ECE 6540: Estimation Theory (Spring 2016)

Transcription

1 ECE 6540: Estimation Theory (Spring 2016) Instructor : Joel B. Harley Joel.Harley@utah.edu Website : ece6540/ Office : MEB 3104 Office hours : By appointment Class meetings : M,W 1:25 PM 2:45 PM in WEB 1450 Course Description: Uncertainty is everywhere in engineering. Communications, radar, medical imaging, and many other applications require we estimate parameters and detect signals in the presence of high levels of uncertainty and noise. For example, in communications, we commonly want to estimate the frequency, amplitude, and phase of a sinusoid. All three of these quantities can carry important information, and there are nearly infinite approaches for estimating these parameters. Yet, what approach is the best in noisy and/or uncertain conditions? Furthermore, how do we define best? What is the best way to know are even looking at a sinusoid? In this class, we explore these types of questions. We explore optimal approaches for estimating parameters and detecting signals. We will start with discussing statistical methods for estimating the unknown parameters of a given signal. We then explore optimal approaches for detecting these signals (with or without unknown parameters). Textbook: The course will use the following textbooks: Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory by Steven Kay Fundamentals of Statistical Signal Processing, Volume II: Detection Theory by Steven Kay Learning Objectives: At the completion of this course, you should be able to: 1. Understand linear models and their relationship with probability distributions 2. Compute Cramer Rao Lower Bounds 3. Estimate parameters with multiple criteria: minimum variance, maximum likelihood, Bayesian assumptions 4. Detect multiple types of signals: deterministic signals, random signals, signals with unknown parameters Prerequisites: ECE 5510 and ECE 5530, or equivalent. Grade Distribution: Homework (best N 1 our of N) 20% Midterm Exam I 20% Midterm Exam II 20% Project Paper 25% Project Poster Presentation 15% 1

2 Evaluation Methods and Criteria: The following section discusses the policies for each of the graded assessments in this course. You should look here first for answers to any general, course-related inquiries. Homework (8 total): When: Assigned roughly once every one or two weeks. Why: Homework is intended to present you with questions from the course material that will require time to complete. Assignments are not meant to be completed in a single day. Grading: Homework is eligible for 100 points. Late policy: Late assignments will not be eligible for 25x points, where x is the number of days late, for up to 4 days. For example, if you receive a 80 for an assignment and submit the assignment 3 days late, the final grade will be a 80 (25)3 = 5. Submission: Homework is due on the due date (see online schedule) at 5:00 PM. Midterm Exams (2 total): When: There are two mid-term exam covering each of the course. Why: Exams are an opportunity to show what you have learned in the course. Grading: The midterm exams is eligible for 100 points. Cheat sheets: You may bring one double-sided 8.5 by 11 inches (or smaller) cheat sheet to each midterm exam. Makeup exams: There will be no makeup exam except under extraordinary conditions. Projects: When: You (as part of a team of 2-3 people) will be responsible for completing a project, writing a report, and giving a poster presentation on your results. Poster presentations will be on the day of the final. What: You will apply concepts from estimation theory in order to solve a problem of your choice (this can originate from your own research if you have one) or a selection provided by myself. Grading: Projects will be graded based on effort, completeness, and clarity of the submitted report and given poster presentation. The poster presentations will be judged by other faculty and students. Final Grades: Guaranteed Grades: A: > 93.33% A-: % B+: % B: % B-: % C+: % C: % C-: % D+: % D: % D-: % E: < 60% Curves: If necessary, the grading criteria may be curved to improve the class s overall scores. Attendance and Participation: Attendance & Participation: Since this is an advanced graduate course, we assume you are very interested in learning about estimation theory concepts. As a result, I expect you want to attend and participate in class and do not require additional extrinsic motivation. 2

3 Teaching and Learning Methods / Course Policies: The following section discusses the course s non-graded activities and policies towards collaboration and cheating. You should look here first for answers to any general, course-related inquiries. Course Structure: Part I: Estimation Theory Part II: Detection Theory Surveys: When: Occasionally at the end of class. What: A few short questions about the course progress. Why: The surveys are intended to let you shape the course by letting me know what you like and what could be improved. Note that while I may not be able to follow-through with every suggestion in a single semester, they will still help me to improve the course in subsequent years. Modifying Syllabus by Class Vote: When: If you and/or other students believe the course would be improved by a change in the syllabus and I agree that it would be a reasonable change. What: The proposed change will be put to an anonymous vote with the entire class. If the majority of the class agrees to this change, it becomes part of the syllabus. Why: In previous years, changes to the syllabus have been necessary do to unforeseen consequences of certain policies. The class vote ensures the entire class agrees with the change. Faculty and Student Responsibilities: Student responsibilities: You are expected to maintain professional behavior in the classroom setting, according to the Student Code, spelled out in the Student Handbook. Students have specific rights in the classroom as detailed in Article III of the Code. The Code also specifies proscribed conduct (Article XI) that involves cheating on tests, plagiarism, and/or collusion (course details described in following section), as well as fraud, theft, etc. You should read the Code carefully and know they are responsible for the content. Faculty responsibilities: According to Faculty Rules and Regulations, it is my responsibility to enforce responsible classroom behaviors, beginning with verbal warnings and progressing to dismissal from class and a failing grade. You have the right to appeal such action to the Student Behavior Committee. Collaboration: Healthy collaboration: To solve homework assignments, healthy discussion and collaboration amongst classmates is encouraged. Healthy collaboration includes: Discussing and explaining general course material Discussing assignments for better understanding Providing assistance for general programming and debugging issues If another student contributes substantially to your understanding of a problem, you should cite this student to let myself and the teaching assistants be aware of your similar interpretations of a problem. You will not be judged negatively for citing another student. 3

