# 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 equivalent) and Random processes (or equivalent).

## Teaching Assistant

• Sravanthi Gurugubelli (email: sravanthig 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.

## Course requirements and grading

• Three mini-projects (theory and programming): 10% each, i.e., 30% in total

• Prepare reports using LaTeX. Template and PDF

• Submit only pdf files using Microsoft Teams. Include Matlab/Python scripts as appendices. 60%, respectively.

• Four homework (problems): 5% each, i.e., 20% in total

• Midterm exam: 10%

• Open book written exam.

• Project: 20%

• Prepare reports using LaTeX. Template and PDF

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

• Upload a 5 minute recorded video presentation explaining your project.

• Final assessment: 20%

• Open book written exam.

## Schedule (Schedule 2022)

 Lecture number Topic Reading Materials Exercises 1 Introduction slides 2 Linear algebra and random processes slides 3 Minimum variance unbiased estimation Ch. 2, T1 slides, notes lab 4 Cramer-Rao lower bound Ch. 3, T1 slides, notes lab 5 Cramer-Rao lower bound Ch. 3, T1 slides, notes lab 6 Cramer-Rao lower bound Ch. 3, T1 slides, notes lab 7 Generalized MVU Ch. 5, T1 slides, notes lab 8 Generalized MVU Ch. 5, T1 slides, notes lab 9 BLUE Ch. 6, T1 slides, notes lab

## Previous exams

• Jun’20 Final exam

• Mar’20 Mid-term exam