IKT721 Statistical Signal Processing

University of Agder

Course contents

The course covers the following main topics:

Part 1: Parameter Estimation

-The statistical estimation problem. Performance metrics: bias, variance, Mean Squared Error (MSE). Minimum Variance Unbiased Estimator (MVUE).

-Fisher Information and Cramer-Rao bound. Slepian-Bangs formula.

-Best Linear Unbiased Estimator (BLUE) and Maximum Likelihood Estimator (MLE): definition, properties, and examples.

-Bayesian estimation: Linear Minimum MSE (LMMSE) estimation and Kalman filtering.

Part 2: Detection Theory

-Hypothesis tests: types. Performance metrics: false positives and false negatives. ROC curves.

-Optimal detection: Neyman-Pearson theorem, likelihood ratio.

-Detection under the Bayesian philosophy: probability of error, risk, optimum detector.

-Examples: deterministic and random signals.

The presentation of the theory will be illustrated with examples of application from signal processing and communications. These applications will be also explored in the assigned homework, which will include both theoretical development and programming tasks.

Learning outcomes

Upon successful completion of this course, the students should:

-understand the underlying concepts and properties related to the parameter estimation and detection theories, as well as to determine and interpret fundamental limits.

-be able to evaluate the performance of estimation and detection techniques, by analytical as well as by Monte Carlo simulation methods.

-know how to recognize, model and formulate research problems from different fields as parameter estimation or hypothesis testing problems.

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