Estimation theory is a product of need and technology. As a result, it is an integral part of many branches of science and engineering. To help readers differentiate among the rich collection of estimation methods and algorithms, this book describes in detail many of the important estimation methods and shows how they are interrelated. Written as a collection of lessons, this book introduces readers o the general field of estimation theory and includes abundant supplementary material.
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To help readers differentiate among the rich collection of estimation methods and algorithms, this book describes in detail many of the important estimation methods and shows how they are intended. Written as a collection of lessons, the book introduces readers to the general field of estimation theory and includes abundant supplementary material. Approximately one half of the book is devoted to parameter estimation while the other half concentrates on state estimation.
From the Inside Flap
Estimation theory is widely used in many branches of science and engineering. No doubt, one could trace its origin back to ancient times, but Karl Friederich Gauss is generally acknowledged to be the progenitor of what we now refer to as estimation theory. R. A. Fisher, Norbert Wiener, Rudolph E. Kalman, and scores of others have expanded upon Gauss's legacy and have given us a rich collection of estimation methods and algorithms from which to choose. This book describes many of the important estimation methods and shows how they are interrelated.
Estimation theory is a product of need and technology. Gauss, for example, needed to predict the motions of planets and comets from telescopic measurements. This ``need'' led to the method of least squares. Digital computer technology has revolutionized our lives. It created the need for recursive estimation algorithms, one of the most important ones being the Kalman filter. Because of the importance of digital technology, this book presents estimation from a discrete-time viewpoint. In fact, it is this author's viewpoint that estimation theory is a natural adjunct to classical digital signal processing. It produces time-varying digital filter designs that operate on random data in an optimal manner.
Although this book is entitled ``Estimation Theory,' computation is essential in order to be able to use its many estimation algorithms. Consequently, computation is an integral part of this book.
It is this author's viewpoint that, whenever possible, computation should be left to the experts. Consequently, I have linked computation into MATLAB\registered\ (MATLAB is a registered trademark of The MathWorks, Inc.) and its associated toolboxes. A small number of important estimation M-files, which do not presently appear in any MathWorks toolbox, have been included in this book; they can be found in Appendix B.
This book has been written as a collection of lessons. It is meant to be an introduction to the general field of estimation theory and, as such, is not encyclopedic in content or in references. The supplementary material, which has been included at the end of many lessons, provides additional breadth or depth to those lessons. This book can be used for self-study or in a one-semester course.
Each lesson begins with a summary that describes the main points of the lesson and also lets the reader know exactly what he or she will be able to do as a result of completing the lesson. Each lesson also includes a small collection of multiple-choice summary questions, which are meant to test the reader on whether or not he or she has grasped the lesson's key points. Many of the lessons include a section entitledr
``Computation.'' When I decided to include material about computation, it was not clear to me whether such material should be collected together in one place, say at the rear of the book in an appendix, or whether it should appear at the end of each lesson, on demand so to speak. I sent letters to more than 50 colleagues and former students asking them what their preference would be. The overwhelming majority recommended having discussions about computation at the end of each lesson. I would like to thank the following for helping me to make this decision: Chong-Yung Chi, Keith Chugg, Georgios B. Giannakis, John Goutsias, Ioannis Katsavounidis, Bart Kosko, Li-Chien Lin, David Long, George Papavassilopoulos, Michael Safonov, Mostafa Shiva, Robert Scholtz, Ananthram Swami, Charles Weber, and Lloyd Welch.
Approximately one-half of the book is devoted to parameter estimation and the other half to state estimation. For many years there has been a tendency to treat state estimation, especially Kalman filtering, as a stand-alone subject and even to treat parameter estimation as a special case of state estimation. Historically, this is incorrect. In the musical Fiddler on the Roof, Tevye argues on behalf of
``Tradition!'' Estimation theory also has its tradition, and it begins with Gauss and parameter estimation. In Lesson 2 we show that state estimation is a special case of parameter estimation; i.e., it is the problem of estimating random parameters when these parameters change from one time instant to the next. Consequently, the subject of state estimation flows quite naturally from the subject of parameter estimation.
There are four supplemental lessons. Lesson A is on sufficient statistics and statistical estimation of parameters and has been written by Professor Rama Chellappa. Lessons B and C are on higher-order statistics. These three lessons are on parameter estimation topics. Lesson D is a review of state-variable models. It has been included because I have found that some people who take a course on estimation theory are not as well versed as they need to be about state-variable models in order to understand state estimation.
This book is an outgrowth of a one-semester course on estimation theory taught at the University of Southern California since 1978, where we cover all its contents at the rate of two lessons a week. We have been doing this since 1978. I wish to thank Mostafa Shiva, Alan Laub, George Papavassilopoulos, and Rama Chellappa for encouraging me to convert the course lecture notes into a book. The result was the first version of this book, which was published in 1987 as {\it Lessons in Digital Estimation Theory}. Since that time the course has been taught many times and additional materials have been included. Very little has been deleted. The result is this new edition.
Most of the book's important results are summarized in theorems and corollaries. In order to guide the reader to these results, they have been summarized for easy reference in Appendix A.
Problems are included for all the lessons (except Lesson 1, which is the Introduction), because this is a textbook. The problems fall into three groups. The first group contains problems that ask the reader to fill in details, which have been ``left to the reader as an exercise.''
