Course Information

Estimation Theory - Fall 2018
Instructor: Prof. Songhwai Oh (오성회)
Email: songhwai (at) snu.ac.kr
Office Hours: Friday 2:00-4:00PM
Office: Building 133 Room 405
Course Number: 430.714
Time: MW 3:30-4:45 PM
Location: Building 301 Room 102
TA: Seunggyu Chang (장승규)
Email: seunggyu.chang (at) cpslab.snu.ac.kr
Office: Building 133 Room 610
 

Course Description

This course introduces classical and modern topics in estimation theory to graduate level students. Topics include minimum variance unbiased estimators, the Cramer-Rao bound, linear models, sufficient statistics, best linear unbiased estimators, maximum likelihood estimators, least squares, exponential family, multivariate Gaussian distribution, Bayes risk, minimum mean square error (MMSE), maximum a posteriori (MAP), linear MMSE, sequential linear MMSE, Bayesian filtering, Kalman filters, extended Kalman filter, unscented Kalman filter, particle filter, data association, multi-target tracking, and Gaussian process regression. Lectures will be in English.

Announcements

  • [11/28] The final exam will be held in class on 12/12 (Wed). The exam is closed-book but you can bring one sheet (A4) of hand written notes on both sides. You have to turn in this cheat sheet with your exam. 
  • [10/15] The room for the midterm is Building 302, Room 105. (We had to change the building to reserve a room with extra time.)
  • [10/10] The midterm will be held in class on 10/24 (Wed). The exam is closed-book but you can bring one sheet (A4) of hand written notes on a single side (the other side must be blank). You have to turn in this cheat sheet with your exam.
  • [09/06] Room change: Lectures will be held in Room 102 starting from 9/10.
  • [08/20] Please read Ethics of Learning.

Schedule

Week Reading Date Lecture Date Lecture
1 Kay Ch. 1, 2
Simon Ch. 1, 2
9/3
  • Introduction
  • Review on linear system theory
9/5
  • Review on probability
2


Kay Ch. 3.1 - 3.9, Ch. 4

9/10
  • Minimum variance unbiased estimators
  • Cramer-Rao lower bound (CRLB)
9/12
  • Cramer-Rao lower bound (CRLB)
  • Linear models
3 Kay Ch. 5, Ch. 6

9/17
  • Sufficient statistics
9/19
  • Best linear unbiased estimators
4   9/24
  • Holiday
9/26
  • Holiday
5   10/1
  • No class
10/3
  • Holiday
6 Kay Ch. 7.1 - 7.6, Ch. 8, Ch. 10 10/8
  • Maximum likelihood estimation
  • Least squares
10/10
  • Least squares
  • Exponential family
7 Kay Ch. 11, Ch. 12 10/15
  • Bayesian approach
  • Multivariate Gaussian
10/17
  • Bayes risk, MMSE, MAP
  • Linear MMSE
8 Kay Ch. 12 10/22
  • Sequential linear MMSE
10/24
  • Midterm
  • Time: 3:30PM
  • Location: Building 302, Room 105
9 Simon Ch. 5 10/29
  • Bayesian filtering
10/31
  • Kalman filter
10 Simon Ch. 6, Ch. 7 11/5
  • Alternate Kalman filter formulations
11/7
  • Kalman filter generalizations
11 Simon Ch. 9 11/12
  • Optimal smoothing
11/14
  • Optimal smoothing
12 Simon Ch. 13, Ch. 14 11/19
  • No class
11/21
  • Nonlinear Kalman filtering
13 Simon Ch. 15 11/26
  • Unscented Kalman filter
11/28
  • Particle filtering
14   12/3
  • No class
12/5
  • No class
 15   12/10
  •  Gaussian process regression
 12/12
  • Final Exam
  • Time: 3:30PM
  • Location: Building 301, Room 102

Textbooks

  • [Recommended] Steven M. Kay, "Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory", Prentice Hall, 1993.
  • [Recommended] Dan Simon, "Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches", Wiley-Interscience, 2006.

Prerequisites

Students must have a solid background in linear algebra, linear system theory, and probability.

Topics

  • Introduction and review of probability and linear system theory
  • Minimum variance unbiased estimators
  • Cramer-Rao lower bound
  • Linear models and sufficient statistics
  • Best linear unbiased estimators and maximum likelihood estimators
  • Least squares, exponential family, and Bayesian approaches
  • Multivariate Gaussian distribution
  • Bayes risk, minimum mean square error (MMSE), and maximum a posteriori (MAP)
  • Linear MMSE and sequential linear MMSE
  • Bayesian filtering
  • Kalman filtering
  • Advanced topics in Kalman filtering
  • Extended Kalman filter, unscented Kalman filter, and particle filter
  • *Data association and multi-target tracking
  • *Gaussian process regression (*if time permits)