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E1 244: Detection and Estimation Theory (3:0) - January 2023

Instructor

Vaibhav Katewa
Assistant Professor
Department of Electrical Communication Engineering (ECE) / Robert Bosch Center for Cyber-Physical Systems (RBCCPS)
Email: vkatewa(at)iisc(dot)ac(dot)in

Class Timings

Tue-Thu, 2:00-3:30 PM. First class on January 03, 2023.

Venue

MP 20 (ECE Dept.)

Class Logistics

Registered students will be added to a Class group in Microsoft Teams. The link to join the Teams group is here. All the course correspondence will happen in this Teams group.

Teaching Assistants

To be announced.

Course Overview and Syllabus

This is a graduate level course on statistical inference that deals with decision making based on observed data. The course is divided into two parts - Detection Theory and Estimation Theory. Detection theory provides a framework to make an intelligent guess regarding which hypothesis is true among a given set of n>2 hypotheses, while Estimation Theory provides a framework to intelligently guess the value of an unknown parameter that can be random or deterministic. The students will learn to mathematically formulate appropriate detection and estimation problems, solve these problems to get good/best detectors and estimators, and analyze their performance. This is a math-oriented course and will use concepts from probability and linear algebra.

We will broadly cover the following topics:

  1. Bayesian and Min-Max Hypothesis Testing

  2. Neyman-Pearson Hypothesis Testing

  3. Multiple Hypothesis Testing

  4. Composite Hypothesis Testing and Generalized Likelihood Ratio Test (GLRT)

  5. Detection of random/deterministic signals in presence of noise

  6. Sequential Hypothesis Testing

  7. Bayesian Estimation

  8. MMSE and ML Estimators

  9. Minimum Variance and Best Linear Unbiased Estimators

  10. Cramer-Rao Bound and Consistency

  11. Kalman Filter

Pre-requisites

  1. A graduate level course on probability. Contact me separately if you haven't taken such a course and still want to credit E1 244.

  2. A fair level of understanding of Linear Algebra/Matrix Theory concepts.

Grading

  1. Quizzes: 10%

  2. Homeworks: 25%

  3. One Midterm Exam: 25%

  4. Final Exam: 40%

References

There is no required textbook for the course. Below is a list of useful reference books:

  1. Fundamentals of Statistical Signal Processing - Volume I: Estimation Theory by Steven M. Kay. Prentice Hall, 1993.

  2. Fundamentals of Statistical Signal Processing - Volume II: Detection Theory by Steven M. Kay. Prentice Hall, 1993.

  3. Statistical Inference for Engineers and Data Scientists by Moulin and Veeravalli. Cambridge University Press, 2019.

  4. An Introduction to Signal Detection and Estimation (2nd Edition) by H. Vincent Poor, Springer-Verlag, 1994.

  5. Statistical Inference (2nd Edition) by Casella and Berger. Duxbury Press, 2002.

  6. Statistical Signal Processing by Louis L. Scharf. Pearson India, 2010.