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.
Course 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 .
Dersin Öğrenme Kazanımları
Teaching Methods
Assessment Methods
1. Determines consistency and bias in estimation.
12, 16, 21, 9
A, E, F
2. Decides which criteria to use to estimate a parameter.
12, 16, 21, 9
A, E, F
3. Derives the performance bounds for estimation problems.
12, 16, 21, 9
A, E, F
4. Analyzes the performance of different estimation techniques by comparing the performance of the estimator with the corresponding bounds.
12, 16, 21, 9
A, E, F
5. Develops classical or Bayesian estimation techniques for a given problem.
12, 16, 21, 9
A, E, F
6. Applies the concept of statistical decision theory to the cases of known and unknown noise.
A: Traditional Written Exam, E: Homework, F: Project Task
Course Outline
Order
Subjects
Preliminary Work
1
Introduction to Estimation Theory and Minimum Variance Unbiased (MVU) estimation
Chapter 2 of Text 1
2
Cramer-Rao Lower Bound (CRLB)
1 nolu kitabın 3. bölümünün okunması.
3
Linear Models
Chapter 4 of Textbook 1.
4
General MVU Estimation
Chapter 5 of Textbook 1.
5
Best Linear Unbiased Estimation (BLUE)
Chapter 6 of Textbook 1.
6
Maximum Likelihood (ML) Estimation
Chapter 7 of Textbook 1.
7
Least Squares (LS) 1
Half chapter 8 of Textbook 1.
8
Least Squares (LS) 2
The rest of Chapter 8 of Textbook 1.
9
The Bayesian Philosophy
Chapter 10 of Textbook 1.
10
General Bayesian Estimators
Chapter 11 of Textbook 1.
11
Linear Bayesian Estimators
Chapter 12 of Texbook 1
12
Kalman Filters
Chapter 13 of Textbook 1
13
Mathematical detection problem and Statistical Decision Theory I
Chapters 1 and 2 of Texbook 2.
14
Statistical Decision Theory II
Chapters 3 and 4 of Textbook 2.
Resources
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-
Course Contribution to Program Qualifications
Course Contribution to Program Qualifications
No
Program Qualification
Contribution Level
1
2
3
4
5
1
Develop and deepen the current and advanced knowledge in the field with original thought and/or research and come up with innovative definitions based on Master's degree qualifications.
X
2
Conceive the interdisciplinary interaction which the field is related with ; come up with original solutions by using knowledge requiring proficiency on analysis, synthesis and assessment of new and complex ideas.
X
3
Evaluate and use new information within the field in a systematic approach and gain advanced level skills in the use of research methods in the field.
X
4
Develop an innovative knowledge, method, design and/or practice or adapt an already known knowledge, method, design and/or practice to another field.
X
5
Broaden the borders of the knowledge in the field by producing or interpreting an original work or publishing at least one scientific paper in the field in national and/or international refereed journals.
X
6
Contribute to the transition of the community to an information society and its sustainability process by introducing scientific, technological, social or cultural improvements.
X
7
Independently perceive, design, apply, finalize and conduct a novel research process.
X
8
Ability to communicate and discuss orally, in written and visually with peers by using a foreign language at least at a level of European Language Portfolio C1 General Level.
X
9
Critical analysis, synthesis and evaluation of new and complex ideas in the field.
X
10
Recognizes the scientific, technological, social or cultural improvements of the field and contribute to the solution finding process regarding social, scientific, cultural and ethical problems in the field and support the development of these values.
X
Assessment Methods
Contribution Level
Absolute Evaluation
Rate of Midterm Exam to Success
50
Rate of Final Exam to Success
50
Total
100
ECTS / Workload Table
Activities
Number of
Duration(Hour)
Total Workload(Hour)
Course Hours
14
3
42
Guided Problem Solving
0
0
0
Resolution of Homework Problems and Submission as a Report
4
30
120
Term Project
0
0
0
Presentation of Project / Seminar
1
40
40
Quiz
0
0
0
Midterm Exam
1
24
24
General Exam
1
24
24
Performance Task, Maintenance Plan
0
0
0
Total Workload(Hour)
250
Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(250/30)
8
ECTS of the course: 30 hours of work is counted as 1 ECTS credit.
