ESTIMATION and DETECTION 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. 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 ,Least Squares (LS) 1,Least Squares (LS) 2,The Bayesian Philosophy,General Bayesian Estimators,Linear Bayesian Estimators,Kalman Filters ,Mathematical detection problem and Statistical Decision Theory I,Statistical Decision Theory II .

1. 1

   1. Determines consistency and bias in estimation.

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

6. 6

   6. Applies the concept of statistical decision theory to the cases of known and unknown noise.

   Taught by: Discussion Method, Problem Solving 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: 1 nolu kitabın 3. bölümünün okunması.

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

   Least Squares (LS) 1

   Preparation: Half chapter 8 of Textbook 1.

8. WEEK 8

   Least Squares (LS) 2

   Preparation: The rest of Chapter 8 of Textbook 1.

9. WEEK 9

   The Bayesian Philosophy

   Preparation: Chapter 10 of Textbook 1.

10. WEEK 10

    General Bayesian Estimators

    Preparation: Chapter 11 of Textbook 1.

11. WEEK 11

    Linear Bayesian Estimators

    Preparation: Chapter 12 of Texbook 1

12. WEEK 12

    Kalman Filters

    Preparation: Chapter 13 of Textbook 1

13. WEEK 13

    Mathematical detection problem and Statistical Decision Theory I

    Preparation: Chapters 1 and 2 of Texbook 2.

14. WEEK 14

    Statistical Decision Theory II

    Preparation: Chapters 3 and 4 of Textbook 2.

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” by Steven Kay, ISBN: 978-0133457117 2. “Fundamentals of Statistical Signal Processing, Volume 2: Detection Theory” by 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