# FEM3210 Estimation Theory 10.0 credits

This is an introductory course to statistical estimation theory given from a signal processing perspective. The aim is to provide the basic principles and tools which are useful to solve many estimation problems in signal processing and communications. It will also serve as the necessary prerequisite for more advanced texts and research papers in the area. The course will cover fundamental concepts such as sufficient statistics, the Rao-Blackwell theorem and the Cramer-Rao lower bound on estimation accuracy. Furthermore, the most common estimation methods are treated, including maximum likelihood, least-squares, minimum variance, method of moments and Bayesian estimation. The course assumes some familiarity with basic matrix theory and statistics.

### Choose semester and course offering

Choose semester and course offering to see current information and more about the course, such as course syllabus, study period, and application information.

Headings with content from the Course syllabus FEM3210 (Spring 2019–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

·        Introduction

·        Minimum Variance Unbiased Estimation, Cramer-Rao Lower Bound

·        Linear Estimators

·        Maximum Likelihood

·        Least Squares

·        The Method of Moments

·        Bayesian Methods

·        Extension to Complex Data

### Intended learning outcomes

After the course the student should be able to:

·        Describe the difference between the classical and Bayesian approach to estimation; describe the notions of estimator bias, variance, and efficiency; and describe the notion of sufficient statistics and its meaning in minimum variance unbiased (MVU) estimation.

·        Formulate system models and parameter estimation problems and derive corresponding Cramer-Rao lower bounds and sufficient statistics. Prove optimality of estimators.

·        Apply appropriate estimators – including linear, least squares, maximum likelihood, and method of moments estimators – after considering estimation accuracy and complexity requirements

·        Work with both real and complex valued data models.

### Course disposition

No information inserted

## Literature and preparations

### Specific prerequisites

Sufficiency in probability theory, calculus and linear algebra (matrix analysis useful but not required).

### Recommended prerequisites

Sufficiency in probability theory, calculus and linear algebra (matrix analysis useful but not required).

### Equipment

No information inserted

### Literature

No information inserted

## Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

P, F

### Examination

• EXA1 - Examination, 10.0 credits, grading scale: P, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

### Other requirements for final grade

A score of 90 on 58 homework problems (78%) grades according to; 0: didn't try or completely incorrect, 1: almost correct (or solved parts of the problem), 2: correct. Completion of 2 project assignments. 50% on 48h take home exam.

### Opportunity to complete the requirements via supplementary examination

No information inserted

### Opportunity to raise an approved grade via renewed examination

No information inserted

### Ethical approach

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

## Further information

### Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web FEM3210

### Main field of study

This course does not belong to any Main field of study.

Third cycle