4 Cheating and plagiarism: While collaboration is encouraged, you are expected to submit your own work. Submitting work completed by another student is considered plagiarism and will be dealt with according to university policy. In general, if you do not fully understand your solution, the work is not your own. Examples of plagiarism or cheating include: Copying (or allowing someone to copy), even partially, an assignment solution or program from the course Submitting material, particularly a program, using material taken from another source without proper a citation Obtaining solutions to assignments or exams through inappropriate means Additional information can be found in Section I.B of the Code of Student Rights and Responsibilities found here: Note that I may elect to use a plagiarism detection service in this course, in which case you will be required to submit your work to such a service as part of your assignment. Consequences: If you are suspected of dishonest academic activity, I will invite you to discuss it further in private. Academic dishonesty will likely result in a grade reduction, with severity depending on the nature of the dishonest activity, and a letter to the department, college, and/or university leadership. Repeat offences will be treated with significantly greater severity. Additional information can be found in Section V of the Code of Student Rights and Responsibilities found here: Americans with Disabilities Act Support: Equal access services: The University of Utah seeks to provide equal access to its programs, services and activities for people with disabilities. If you will need accommodations in the class, reasonable prior notice needs to be given to the Center for Disability Services, 162 Union Building, (V/TDD). CDS will work with you and the instructor to make arrangements for accommodations. ( Legal Note: Note: The syllabus is not a binding legal contract. It may be modified by the instructor when the student is given reasonable notice of the modification. See Modifying Syllabus by Class Vote for additional information. 4

5 Tentative Course Outline: Note: This schedule is likely to change. Any HW changes will be announced in class and displayed on the course website. Part I : Estimation Theory Mon Jan 11 Introduction, policies, Linear models Ch. I.4 Wed Jan 13 Linear Algebra / Linear models Ch. I.4 Mon Jan 18 Martin Luther King Jr. Day Wed Jan 20 Linear Algebra / Linear models Ch. I.4 HW 1 due Mon Jan 25 Minimum Variance Unbiased Estimation. Ch. I.2, I.5 Wed Jan 27 Minimum Variance Unbiased Estimation. Ch. I.2, I.5 Mon Feb 01 Cramer-Rao Lower Bound. Ch. I.3 HW 2 due Wed Feb 03 Cramer-Rao Lower Bound. Ch. I.3 Mon Feb 08 Maximum Likelihood Estimation. Ch. I.7 Wed Feb 10 Maximum Likelihood Estimation. Ch. I.7 HW 3 due Mon Feb 15 President s Day Wed Feb 17 Bayesian Estimators Ch. I.10 I.12 Mon Feb 22 Bayesian Estimators Ch. I.10 I.12 HW 4 due Wed Feb 24 Kalman Filtering Ch. I.13 Mon Feb 29 Kalman Filtering Ch. I.13 Wed Mar 02 Mid-term Exam I Part II: Detection Theory Mon Mar 07 Statistical Detection Theory Ch. II.3 Wed Mar 09 Statistical Detection Theory Ch. II.3 HW 5 due Mon Mar 14 Spring break (no class) Wed Mar 16 Spring break (no class) Mon Mar 21 Deterministic Signals Ch. II.4 Wed Mar 23 Deterministic Signals Ch. II.4 Mon Mar 28 Random Signals Ch. II.5 HW 6 due Wed Mar 30 Random Signals Ch. II.5 Mon Apr 04 Statistical Detection Theory Ch. II.6 Wed Apr 06 Statistical Detection Theory Ch. II.6 HW 7 due Mon Apr 11 Deter. Signals With Unknown Para. Ch. II.7 Wed Apr 13 Deter. Signals With Unknown Para. Ch. II.7 Mon Apr 18 Random Signals With Unknown Para. Ch. II.8 HW 8 due Wed Apr 20 Random Signals With Unknown Para. Ch. II.8 Mon Apr 25 Mid-term Exam II 5