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Recursive Estimation (Spring 2010)
Recursive Filtering and Estimation
4 credit points
Start: 03.03.10
End: 02.06.10
Frequency: Annually, Spring semester
Lecturer
Assistants
Angela Schöllig, Sebastian Trimpe
Day/Time/Location
Wednesdays
13:15-16:00, NO C 6
(on April 14 only: HG F 5)
Description: Probability review; Bayes theorem; recursive estimation using Bayes theorem; introduction to estimation; standard Kalman filter; extended Kalman filter; particle filtering.
Literature: Notes (available online): Introduction to Estimation and the Kalman Filter by H. Durrant-Whyte and other notes.
Requirements: Introductory probability theory and matrix-vector algebra.
Announcements
|
Sep 10 |
The sample solution of the final exam may be downloaded here. |
|
Sep 07 |
The final marks (percentages) for the class may be found here. For Master students, the final grades will be published by the ETH student administrations. Please contact the teaching assistants if you have any question regarding the grading. If you want to take a look at your graded exam, please come to ML K33 on Sep 16 from 14:00 to 15:00. |
|
July 30 |
The results of the second programming exercise are online. If you have questions or if you want to take a look at the sample solution (will not be available online), please make an appointment with Angela. |
|
July 19 |
There will be office hours held by Angela and Sebastian during the semester break on the following dates:
If you have questions regarding the preparation for the exam, please come to one of these dates. |
|
June 30 |
Final Examination: According to the information by the ETH examination office, the final exam will take place on August 23, 2010 from 14:00-16:30 in ETA F5. We will offer office hours before the final examination; they will be announced here. |
|
June 03 |
Example solution of Programming Exercise 2: A complete package including the Matlab Compiler and a Readme File was uploaded. |
|
May 30 |
The results of the first programming exercise are online. If you have questions or if you want to take a look at the sample solution (will not be available online), please make an appointment with Sebastian. |
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May 28 |
Programming Exercise 2: An example solution was uploaded, see 'Quizzes and Programming Exercises' section. You can use it to compare your code with. |
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May 27 |
Programming Exercise 2: An updated template was uploaded. The half-plane measurement was incorrect before. |
|
May 25 |
In class, the variance update equation for the Kalman Filter (2nd step) was derived as follows: P(k|k) = (I - KH) P(k|k-1) (I - KH)^T + KRK^T. Some students asked why we weren't using the shorter formula P(k|k) = (I - KH) P(k|k-1) which can be derived from the first by using the equation of the filter gain K. The reason why the first equation for P(k|k) is preferred over the second is that it is symmetric and therefore preserves the symmetry of P(k|k) in the case of numerical errors. |
|
May 17 |
A link to the class notes for the two lectures on particle filtering has been added in the Lectures section below. The Matlab script that will be used in this week's lecture (May 19) to generate approximations of a Gaussian distribution can be downloaded here. |
|
Apr 30 |
An updated version of the programming exercise has been uploaded (Ver 2). We have added in the problem description that all random variables are assumed to be mutually independent and independent over time. (Thanks for pointing this out.) |
|
Apr 28 |
The first programming exercise is online. It is due on May 12. |
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Apr 19 |
The quiz results and sample solutions are available (see section Quizzes and Programming Exercises below). |
|
Mar 31 |
Information regarding the Quiz:
|
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Mar 26 |
Please notice an update on the class schedule: the lecture #7 will be given by Prof. D'Andrea on Apr 15 (Thu) from 18:15 to 20:00; the same lecture will be repeated by Sebastian on Apr 21 (regular lecture time). The date for the exercise class remains unchanged (Apr 21, 15:15 to 16:00). |
|
Mar 24 |
The .m file for Problem 12 (Problem Set 2) is added and a slightly updated version of Problem Set 2 is uploaded. |
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Mar 17 |
Additional material for today's exercise class can be downloaded here (two different implementations of the random number generator for the joint pdf example, script for plotting the results, and the derivation of the second implementation that was not covered in class). |
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Mar 12 |
Due to unavailability of bigger rooms, the classroom for the lecture and the exercise remains the same (NO C 6). There is one exception: On April 14 (day of the quiz), the class will take place in HG F 5. |
