# 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 ET4235 Statistical Digital Signal Processing, and gives a solid background for IN4182 Digital Audio and Speech Processing and ET 4147 Signal Processing for Communications.

### Preliminary knowledge

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

### Exam

The exam for et4386 Estimation and Detection Theory 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 can be done in pairs. To sign up for a project, go to brightspace, enroll for the course, and then go to the tab "collaboration", and select "groups".

The final report on the project needs
to be uploaded in **pdf before January 10th
2020** via brightspace.

The project report will be graded and counts for 20 % of the final grade. Access to the final exam will only be granted if the project is handed in.

### Projects

- Project 1: "Multi-Microphone Speech Enhancement". Description - Data
- Project 2: "Signal Detection". Description - Data
- Project 3: "Cognitive radio". Description - Data
- Project 4: "Clock Synchronization for wireless sensor networks". 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. After that the enrolment for the projects will close. To upload your final assignment (before January 10th 2020), do this via "assignments" in brightspace.

For questions on the projects, please contact Dr. Raj Thilak Rajan.

### 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 will be given by Dr. ir. Richard C. Hendriks (RCH), Dr. Jorge Martinez (JMC) and Dr. Raj Thilak Rajan (RTR).### Contact

Please use the following email address for any inquiries regarding the course and the mini projects:### 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 2019/2020 is as follows:

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

1. | Nov. 14 | RCH |
Introduction. Estimation theory - MVU, CRB | Vol.1 Chapters 1 and 2 | Introduction. MVU - CRB | Introduction/MVU | |

2. | Nov. 15 |
RCH |
Estimation theory: Cramer Rao Lower Bound (CRB) | Vol.1 Chapter 3 - 3.5 | CRB | ||

3. | Nov 21 | RCH | 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 | BLUE/MLE | ||

4. | Nov 22 | RTR | Estimation theory: Least squares (LS) | Vol.1: Ch. 8.1 - 8.4 and 8.8-8.9 | LS | LS | |

5. | Nov 28 | RTR | Estimation theory - Bayesian philosophy |
Vol.1 Ch. 10-10.6 | Bayesian, Exercise 10.3 | Bayesian philosophy | |

6. | Nov 29 | JMC | Estimation theory - Maximum a posteriori (MAP) and linear Bayesian estimators |
Vol.1 Ch. 11-11.5 vol. 1 Ch. 12-12.5 | MAP/LMMSE | ||

7. | Dec 5 | RTR | Detection theory - Introduction, Neyman Pearson theorem | Vol.2 Chapters Ch. 3-3.7 | Introduction detection | Intro Dec. Theory | |

8. | Dec 6 | RTR | Detection theory - Deterministic signals | Vol.2 Chs. 4-4.4 | Deterministic Signals | ||

9. | Dec 12 | RCH | Detection theory - Random Signals | Vol.2 Chapters 5-5.6 | Detection - Random signals | Random Signals/GLRT | |

10. | Dec 13 | JMC | Detection theory - Random Signals | Vol.2 Chapters 5-5.6 | Random Signals/GLRT | ||

11. | Dec 19 | RCH | Detection theory - GLRT | Vol.2 Chs. 6,7 & 8 | Random Signals/GLRT | ||

12. | Dec 20 | JMC | Detection theory - GLRT | ||||

13. | Jan 9 | Andreas Koutrouvelis | Estimation & Detection for pulsar navigation | ||||

14. | Jan 10 | RTR | Estimation & Detection: Sensor calibration |

## 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 above lecture schedule.## Example exams