**Estimation and Detection**

**Course Description**

This course examines the fundamentals of estimation and detection for signal processing, communications, and control. In (parameter) estimation part we cover Bayesian and nonrandom parameter estimation, minimum-variance unbiased estimators and the Cramér-Rao bounds; representations for stochastic processes, shaping and whitening filters, and Karhunen-Loève expansions. For the detection aspects, the covered topics are vector spaces of random variables, Bayesian and Neyman-Pearson hypothesis testing.

**Prerequisites**

Some knowledge of probability and stochastic processes and signal processing is required.

**Course Goal**

To provide students with the ability to derive estimation methods for both determinist and random parameters and apply those to problems in different areas of communications, radar, learning among others. Also, aim to provide the students the capacity to design a hypothesis test for signal detection and analyse the best criterion to be used for some applications.

**Program / Syllabus**

**Estimation Theory**
- Introduction to Estimation
- Minimum Variance Unbiased Estimators
- Linear Models and Estimators and Least Squares,
- Cramér-Rao Lower Bound (CRLB)
- Bayesian Estimation
- Maximum Likelihood Estimation

**Detection Theory**
- Introduction
- Statistical Decision Theory
- Binary Hypothesis
- Likelihood Ratio Test
- Bayes Risk
- Neyman-Pearson Detectors

**Textbooks**

- Steven M. Kay,
*Fundamentals of Statistical Signal Processing: Estimation Theory*, Volume 1, Prentice Hall Signal Processing Series. Prentice-Hall, 1993.
- Steven M. Kay,
*Fundamentals of Statistical Signal Processing: Detection Theory*, Volume 2, Prentice Hall Signal Processing Series. Prentice-Hall, 1998.
- Bernard C. Levy,
*Principles of Signal Detection and Parameter Estimation*. Springer, 2008.

**Material**