S-114.4220 Research Seminar on Computational Science
	TKK / Units / LCE / Teaching / Courses / S-114.4220 / s2006

The topic of the course in fall 2006 is

Bayesian Estimation of Time-Varying Processes (5 p) L V

The topic of the seminar is Bayesian estimation of time-varying processes, which in its recursive form is more often referred to as optimal filtering. Optimal filtering refers to the methodology that can be used for estimating the states of time varying systems, which are indirectly observed through noisy measurements. This seminar concentrates to Bayesian optimal filtering methods suitable for estimating non-linear and non-Gaussian time varying processes from potentially non-linear and non-Gaussian measurements.

Phenomena, which can be modeled as time varying systems of the above type are very common in engineering applications. These kind of models can be found, for example, in navigation, aerospace engineering, space engineering, biology, remote surveillance, telecommunications, physics, chemistry, audio signal processing, control engineering, finance and several other fields.

Teachers

Dr.Tech. Simo Särkkä, Dr.Tech. Aki Vehtari

Prerequisites

Basics of Bayesian inference and matrix algebra. Basic knowledge or ability to learn to use Matlab is needed for completing the exercise.

Place and time

The seminars take place on Thursdays at 12:15 in Innopoli 2, B317 (the seminar room of Laboratory of computational engineering, see map) First lecture is 21.9. 12:15.

Course Registration

Please register for the course by sending email to ssarkka@lce.hut.fi. Remember to mention the student id. If you have an suggestion for the topic of your presentation, you may mention it in the email also.

Language

English if at least one English speaking participant.

Contents

Course requirements:

• Active participation in the seminars
• Seminar presentation
• Homework exercises (pen & paper)
• Exercise work (computer simulation)

• [1] Y. Bar-Shalom and X.-R. Li and T. Kirubarajan (2001). Estimation with Applications to Tracking and Navigation. Wiley Interscience.
• [2] B. Ristic and S. Arulampalam and N. Gordon (2004). Beyond the Kalman Filter. Artech House.
• [3] A. H. Jazwinski (1970). Stochastic Processes and Filtering Theory. Academic Press.
• [4] P. Maybeck (1979). Stochastic Models, Estimation and Control, Volume 1. Academic Press.
• [5] P. Maybeck (1982). Stochastic Models, Estimation and Control, Volume 2. Academic Press.
• [6] A. Doucet and N. de Freitas and N. Gordon (2001). Sequential Monte Carlo Methods in Practice. Springer.

Potential topics of presentations include, but are not limited to:

• Kalman filtering: extended Kalman filtering, unscented Kalman filtering, sigma-point filtering, statistical linearization
• Particle filtering: bootstrap filter, sequential importance sampling/resampling, Rao-Blackwellized filters
• Other optimal filtering methods: multiple model filters, grid based filters
• Theory of optimal filtering: non-linear filtering theory, Fokker-Planck-Kolmogorov equations, theory of continuous-time filtering, Kushner-Stratonovich equations, Zakai equations
• Optimal smoothing: Rauch-Tung-Striebel smoothers, non-linear smoothing theory, continuous-time optimal smoothing
• Applications: navigation, target tracking, time-series prediction, audio signal processing, biomedical signal processing, estimation of physical and chemical processes, financial applications, adaptive filtering, adaptive control, etc.

Schedule

Because there are two presentations in each seminar session, each talker shall be the opponent of the other talker in the same seminar session.

General instructions

In every seminar talk, there is the author who writes a 2-4 page summary paper about the subject and gives the talk, and an opponent, whose task is to make questions and stimulate discussion after the presentation. Every student is the author for (at least) one talk and the opponent for another talk. The author should send the summary paper to the opponent and to the teachers on the monday preceding the presentation day. The slides should be sent to the teacher lastest on the day preceding the presentation. The opponent prepares at least 2-3 questions about the topic to stimulate discussion after the talk. Normal talk is 30-40 minutes.

Homework exercises

The home work exercises can be found behind the following link:

homework.pdf

The answers to the exercises should be returned in two phases:

• The deadline for exercises 1-3 is October 27, 2006.
• The deadline for exercises 4-6 is November 30, 2006.

The answers should be sent as email to the teacher (ssarkka@lce.hut.fi) in PDF form. When sending the email,please add "S-114.4220" or "1144220" to subject. The answers can also be returned on paper to the teacher.

Exercise work

The computer exercises can be found behind the following link:

exwork.pdf

Your task is to write the actual filtering algorithms to the script files kf_ex.m and angle_ex.m. The script files are compatible with Matlab 6.x/7.x and with recent versions of GNU Octave and you can use either of these programs for making the exercise. These files and some additional files can be found in the following directory:

http://www.lce.hut.fi/teaching/S-114.4220/s2006/matlab/

The exercise report should be returned before December 15, 2006. The report should be sent as email to the teacher (ssarkka@lce.hut.fi) in PDF form. The Matlab/Octave-files should be returned as a ZIP or TAR.GZ file together with the PDF report. In the report, in addition to the results and figures, document the Matlab/Octave-codes that you have written. When sending the email, please add "S-114.4220" or "1144220" to subject. The report can also be returned on paper to the teacher.

Additional Online Material:

• Chapter 1 from book Stochastic Models, Estimation and Control, Volume I by Peter S. Maybeck (1979)
• Sam Roweis' Matrix Identities and Gaussian Identities.
• Greg Welch and Gary Bishop: An Introduction to the Kalman Filter. http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf
• A. Doucet, S. J. Godsill, and C. Andrieu. On sequential Monte Carlo sampling methods for Bayesian filtering. Statistics and Computing, 10:197-208, 2000. http://www-sigproc.eng.cam.ac.uk/~sjg/papers/99/statcomp_final.ps
• R. van der Merwe (2004). Sigma-Point Kalman Filters for Probabilistic Inference in Dynamic State-Space Models. Ph.D thesis. http://www.cse.ogi.edu/~rudmerwe/pubs/pdf/rvdmerwe_phd_thesis.pdf.
• Simo Särkkä (2006). Recursive Bayesian Inference on Stochastic Differential Equations. Doctoral dissertation. http://lib.tkk.fi/Diss/2006/isbn9512281279/isbn9512281279.pdf.

WWW Pages:

• Kalman filter in Wikipedia.
• Particle filter in Wikipedia.
• Nonlinear filtering - Online Survey
• Sequential Monte Carlo Methods Home Page

Contact:

When sending email concerning the course, please add "S-114.4220" or "1144220" to subject.

Dr.Tech. Simo Särkkä
ssarkka@lce.hut.fi
http://www.lce.hut.fi/~ssarkka/

Dr.Tech. Aki Vehtari
Aki.Vehtari@hut.fi
http://www.lce.hut.fi/~ave/