Estimation Theory (430.714) Fall 2026

Instructor: Prof. Songhwai Oh (오성회)
Email: songhwai (at) snu.ac.kr
Office Hours: Friday 3:00-4:00PM
Office: Building 133 Room 503

Course Number: 430.714
Time: MW 5:00-6:15 PM
Location: Building 301 Room 201

TA: Yoseph Park (박요셉)
Email: yoseph.park (at) rllab.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, Gaussian process regression, and deep learning. Lectures will be in English.

Announcements

Schedule

WEEK

READING

DATE

LECTURE

DATE

LECTURE

1

Kay Ch. 1; Simon Ch. 1, Ch. 2

8/31

9/2

  • Introduction
  • Review on linear system theory

2

Kay Ch. 2

9/7

  • Review on probability

9/9

  • Minimum variance unbiased estimators

3

Kay Ch. 3.1-3.9, Ch. 4

9/14

  • Cramer-Rao lower bound (CRLB)

9/16

  • Linear models

4

Kay Ch. 5, Ch. 6

9/21

  • Sufficient statistics

9/23

  • Best linear unbiased estimators

5

Kay Ch. 7.1 - 7.6, Ch. 8

9/28

  • Maximum likelihood estimation

9/30

  • Least squares

6

Kay Ch. 10

10/5

  • Holiday

10/7

  • Exponential family
  • Bayesian approach

7

Kay Ch. 11

10/12

  • Multivariate Gaussian

10/14

  • Bayes risk, MMSE, MAP

8

Kay Ch. 12

10/19

  • Linear MMSE

10/21

  • Midterm 5:00-6:30 PM, 301-201

9

10/26

  • Sequential linear MMSE

10/28

  • Bayesian filtering

10

Simon Ch. 5, Ch. 6

11/2

  • Kalman filter

11/4

  • Alternate Kalman filter formulations

11

Simon Ch. 7, Ch. 9

11/9

  • Kalman filter generalizations

11/11

  • Optimal smoothing (1)

12

Simon Ch. 9, Ch. 13

11/16

  • Optimal smoothing (2)

11/18

  • Nonlinear Kalman filtering

13

Simon Ch. 14, Ch. 15

11/23

  • Unscented Kalman filter

11/25

  • Data association and multi-target tracking

14

11/30

  • Data association and multi-target tracking

12/2

  • Gaussian process regression

15

12/7

12/9

16

12/14

  • Final Exam 5:00-7:00 PM, 301-201

12/16

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)