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2.160 Identification, Estimation, and Learning

Spring 2006

A photograph of the Mars rover.The Mars rover relies on sophisticated identification and estimation techniques to navigate the Martian terrain. (Image courtesy of NASA.)

Course Highlights

This course features extensive lecture notes and many assignments.

Course Description

This course provides a broad theoretical basis for system identification, estimation, and learning. Students will study least squares estimation and its convergence properties, Kalman filters, noise dynamics and system representation, function approximation theory, neural nets, radial basis functions, wavelets, Volterra expansions, informative data sets, persistent excitation, asymptotic variance, central limit theorems, model structure selection, system order estimate, maximum likelihood, unbiased estimates, Cramer-Rao lower bound, Kullback-Leibler information distance, Akaike's information criterion, experiment design, and model validation.

Technical Requirements

Special software is required to use some of the files in this course: .zip. The .txt files in the assignments section are used for MATLAB®.





Syllabus

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Course Description

This course covers the following topics, with the aim of providing students with a broad theoretical basis for system identification, estimation, and learning:

Least squares estimation and its convergence properties, Kalman filter and extended Kalman filter, noise dynamics and system representation, function approximation theory, neural nets, radial basis functions, wavelets, Volterra expansions, informative data sets, persistent excitation, asymptotic variance, central limit theorems, model structure selection, system order estimate, maximum likelihood, unbiased estimates, Cramer-Rao lower bound, Kullback-Leibler information distance, Akaike's information criterion, experiment design, and model validation.



Prerequisites

Advanced System Dynamics and Control (2.151)



Textbooks

There is no primary textbook for this course. Most of the course materials have been developed based on the following references:

Amazon logo Ljung, Lennart. System Identification: Theory for the User. 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 1999. ISBN: 9780136566953.

Amazon logo Goodwin, Graham, and Kwai Sang Sin. Adaptive Filtering, Prediction, and Control. Englewood Cliffs, NJ: Prentice-Hall, 1984. ISBN: 9780130040695.

Amazon logo Burnham, Kenneth, and David Anderson. Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach. 2nd ed. New York, NY: Springer, 2003. ISBN: 9780387953649.

Amazon logo Brown, Robert, and Patrick Hwang. Introduction to Random Signals and Applied Kalman Filtering. 3rd ed. New York, NY: Wiley, 1996. ISBN: 9780471128397.



Grading Policy

There will be 7 homework assignments and 2 two-hour exams. Each student is also expected to complete 1 project.


ActivitiesPercentages
First Exam30%
Second Exam30%
Homework Assignments20%
Term Project20%




Calendar

Lec #TopicsKey Dates
1Introduction
Part I: Estimation
2Recursive Least Square (RLS) Algorithms
3Properties of RLS
4Random Processes, Active Noise Cancellation
5Discrete Kalman Filter-1Problem set 1 due
6Discrete Kalman Filter-2
7Continuous Kalman FilterProblem set 2 due
8Extended Kalman Filter
Part 2: Representation and Learning
9Prediction Modeling of Linear SystemsProblem set 3 due
10Model Structure of Linear Time-invariant Systems
11Time Series Data Compression, Laguerre Series ExpansionProblem set 4 due
12Non-linear Models, Function Approximation Theory, Radial Basis Functions
13Neural NetworksProblem set 5 due
Mid-term Exam
14Error Back Propagation Algorithm
Part 3: System Identification
15Perspective of System Identification, Frequency Domain Analysis
16Informative Data Sets and ConsistencyProblem set 6 due
17Informative Experiments: Persistent Excitation
18Asymptotic Distribution of Parameter Estimates
19Experiment Design, Pseudo Random Binary Signals (PRBS)
20Maximum Likelihood Estimate, Cramer-Rao Lower Bound and Best Unbiased EstimateProblem set 7 due
21Information Theory of System Identification: Kullback-Leibler Information Distance, Akaike's Information Criterion
Final Exam




Lecture Notes

Lecture Notes Table of Contents (PDF)

Available lecture notes are listed below.


Lec #Topics
1Introduction (PDF 1) (PDF 2)
Part I: Estimation
2Recursive Least Square (RLS) Algorithms (PDF)
3Properties of RLS (PDF)
4Random Processes, Active Noise Cancellation (PDF)
5Discrete Kalman Filter-1 (PDF)
6Discrete Kalman Filter-2 (PDF)
7Continuous Kalman Filter (PDF)
8Extended Kalman Filter (PDF)
Part 2: Representation and Learning
9Prediction Modeling of Linear Systems (PDF)
10Model Structure of Linear Time-invariant Systems (PDF)
11Time Series Data Compression, Laguerre Series Expansion (PDF)
12Non-linear Models, Function Approximation Theory, Radial Basis Functions (PDF)
13Neural Networks (PDF)
14Error Back Propagation Algorithm (PDF)
Part 3: System Identification
15Perspective of System Identification, Frequency Domain Analysis (PDF)
16Informative Data Sets and Consistency (PDF)
17Informative Experiments: Persistent Excitation (PDF)
18Asymptotic Distribution of Parameter Estimates (PDF)
19Experiment Design, Pseudo Random Binary Signals (PRBS) (PDF)
20Maximum Likelihood Estimate, Cramer-Rao Lower Bound and Best Unbiased Estimate (PDF)
21Information Theory of System Identification: Kullback-Leibler Information Distance, Akaike's Information Criterion (PDF)




Assignments

Special software is required to use some of the files in this section: .zip. The .txt files are used for MATLAB®. This section contains documents that could not be made accessible to screen reader software. A "#" symbol is used to denote such documents.

Each set of related files includes a "Read Me" document, which details how those files relate to the problem set.


AssignmentsRelated Files
Problem Set 1 (PDF)ps1files.zip (ZIP) (The ZIP file contains: 13 .txt files.)
Problem Set 2 (PDF)ps2files.zip (ZIP) (The ZIP file contains: 6 .txt files.)
Problem Set 3 (PDF)ps3files.zip (ZIP) (The ZIP file contains: 6 .txt files.)
Problem Set 4 (PDF)
Problem Set 5 (PDF)ps5files.zip (ZIP) (The ZIP file contains: 3 .txt files.)
Problem Set 6 (PDF)#
Problem Set 7 (PDF)




Exams

Mid-term Exam (PDF)

Final Exam (PDF)





Projects

Students are required to complete one project, which counts towards 20% of their final grade.



Topics

Find a project topic of your interest. Use identification, estimation, and learning techniques relevant to the course material. Possible topics include, but are not limited to:

A good term project will contain a mixture of theory and practice. Please include an interesting context or application background, address how you achieved the goal, and discuss specific technical details. Don't forget that the focus of this subject is data; let the data speak about the system.



Requirements

The project should be a maximum of ten pages long, excluding figures. Please include a title, name, and an abstract. The paper should contain the following sections:




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