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 2021/2022 will be a written exam. However, depending on the developments of the Covid-19 Pandemic, the course is subject to change. In case the Covid-19 pandemic makes it difficult to have a written exam, this will be changed into an oral 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 2022 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.




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 2021. After that the enrolment for the projects will close. To upload your final assignment (before January 10th 2022), do this via "assignments" in brightspace.

For questions on the projects, please email at


  • 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 will be given by Dr. ir. Richard C. Hendriks (RCH) and Dr. Raj Thilak Rajan (RTR).


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.


The schedule for 2021/2022 is as follows:


Book Slides lecture videos
1. Nov. 8


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


2. Nov. 11


Estimation theory: Cramer Rao Lower Bound (CRB) Vol.1 Chapter 3 - 3.5 , Chapter 5


3. Nov 15 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 18 RTR Estimation theory - Least squares (LS) Vol.1: Ch. 8.1 - 8.4 and 8.8-8.9 Least Squares

5. Nov 22 RTR Estimation theory - Bayesian philosophy Vol.1 Ch. 10-10.6Bayesian

Bayesian philosophy
6. Nov 25 RTR

Estimation theory - Bayesian estimators

Vol.1 Ch. 11-11.5

vol. 1 Ch. 12-12.5


7. Nov 29 RTR Wiener filters

Vol.1 Ch. 12.7

Wiener filtering

8. Dec 2 RCHDetection theory - Introduction, Neyman Pearson theorem Vol.2 Chapters Ch. 3-3.7Introduction detection Intro Det. Theory
9. Dec 6 RCH Detection theory - Deterministic signals Vol.2 Chs. 4-4.4

Detection - Deterministic signals

Deterministic Signals
10. Dec 9 RCH Detection theory - Random Signals Vol.2 Chapters 5-5.6 Detection - Random signals Random Signals/GLRT
11. Dec 13 RCH Detection theory - GLRT Vol.2 Chapters 6-6.4

Detection - GLRT

12. Dec 16 RCH/RTR Exercises  
13. Dec 20 RCH Estimation of Sensor Array Signal Model Parameters Using Factor Analysis: Biomedical and audio array processing  

Factor Analysis

14. Dec 23 RTR Estimation & Detection: Sensor calibration  

Sensor calibration



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