# ET4386 Estimation and Detection

# Introduction

This course covers the basics of detection and estimation theory, as used in statistical signal processing, adaptive beamforming, speech enhancement, radar, telecommunication, loclization, system identification, and elsewhere.Part I: Optimal estimation covers minimum variance unbiased (MVU) estimators, the Cramer-Rao bound (CRB), best linear unbiased estimators (BLUE), maximum likelihood estimation (MLE), recursive least squares (RLE), Bayesian estimation techniques, and the Wiener filter.

Part II: Detection theory covers simple and multiple hypothesis testing, the Neyman-Pearson Theorem, Bayes Risk, and testing with unknown signal and noise parameters.

The course complements EE4c03 Statistical digital signal processing and modeling, and gives a solid background for EE4715 Array Processing and EE4685 Machine learning, a Bayesian perspective.

### Preliminary knowledge

To follow the course with profit, you will need the background knowledge provided by an elementary course in Random Signals.

### Exam

In principle, the exam in the study year 2023/2024 will be a written exam.

The exam is closed book, but, students are allowed to bring a double sided **self handwritten** A4 formula sheet.

As part of the course, there is a compulsary mini project, which helps you to get experienced with the theory and to apply this to a practical problem. The available mini projects will be announced via the course website, after which students can sign in via Brightspace. The mini projects are encourage to be performed in groups of 2.

### Projects

- Project 1: "Multi-Microphone Speech Enhancement". Description - Data
- Project 2: "Drone swarms formation control". Description - Data
- Project 3: "EEG eye blink artifact removal". Description - Data
- Project 4: "Clock Synchronization for wireless sensor networks". Description - Data
- Project 5: "Accelerometer Calibration". Description - Data

To sign up for the mini-projects, go to the course page on brightspace. Then go to the tab "collaboration", and then select groups. **Signing up can be done until December 1st 2023**. After that the enrolment for the projects will close. The final report on the project needs
to be uploaded in **pdf before January 8th 2024** via "assignments" in brightspace.

For questions on the projects and lecture content, please use the brightspace forums.

### Books

- Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory; S.M. Kay, Prentice Hall 1993; ISBN-13: 978-0133457117.
- Fundamentals of Statistical Signal Processing, Volume II: Detection Theory; S.M. Kay, Prentice 1993; ISBN-13: 978-0135041352.

### Instructors

The lectures this academic year will be given by Dr. Raj Thilak Rajan (RTR) and Dr. Justin Dauwels (JD)### Contact

For any individual inquiries and requests, use the following email address:### Course material

Individual files in PDF format are available below. As the course develops additional files with e.g., solutions to the exercises, will be posted.## Schedule

The schedule for 2023/2024 is as follows:

Date | Book | Slides | ||||||
---|---|---|---|---|---|---|---|---|

1. | Nov. 13 | RTR |
Introduction. Estimation theory - MVU, CRB | Vol.1 Chapters 1 and 2 | MVU | |||

2. | Nov. 16 |
RTR |
Estimation theory: Cramer Rao Lower Bound (CRB) | Vol.1 Chapter 3 - 3.5 , Chapter 5 | ||||

3. | Nov. 20 | RTR | Estimation theory: Best Linear Unbiased Estimators (BLUE), Maximum likelihood estimation (MLE) |
Vol.1: Ch. 3.7, Ch. 6.1 - 6.5 and Ch. 7.1 - 7.6 | ||||

4. | Nov. 23 | RTR | Estimation theory - Least squares (LS) | Vol.1: Ch. 8.1 - 8.4 and 8.8-8.9 | Least Squares | |||

5. | Nov. 27 | JD | Detection theory - Introduction, Neyman Pearson theorem | Vol.2 Chapters Ch. 3-3.7 | Introduction detection | |||

6. | Nov 30 | RTR | Estimation theory - Bayesian philosophy | Vol.1 Ch. 10-10.6 | Bayesian | |||

7. | Dec. 4 | RTR | Estimation theory - Bayesian estimators |
Vol.1 Ch. 11-11.5 vol. 1 Ch. 12-12.5 |
MAP - LMMSE | |||

8. | Dec.7 | RTR | Wiener filters |
Vol.1 Ch. 12.7 | ||||

9. | Dec 11 | JD | Detection theory - Deterministic signals | Vol.2 Chs. 4-4.4 | ||||

10. | Dec 14 | JD | Detection theory - Random Signals | Vol.2 Chapters 5-5.6 | Detection - Random signals | |||

11. | Dec 18 | JD | Detection theory - GLRT | Vol.2 Chapters 6-6.4 | ||||

12. | Dec 21 | Guest + TA |
Part 1: Lecture: Lower bound for acoustic transfer functions
Part 2: Excercise session : Estimation |
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13. | Jan 8 | Guest + TA |
Part 1: Lecture: Estimation Techniques for Underwater Communications and its Challenges Part 2: Excercise session: Detection |
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14. | Jan 11 | RTR | Applications of Estimation theory |

## Exercises

The book contains many examples and exercises. A (incomplete) list with recommanded exercises from the book can be downloaded here. In addition, some extra examples and exercises are given in the list below:

- Example MVU & CRLB
- Exercise 10.3
- Example MVU, CRLB & Bayesian Estimation.
- Bayesian Estimation (Answers)
- Detection Theory (Answers)
- Estimation Theory (Answers)

## Example exams