition, availability, ... | Examination material | Language |
| Other literature | Measurement Information Theory (manuscript) | Risto Ritala | 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 bakground 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 |
| Methods for describing state information for a stochastic system, and methods for updating this information with measurement data. Systems that are static, have discrete time or continuous time. | Lectures Excercises Practical works |
Contact teaching: 40 % Distance learning: 0 % Self-directed learning: 60 % |