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 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.


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.



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.


  • 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), Dr. Jorge Martinez (JMC) 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 2019/2020 is as follows:


Book Slides Collegerama
1. Nov. 14


Introduction. Estimation theory - MVU, CRB Vol.1 Chapters 1 and 2 Introduction. MVU - CRB Introduction/MVU
2. Nov. 15


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


Example lec. 2.

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


Extract from the board

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

Example lec. 5.

Bayesian philosophy
6. Nov 29 JMCEstimation theory - Maximum a posteriori (MAP) and linear Bayesian estimators

Vol.1 Ch. 11-11.5

vol. 1 Ch. 12-12.5


Exercises (Answers)

Example lec. 6.

7. Dec 5 RTRDetection theory - Introduction, Neyman Pearson theorem Vol.2 Chapters Ch. 3-3.7Introduction detection Intro Dec. Theory
8. Dec 6 RTR Detection theory - Deterministic signals Vol.2 Chs. 4-4.4

Detection - Deterministic signals

Exercises (Answers)

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

Detection - Random signals

Exercises (Answers)

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

Pulsar navigation

14. Jan 10 RTR Estimation & Detection: 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 above lecture schedule.

Example exams

Jan. 2017

April 2017

Jan. 2018

April 2018