ESTIMATION THEORY

AIM

This course aims to provide the fundamentals of estimation and detection theory. It intends to provide a thorough understanding of the modelling of the systems with noise and how the estimation and detection techniques can be applied. The estimation part introduces estimation techniques from simple to complex approaches and it covers classical and Bayesian type approaches. It then extends the problem of detection for the cases where the parameters of the noise are unknown and when the signal in present is either deterministic or random.

CONTENT

This course contains; Introduction to Estimation Theory and Minimum Variance Unbiased (MVU) estimation,Cramer-Rao Lower Bound (CRLB),Linear Models,General MVU Estimation,Best Linear Unbiased Estimation (BLUE),Maximum Likelihood (ML) Estimation,Maximum Likelihood (ML) Estimation,Midterm,Least Squares (LS),Least Squares (LS) - RLS,The Bayesian Philosophy,General Bayesian Estimators - 2,General Bayesian Estimators - 2,Linear Bayesian Estimators,Kalman Filters.

1. 1

   1. Determines consistency and bias in estimation.

   Taught by: Discussion Method, Question - Answer Technique, Simulation Technique, Lecture Method · Assessed by: Traditional Written Exam, Homework, Project Task

2. 2

   2. Decides which criteria to use to estimate a parameter.

   Taught by: Discussion Method, Question - Answer Technique, Simulation Technique, Lecture Method · Assessed by: Traditional Written Exam, Homework, Project Task

3. 3

   3. Derives the performance bounds for estimation problems.

   Taught by: Question - Answer Technique, Simulation Technique, Lecture Method · Assessed by: Traditional Written Exam, Homework, Project Task

4. 4

   4. Analyzes the performance of different estimation techniques by comparing the performance of the estimator with the corresponding bounds.

   Taught by: Discussion Method, Question - Answer Technique, Simulation Technique, Lecture Method · Assessed by: Traditional Written Exam, Homework, Project Task

5. 5

   5. Develops classical or Bayesian estimation techniques for a given problem.

   Taught by: Discussion Method, Question - Answer Technique, Simulation Technique, Lecture Method · Assessed by: Traditional Written Exam, Homework, Project Task

WEEKLY PLAN

1. WEEK 1

   Introduction to Estimation Theory and Minimum Variance Unbiased (MVU) estimation

   Preparation: Chapter 2 of Text 1

2. WEEK 2

   Cramer-Rao Lower Bound (CRLB)

   Preparation: Chapter 3 of Textbook 1.

3. WEEK 3

   Linear Models

   Preparation: Chapter 4 of Textbook 1

4. WEEK 4

   General MVU Estimation

   Preparation: Chapter 5 of Textbook 1.

5. WEEK 5

   Best Linear Unbiased Estimation (BLUE)

   Preparation: Chapter 6 of Textbook 1.

6. WEEK 6

   Maximum Likelihood (ML) Estimation

   Preparation: Chapter 7 of Textbook 1

7. WEEK 7

   Maximum Likelihood (ML) Estimation

   Preparation: Chapter 7 of Textbook 1.

8. WEEK 8

   Midterm

   Preparation: Chapters 1-7 of Textbook 1.

9. WEEK 9

   Least Squares (LS)

   Preparation: Half chapter 8 of Textbook 1.

10. WEEK 10

    Least Squares (LS) - RLS

    Preparation: The rest of Chapter 8 of Textbook 1.

11. WEEK 11

    The Bayesian Philosophy

    Preparation: Chapter 10 of Textbook 1.

12. WEEK 12

    General Bayesian Estimators - 2

    Preparation: Chapter 11 of Textbook 1.

13. WEEK 13

    General Bayesian Estimators - 2

    Preparation: Chapter 11 of Textbook 1.

14. WEEK 14

    Linear Bayesian Estimators

    Preparation: Chapter 12 of Textbook 1

15. WEEK 15

    Kalman Filters

    Preparation: Chapter 13 of Textbook 1

ASSESSMENT

• Rate of Midterm Exam to Success50%
• Rate of Final Exam to Success50%

WORKLOAD

READING

• 1. "Fundamentals of Statistical Signal Processing, Volume 1: Estimation Theory” Steven Kay, ISBN: 978-0133457117 2. “Fundamentals of Statistical Signal Processing, Volume 2: Detection Theory” Steven Kay, ISBN-13: 007-6092032243
• 1. "An Introduction to Signal Detection and Estimation” by Vincent Poor, ISBN: 978-0387941738 2. “Detection, Estimation, and Modulation Theory, Part I” by Harry L. Van Trees, ISBN: 978-

TEACHING STAFF

• Prof.Dr. Mehmet Kemal ÖZDEMİRCOORDINATOR
• Prof.Dr. Mehmet Kemal ÖZDEMİR