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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS EEE 5087 STATISTICAL ESTIMATION THEORY IN SIGNAL PROCESSING ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

PROFESSOR DOCTOR OLCAY AKAY

Offered to

ELECTRICAL AND ELECTRONICS ENGINEERING (ENGLISH) ELECTRICAL AND ELECTRONICS ENGINEERING (ENGLISH) ELECTRICAL AND ELECTRONICS ENGINEERING (ENGLISH)

Course Objective

The main purpose of this course is to describe the estimation problem under various mathematical models and to provide the fundamental methods as tools of the estimation theory in signal processing.

Learning Outcomes of the Course Unit

1   The students are expected to describe the estimation problem in signal processing and basic requirement for estimation process. 2   The students are expected to perceive the significant parameters involving minimum variance and unbiasedness of an estimator and its boundary given by Cramer Rao Lower Bound. 3   The students are expected to realize the estimation problems without using probability density using the methods such as Best Linear Unbiased Estimation and Least Squares Method. 4   The students are expected to formulate the estimation problem using the Method of Maximum Likelihood Estimation which is the most frequently used method in estimation theory. 5   The students are expected to analytically and numerically solve the signal or parameter estimation problems according to the specified method.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

EEE 5129 - Random Variables and Stochastic Processes

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Mathematical Estimation Problem, Estimation in Signal Processing 2 Unbiased Estimators, Minimum Variance Criterion, Finding Minimum Variance Unbiased (MVU) Estimator 3 Determining Estimator Accuracy. Cramer Rao Lower Bound (CRLB). CRLB for Signals in White Gaussian Noise 4 Transformation of Parameters. Extension to a Vector Parameter. CRLB for the General Gaussian Case. Signal Processing Examples. 5 Linear Models. Properties of Linear Models and Examples. Extension to the Linear Model. 6 General Minimum Variance Unbiased Estimation. Finding Sufficient Statistics. Using Sufficiency to Find MVU Estimator. 7 Best Linear Unbiased Estimators (BLUE). Definition of BLUE. Finding BLUE. Extension to a Vector Parameter. Signal Processing Example. 8 Extension of BLUE to a Vector Parameter. Signal Processing Example. 9 Maximum Likelihood Estimation (MLE). Finding the MLE. Properties of the MLE. MLE for Transformed Parameters. 10 Numerical Determination of MLE. Extension to a Vector Parameter. Asymptotic MLE. Signal Processing Examples. 11 The Least Squares Approach. Linear Least Squares. Order Recursive Least Squares. 12 Sequential Least Squares. Nonlinear Least Squares. Signal Processing Examples. 13 Method of Moments. Extension to a Vector Parameter. Statistical Evaluation of Estimators. 14 Bayesian Philosophy. Prior Knowledge and Estimation. Choosing A Prior PDF.

Recomended or Required Reading

S. Kay. "Fundamentals of Statistical Signal Processing - Estimation Theory", Prentice Hall, 1993.

Planned Learning Activities and Teaching Methods

Lecture presentations, homeworks, term project, midterm exam.

Assessment Methods

Successful / Unsuccessful

Further Notes About Assessment Methods

None

Assessment Criteria

Homeworks, Term Project, Midterm Exam.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

0 232 301 7196 olcay.akay@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 14 3 42 Preparations before/after weekly lectures 12 6 72 Preparing presentations 1 5 5 Preparing presentations 1 5 5 Preparing assignments 6 5 30 Preparing Term Project 1 10 10 Treating Homeworks/Projects 7 5 35 Project Assignment 1 3 3 Project Final Presentation 1 3 3 Midterm 1 2 2 TOTAL WORKLOAD (hours) 207

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 PO.12 PO.13 PO.14 PO.15 LO.1 5 4 LO.2 5 5 LO.3 5 5 LO.4 5 4 5 LO.5 5 4 4 4 4