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TSKS15 Detection and Estimation of Signals

Erik G. Larsson
Erik G. Larsson

Course Director

TSKS15 Detection and Estimation of Signals treats statistical signal processing, specifically parameter estimation and detection of signals. The purpose of the course is to provide a solid foundation in algorithms, models, methods and theory for the extraction of information from noisy signals. Applications are found within radar systems, communications systems, positioning systems and image analysis.

Course topics:

  • Problems in radar, communications and source localization systems.
  • Classical versus Bayesian approaches.
  • Hypothesis testing. Binary and M-ary tests. Bayes cost and error probability. Neyman-Pearson theorem.
  • Classical estimation. Maximum-likelihood, Fisher information, Cramer-Rao bound.
  • Bayesian estimation theory. MMSE and LMMSE.
  • Composite hypothesis testning. GLRT. Marginalization. Model selection.
  • Linear and nonlinear models with Gaussian noise. Slepian-Bang formula. Noise whitening.
  • Detection of signals in continuous time.
  • Performance and variance analysis. Asymptotic properties of estimates.
  • Complex-valued data and noise. Circularly symmetric noise.
  • Applications: amplitude, frequency, phase, time-delay and angle estimation.

The course consists of a lecture series and two computer lab projects:

  1. Time-of-arrival (range) estimation. The purpose of this project is to implement a maximum-likelihood time-of-arrival (range) estimation algorithm, perform Monte-Carlo simulation of its performance, and compare with theoretical bounds.
  2. Music recognition. The purpose of this project is to design a classifier algorithm for the recognition of music, implement this algorithm, and evaluate its performance and robustness to model assumptions using Monte-Carlo simulation.

For prospective students, to get a more detailed idea of the course contents:

  • You may watch this short video.
  • I teach the lectures almost entirely on the whiteboard, and only use very few Powerpoint slides with diagrams and examples. These Powerpoints, along with some other, supplementary course material can be accessed here (from 2018). You may also look at the descriptions of the two computer labs (radar ranging and music recognition), and at previous years written exams.
  • Here is a poster from the department's open house with some pictures that illustrate the course themes.


  • Course director and lecturer: Erik G. Larsson
  • Tutorial and lab assistant: TBA

Compulsory reading:

  • S. Kay, Statistical Signal Processing: Estimation Theory (Volume I) and Statistical Signal Processing: Detection Theory (Volume II), Prentice-Hall.

  • A bundle with both volumes is sold at Bokab, Karallen, Campus Valla, for 1198 SEK.

    We will cover selected material from Chapters 1-4, 6-12 and 15 in Volume I, and from Chapters 1-9 in Volume II.

Documents and files:


  • TBA

Video lectures with material from pre-requisite courses: (for registered students only, requires LiU-login)

  1. Recap of some concepts from linear algebra: vectors and matrices, norms, quadratic forms, eigen-decomposition, trace, determinant, and inverses
  2. Recap of orthogonal projections (from linear algebra)
  3. Recap of least squares (from linear algebra)
  4. About the Chi-square probability distribution

General information:

Page responsible: Erik G. Larsson
Last updated: 2019 08 14   08:39