TSKS15 
Detection and Estimation of Signals, 6 ECTS credits.
/Detektion och estimering av signaler/
For:
D
I
Ii
IT
MMAT
SY
Y


Prel. scheduled
hours:
Rec. selfstudy hours: 160


Area of Education: Technology
Main field of studies: Electrical Engineering


Advancement level
(G1, G2, A): A


Aim:
After completed course the student should:
 with adequate terminology, in a wellstructured manner and logically coherent, be able to describe and conduct simpler calculations that relate to classical and Bayesian estimation and detection theory, specifically the NeymanPearson theorem, error probabilities, decision regions, maximumlikelihood, linear and nonlinear models, Fisher information, CramerRao bound, circularly symmetric noise, noise whitening, MMSE and LMMSE, GLRT, model order selection, coherent and noncoherent detection, composite hypothesis testing and nuisance parameters and basis expansions of waveforms in continuous time
 be able to describe, apply and implement in a conventional programming language, and show engineering understanding of, the theory and models used in the course


Prerequisites: (valid for students admitted to programmes within which the course is offered)
Linear algebra, probability theory, and a course similar to Signals, Information and Communications.
Note: Admission requirements for nonprogramme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.


Organisation:
Lectures, problem classes and computer laboratory work. Individual (inclass) oral examination of laboratory work.


Course contents:
Binary hypothesis tests, NeymanPearson theorem, error probability. Mary detection problems. Bayes cost, minimum probability of error. Nuisance parameters. Classical estimation: Maximumlikelihood. CramerRao bound, SlepianBang's formula, efficiency. Linear, vectorvalued models with Gaussian noise. Nonlinear models. Noise whitening, complexvalued data, Gaussian noise, circularly symmetric noise. Bayesian estimation: MMSE and LMMSE. Composite hypothesis testing: GLRT and Bayesian approach, model selection. Performance calculations, asymptotic properties of estimators. Applications to amplitude and phase estimation, frequency estimation, angleofarrival estimation, timeofarrival estimation, source localization, coherent and noncoherent detection of waveforms.


Course literature:
S. Kay, Statistical Signal Processing: Estimation Theory and
Statistical Signal Processing: Detection Theory, PrenticeāHall.


Examination: 

A written examination Laboratory work 
4 ECTS 2 ECTS




Course language is Swedish/English.
Department offering the course: ISY.
Director of Studies: Klas Nordberg
Examiner: Erik G. Larsson
Link to the course homepage at the department

