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E1 244: Detection and Estimation Theory (3:0) - January 2025

Instructor

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

Class Timings

Tue-Thu, 3:30-5:00 PM. First class on January 02, 2025.

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 decided.

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 (Best 2 out of 3): 20%

  2. Two Midterm Exams: 40%

  3. Final Exam: 40%

  4. Assignments will be provided but will not be graded

References

The course material is taken from the below 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.