Welcome to the home page for ECE531 "Principles of Detection and Estimation Theory" for Spring 2013.

# announcements

- [27-Feb-2013] A .mat file with process and measurement noises as well as states and observations has been posted. You can use this to confirm you are correctly generating states and observations with your dynamic model.
- [25-Feb-2013] The Kalman filter midterm Matlab project has been posted. The project is due by 6pm on March 12.
- [15-Jan-2013] An email was sent to the class mailing alias ece531@ece.wpi.edu today. If you did not receive this email, please contact Prof. Brown.

# general

The required course textbooks are Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory and Fundamentals of Statistical Signal Processing, Volume 2: Detection Theory, both by Steven Kay.

The course syllabus (pdf format) including expected course outcomes, grading information, and late policies.

ECE531 academic honesty policies.

ECE531 students with disabilities statement.

# screencasts, notes, and handouts

## First class meeting (Jan 15)

- Course introduction slides.

## Week 1 (Jan 15 - Jan 22)

The focus this week is on reviewing probability and statistics if necessary, becoming familiar with estimation problems, the mathematical framework for estimation, finding unbiased estimators, and evaluating estimator performance in terms of variance. The assigned reading is Kay vI:1-2.

- Week 1 screencasts and slides.
- Suggested practice problems: Kay vI 1.4, 2.1, 2.6, 2.10, 2.11.
- Quiz 1 solution.

## Week 2 (Jan 22 - Jan 29)

The focus this week is on understanding Fisher information and the Cramer-Rao Lower Bound. The assigned reading is Kay vI:3.

- Week 2 screencasts and slides.
- Suggested practice problems: Kay vI 3.3, 3.4, 3.9, 3.12, 3.17.
- Quiz 2 solution.

## Week 3 (Jan 29 - Feb 05)

The focus this week is on understanding MVU estimators and their performance in the special case of linear Gaussian models and on understanding and using the Rao-Blackwell-Lehmann-Sheffe theorem to find MVU estimators. The assigned reading is Kay vI:4 and Kay vI:5.

- Week 3 screencasts and slides.
- Suggested practice problems: Kay vI 4.10, 4.11, 5.3, 5.7, 5.13, 5.17, 5.18. Several of these problems say that you can assume your sufficient statistic is complete, but it is a good idea to try to prove completeness if you can (you can usually use the exponential families theorem). Also, in 5.3, use RBLS to find a MVU estimator.
- Here are some one page handouts on exponential families: Arnold and Lindgren.
- Some links on Cholesky factorization: UCLA lecture and a nice example of how to do a 2x2 Cholesky factorization by hand.
- Quiz 3 solution.

## Week 4 (Feb 06 - Feb 12)

The focus this week is on maximum likelihood estimation. The assigned reading is Kay vI:7.

- Week 4 screencasts and slides.
- Suggested practice problems: Kay vI 7.3, 7.7, 7.8, 7.9, 7.10, 7.20.
- Quiz 4 solution.

## Week 5 (Feb 13 - Feb 19)

The focus this week is on Bayesian estimation. The assigned reading is Kay vI:10-11.

- Week 5 screencasts and slides.
- Suggested practice problems: Kay vI 10.1, 10.3, 10.9, 11.1, 11.2, 11.4
- Quiz 5 solution.

## Week 6 (Feb 20 - Feb 26)

The focus this week is on linear MMSE Bayesian estimation. The assigned reading is Kay vI:12.

- Week 6 screencasts and slides.
- Suggested practice problems: Kay vI 12.2, 12.4, 12.6, 12.9 12.19
- Quiz 6 solution.

## Week 7 (Feb 27 - Mar 12)

The focus this week is on Kalman filtering. The assigned reading is Kay vI:13.

- Week 7 screencasts and slides.
- Suggested practice problems: Kay vI 13.8, 13.9, 13.10, 13.12, 13.14, 13.23
- The Kalman filter midterm Matlab project worth 100 points. The project is due by 6pm on March 12. You can download the .mat file for part 1 containing process and measurement noises as well as states and observations here. has been posted. This .mat file will allow you to confirm you are correctly generating states and observations with your dynamic model. Note: the process noises are indexed U(:,1) to U(:,50) where U(:,1) corresponds to U[0]. The measurement noises are indexed V(:,1) to V(:,51) where V(:,1) corresponds to V[0].
- Quiz 7 solution.

## Week 8 (Mar 13 - Mar 19)

The focus this week is on getting started with detection and Neyman-Pearson detection in scenarios with a finite number of possible observations. The assigned reading is Kay VII, Chapter 1 and Chapter 3.1-3.5.

- Week 8 screencasts and slides.
- Suggested practice problems: Kay VII problems 1.1, 1.2, 1.4, 1.5, and Homework 2 from 2011.
- Quiz 8 solution.

## Week 9 (Mar 20 - Mar 26)

The focus this week is on Neyman-Pearson and Bayesian detection for observation models with an infinite number of possible observations. The assigned reading is Kay vII:3.6 - end of Chap 3.

- Week 9 screencasts and slides.
- Suggested practice problems: Homework 3 from 2011 and Kay VII problems 3.12, 3.14, 3.17, 3.20.
- Quiz 9 solution.

## Week 10 (Mar 27 - Apr 02)

The focus this week is on detection of deterministic signals in Gaussian noise. The assigned reading is Kay vII:4.

- Week 10 screencasts and slides.
- Suggested practice problems: Homework 4 problem 1 from 2011 and Kay VII problems 4.7, 4.10, 4.15, 4.19, 4.24, 4.28.
- Quiz 10 solution.

## Week 11 (Apr 03 - Apr 09)

The focus this week is on composite hypothesis testing and detection of signals with unknown parameters. The assigned reading is Kay VII, Chapter 6.1-6.4, 6.7-6.8. You are not responsible for the Rao or Wald tests, although you are encouraged to skim that material.

- Week 11 screencasts and slides.
- Suggested practice problems: Homework 4 problems 4 and 5 from 2011 and Kay VII problems 6.2, 6.6, 6.8, 6.21.
- Quiz 11 solution.

## Week 12 (Apr 10 - Apr 16)

The focus this week is on detection of deterministic signals with unknown parameters in Gaussian noise. The assigned reading is Kay vII:7.

- Week 12 screencasts and slides.
- Suggested practice problems: Kay VII problems 7.4, 7.5, 7.7, 7.10, 7.23.
- Quiz 12 solution.

## Week 13 (Apr 17 - Apr 23)

The focus this week is on detection of deterministic signals in additive white Gaussian noise when the noise variance is unknown. The assigned reading is Kay vII:9.1-9.4 (skipping 9.4.2). You are encouraged to skim 9.5 and 9.6 for some details on detection in correlated noise with unknown correlation parameters.

- Week 13 screencasts and slides.
- Suggested practice problems: Kay VII problems 9.3, 9.4, 9.7, 9.12, 9.15.
- Quiz 13 solution.