Detail Informations of the Course
Course Description
Course
Code
Semester
T+P (Hour)
Credit
ECTS
ESTIMATION and DETECTION THEORY
-
Fall Semester
3+0
3
8
Course Program
Prerequisites Courses
Recommended Elective Courses
Language of Course
English
Course Level
Second Cycle (Master's Degree)
Course Type
Elective
Course Coordinator
Prof.Dr. Mehmet Kemal ÖZDEMİR
Name of Lecturer(s)
Prof.Dr. Mehmet Kemal ÖZDEMİR
Assistant(s)
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.
Course 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 .
Dersin Öğrenme Kazanımları
Teaching Methods
Assessment Methods
1. Determines consistency and bias in estimation.
12, 16, 21, 9
A, E, F
2. Decides which criteria to use to estimate a parameter.
12, 16, 21, 9
A, E, F
3. Derives the performance bounds for estimation problems.
12, 16, 21, 9
A, E, F
4. Analyzes the performance of different estimation techniques by comparing the performance of the estimator with the corresponding bounds.
12, 16, 21, 9
A, E, F
5. Develops classical or Bayesian estimation techniques for a given problem.
12, 16, 21, 9
A, E, F
6. Applies the concept of statistical decision theory to the cases of known and unknown noise.
A: Traditional Written Exam, E: Homework, F: Project Task
Course Outline
Order
Subjects
Preliminary Work
1
Introduction to Estimation Theory and Minimum Variance Unbiased (MVU) estimation
Chapter 2 of Text 1
2
Cramer-Rao Lower Bound (CRLB)
1 nolu kitabın 3. bölümünün okunması.
3
Linear Models
Chapter 4 of Textbook 1.
4
General MVU Estimation
Chapter 5 of Textbook 1.
5
Best Linear Unbiased Estimation (BLUE)
Chapter 6 of Textbook 1.
6
Maximum Likelihood (ML) Estimation
Chapter 7 of Textbook 1.
7
Least Squares (LS) 1
Half chapter 8 of Textbook 1.
8
Least Squares (LS) 2
The rest of Chapter 8 of Textbook 1.
9
The Bayesian Philosophy
Chapter 10 of Textbook 1.
10
General Bayesian Estimators
Chapter 11 of Textbook 1.
11
Linear Bayesian Estimators
Chapter 12 of Texbook 1
12
Kalman Filters
Chapter 13 of Textbook 1
13
Mathematical detection problem and Statistical Decision Theory I
Chapters 1 and 2 of Texbook 2.
14
Statistical Decision Theory II
Chapters 3 and 4 of Textbook 2.
Resources
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-
Course Contribution to Program Qualifications
Course Contribution to Program Qualifications
No
Program Qualification
Contribution Level
1
2
3
4
5
1
Develop and deepen the current and advanced knowledge in the field with original thought and/or research and come up with innovative definitions based on Master's degree qualifications.
X
2
Conceive the interdisciplinary interaction which the field is related with ; come up with original solutions by using knowledge requiring proficiency on analysis, synthesis and assessment of new and complex ideas.
X
3
Evaluate and use new information within the field in a systematic approach and gain advanced level skills in the use of research methods in the field.
X
4
Develop an innovative knowledge, method, design and/or practice or adapt an already known knowledge, method, design and/or practice to another field.
X
5
Broaden the borders of the knowledge in the field by producing or interpreting an original work or publishing at least one scientific paper in the field in national and/or international refereed journals.
X
6
Contribute to the transition of the community to an information society and its sustainability process by introducing scientific, technological, social or cultural improvements.
X
7
Independently perceive, design, apply, finalize and conduct a novel research process.
X
8
Ability to communicate and discuss orally, in written and visually with peers by using a foreign language at least at a level of European Language Portfolio C1 General Level.
X
9
Critical analysis, synthesis and evaluation of new and complex ideas in the field.
X
10
Recognizes the scientific, technological, social or cultural improvements of the field and contribute to the solution finding process regarding social, scientific, cultural and ethical problems in the field and support the development of these values.
