ET4386 Estimation and Detection


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.


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.




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.


  • 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.


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


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.


The schedule for 2023/2024 is as follows:


Book Slides
1. Nov. 13


Introduction. Estimation theory - MVU, CRB Vol.1 Chapters 1 and 2


2. Nov. 16


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. 3-3.7Introduction detection

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

7. Dec. 4 RTR

Estimation theory - Bayesian estimators

Vol.1 Ch. 11-11.5

vol. 1 Ch. 12-12.5


8. Dec.7 RTR Wiener filters

Vol.1 Ch. 12.7

Wiener filtering

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

Detection - Deterministic signals

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

Detection - GLRT

12. Dec 21 Guest
+ TA
Part 1: Lecture: Lower bound for acoustic transfer functions
Part 2: Excercise session : Estimation

Lower bound for acoustic transfer functions

13. Jan 8 Guest
+ TA
Part 1: Lecture: Estimation Techniques for Underwater Communications and its Challenges
Part 2: Excercise session: Detection
14. Jan 11 RTR Applications of Estimation theory


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 exams

Jan. 2017

April 2017

Jan. 2018

April 2018

Jan. 2019

April 2019

Jan. 2020