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Mar 03 |
The factsheet that was handed out in class today can be downloaded here. |
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Feb 10 |
The first class will take place on March 3. |
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Feb 10 |
This website has been updated with the syllabus and other class information. |
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Jan 27 |
The class Introduction to Recursive Filtering and Estimation will be held by Prof. Raffaello D'Andrea in Spring 2010. The syllabus is currently under revision; more details will be announced here soon. |
Class Facts
| Instructor | Prof. Raffaello D'Andrea |
|
Teaching Assistants |
Angela Schoellig, Sebastian Trimpe |
| Lectures |
Wednesday, 13:15 to 15:00, NO C 6, (on April 14 only: HG F 5) |
| Exercise class | Wednesday, 15:15 to 16:00, NO C 6, (on April 14 only: HG F 5) |
|
Office hours |
During the break: Aug 11/16/20, 14:00-15:00, ML K33. During the semester: By appointment (please send an e-mail to the teaching assistants). |
| Exam | Final written exam during the examination session, covers all material. |
|
Grading |
40% quiz/programming exercises, 60% final exam if the grade for quiz and programming exercises is better than the grade in the final exam; 100% final exam otherwise. |
|
Only the two best grades from the quiz and the programming exercises will count towards the 40% above. |
|
| PhD students will get credits for the class if they pass the class (final grade of 4.0 or higher). | |
| Repetition | The final exam is only offered in the session after the course unit. Repetition is only possible after re-enrolling. Students who took the class in Spring 09 and have to retake the course should inform the teaching assistants before the beginning of the new class. |
Lectures
| # | date | topic | reading |
|
1 |
Mar 03 |
Probability Review |
DW: 1, 2 |
|
2 |
Mar 10 |
Probability Review |
DW: 1, 2 |
| 3 |
Mar 17 |
Bayes Theorem |
DW: 1, 2 |
| 4 |
Mar 24 |
Bayesian Tracking |
DW: 1, 2 |
| 5 |
Mar 31 |
Introduction to Estimation |
DW: 3 |
| - |
Apr 7 |
Easter break |
- |
| 6 |
Apr 14 |
Standard Kalman Filter |
DW: 4, 5, 6 |
|
7 (*) |
Apr 15 |
Standard Kalman Filter |
DW: 4, 5, 6 |
|
7R (*) |
Apr 21 |
" |
" |
| 8 |
Apr 28 |
Extended Kalman Filter |
DW: 7 |
| - |
May 05 |
No class |
- |
|
- |
May 12 |
No class |
- |
| 9 |
May 19 |
Particle Filtering |
PF Tutorial |
|
10 |
May 26 |
Particle Filtering |
PF Tutorial |
|
- |
Jun 02 |
No class |
- |
Remarks:
(*) The lecture will be held by Prof. D'Andrea on April 15 (Thu) from 18:15 to 20:00 in NO C6. The same lecture will be repeated by one of the teaching assistants on April 21 at the regular place/time.
Reading Material:
The notes Introduction to Estimation and Kalman Filter by Durrant-Whyte are the primary class reference. The sections relevant to the lectures are indicated above.
- DW: Introduction to Estimation and the Kalman Filter, H. Durrant-Whyte, University of Sydney, 2001.
- Probability Theory: The Logic of Science, E. T. Jaynes, 2005.
- PF Tutorial: A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking, M. S. Arulampalam et al., IEEE Transactions on Signal Processing, 2002. link (You should be able to download the paper if you are at ETH; send an e-mail to the TAs if you have problems.)
Quizzes and Programming Exercises
During the semester, there will be a graded quiz and programming exercises, which can be used to improve the final grade for the course (see "grading"). The quiz will take place at the beginning of the lecture and will test the student's understanding of the corresponding topic. The programming exercises will require the student to apply the lecture material.
Up
to three students can work together on the programming exercises. If
they do, they have to hand in one solution per group and will all
receive the same grade.
| # | type | topic | dates | download |
| Q1 | Quiz |
Probability, Bayes Theorem, Estimation (Lectures #1 to #5) |
Apr 14 |
Results |
| P1 | Programming |
Kalman filter |
Apr 28 (issued)
May 12 (due) |
Exercise MatlabTemplate |
| P2 | Programming |
Particle filter |
May 26 (issued)
Jun 09 (due) |
Exercise MatlabTemplate ExampleSolution (.exe, complete package with compiler) |
Problem Sets
We will make sets of problems and solutions available online for the topics covered in the lecture. It is the student's responsibility to solve the problems and understand their solutions. The TAs will answer questions in office hours and some of the problems might be covered during the exercise classes.
| # |
topic |
download |
|
1 |
Probability review |
ProblemSet1 |
| 2 |
Bayes theorem, recursive estimation using Bayes theorem |
ProblemSet2 |
| 3 | Introduction to estimation | ProblemSet3 |
| 4 | Kalman filter |
ProblemSet4 |
| 5 |
Particle filter |
ProblemSet5 |
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