# E1 244 Detection and Estimation

## About E1 244 Detection and Estimation

The main goal of E1 244 is to cover the two major domains of statistical signal processing, namely, detection and estimation, which include the many mathematical tools that engineers and statisticians use to draw inference from imperfect or incomplete measurements. The first part of the course develops statistical parameter estimation methods to extract information from signals in noise. The second part of this course is about the application of statistical hypothesis testing to the detection of signals in noise.

## Prerequisite

Matrix theory (or computational linear algebra) and Random processes.

## Lectures

• Wednesday and Fridays 1:45-3:15pm, ECE/MP 20 (Auditorium).

• Exercise and tutorial sessions on the 1st and 3rd Saturdays, 11-12.30pm, ECE/MP 20.

## Teaching Assistant

Krishna Chaythanya (email: krishnackv AT iisc.ac.in)

## Syllabus

Review of linear algebra and random processes. Maximum likelihood theory, minimum variance unbiased estimators, the Cramér-Rao bound, best linear unbiased estimators, least squares and recursive least squares, Bayesian estimation techniques, the Wiener and Kalman filters, binary and multiple hypothesis testing, Neyman-Pearson detector, Bayes detector, composite hypothesis testing with unknown signal and noise parameters, and sequential probability ratio test.

## Textbooks

• 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.

• Other useful resources

• Statistical Signal Processing, L.L. Scharf, Pearson India, 2010, ISBN-13: 978-8131733615.

• An Introduction to Signal Detection and Estimation, H.V. Poor, Springer, 2nd edition, 1998, ISBN-13: 978-0387941738.

• Three homeworks (problems and programming): 10% each, i.e., 30% in total

• Prepare reports using LaTeX.

• Submit only pdf files using Microsoft Teams. Include Matlab/Python scripts as appendices.

• Late submissions are allowed, but will not be graded.

• Midterm exam on Feb 19, 2020 (Tentative): 20%

• Written exam. A4 cheat sheet will be allowed.

• Final exam, somewhere during the fourth week of April: 50%

• Written exam. A4 cheat sheet will be allowed.

## Schedule

 Lecture number Date Topic Reference Slides 1 08-01-2020 Introduction slides 2 10-01-2020 Linear algebra and random processes slides slides x 15-01-2020 Makara Sankrati - NO CLASS - 3 17-01-2020 Minimum variance unbiased estimation Ch. 2 4 22-01-2020 Cramer-Rao lower bound Ch. 3