The second group contains problems that are related to the material in the lesson. They range from theoretical to easy computational problems, easy in the sense that the computations can be carried out by hand. The third group contains computational problems that can only be carried out using a computer. Many of the problems were developed by students in my Fall 1991 and Spring 1992 classes at USC on Estimation Theory. For these problems, the name(s) of the problem developer(s) appears in parentheses at the beginning of each problem. The author wishes to thank all the problem developers.
While writing the first edition of the book, the author had the benefit of comments and suggestions from many of his colleagues and students. I especially want to acknowledge the help of Georgios B. Giannakis, Guan-Zhong Dai, Chong-Yung Chi, Phil Burns, Youngby Kim, Chung-Chin Lu, and Tom Hebert. While writing the second edition of the book, the author had the benefit of comments and suggestions from Georgios B. Giannakis, Mithat C. Dogan, Don Specht, Tom Hebert, Ted Harris, and Egemen Gonen. Special thanks to Mitsuru Nakamura for writing the estimation algorithm M-files that appear in Appendix B; to Ananthram Swami for generating Figures B 4, B 5, and B 7; and to Gent Paparisto for helping with the editing of the galley proofs.
Additionally, the author wishes to thank Marcel Dekker, Inc., for permitting him to include material from J. M. Mendel, Discrete Techniques of Parameter Estimation: The Equation Error Formulation}, 1973, in Lessons 1--3, 5--9, 11, 18, and 23; Academic Press, Inc., for permitting him to include material from J. M. Mendel, Optimal Seismic Deconvolution: An Estimation-based Approach}, copyright\,\copyright\,1983 by Academic Press, Inc., in Lessons 11--17, 19--21, and 25; and the Institute of Electrical and Electronic Engineers (IEEE) for permitting him to include material from J. M. Mendel, Kalman Filtering and Other Digital Estimation Techniques: Study Guide}, copyright, 1987 IEEE, in Lessons 1--3, 5--26, and D. I hope that the readers do not find it too distracting when I reference myself for an item such as a proof (e.g., the proof of Theorem 17-1). This is done only when I have taken material from one of my former publications (e.g., any one of the preceding three), to comply with copyright law, and is in no way meant to imply that a particular result is necessarily my own.
I am very grateful to my editor Karen Gettman and to Jane Bonnell and other staff members at Prentice Hall for their help in the production of this book.
Finally, I want to thank my wife, Letty, to whom this book is dedicated, for providing me, for more than 30 years, with a wonderful environment that has made this book possible.
Estimation theory is a product of need and technology. Gauss, for example, needed to predict the motions of planets and comets from telescopic measurements. This ``need'' led to the method of least squares. Digital computer technology has revolutionized our lives. It created the need for recursive estimation algorithms, one of the most important ones being the Kalman filter. Because of the importance of digital technology, this book presents estimation from a discrete-time viewpoint. In fact, it is this author's viewpoint that estimation theory is a natural adjunct to classical digital signal processing. It produces time-varying digital filter designs that operate on random data in an optimal manner.
Although this book is entitled ``Estimation Theory,' computation is essential in order to be able to use its many estimation algorithms. Consequently, computation is an integral part of this book.
It is this author's viewpoint that, whenever possible, computation should be left to the experts. Consequently, I have linked computation into MATLAB\registered\ (MATLAB is a registered trademark of The MathWorks, Inc.) and its associated toolboxes. A small number of important estimation M-files, which do not presently appear in any MathWorks toolbox, have been included in this book; they can be found in Appendix B.
This book has been written as a collection of lessons. It is meant to be an introduction to the general field of estimation theory and, as such, is not encyclopedic in content or in references. The supplementary material, which has been included at the end of many lessons, provides additional breadth or depth to those lessons. This book can be used for self-study or in a one-semester course.
Each lesson begins with a summary that describes the main points of the lesson and also lets the reader know exactly what he or she will be able to do as a result of completing the lesson. Each lesson also includes a small collection of multiple-choice summary questions, which are meant to test the reader on whether or not he or she has grasped the lesson's key points. Many of the lessons include a section entitledr
``Computation.'' When I decided to include material about computation, it was not clear to me whether such material should be collected together in one place, say at the rear of the book in an appendix, or whether it should appear at the end of each lesson, on demand so to speak. I sent letters to more than 50 colleagues and former students asking them what their preference would be. The overwhelming majority recommended having discussions about computation at the end of each lesson. I would like to thank the following for helping me to make this decision: Chong-Yung Chi, Keith Chugg, Georgios B. Giannakis, John Goutsias, Ioannis Katsavounidis, Bart Kosko, Li-Chien Lin, David Long, George Papavassilopoulos, Michael Safonov, Mostafa Shiva, Robert Scholtz, Ananthram Swami, Charles Weber, and Lloyd Welch.
Approximately one-half of the book is devoted to parameter estimation and the other half to state estimation. For many years there has been a tendency to treat state estimation, especially Kalman filtering, as a stand-alone subject and even to treat parameter estimation as a special case of state estimation. Historically, this is incorrect. In the musical Fiddler on the Roof, Tevye argues on behalf of
``Tradition!'' Estimation theory also has its tradition, and it begins with Gauss and parameter estimation. In Lesson 2 we show that state estimation is a special case of parameter estimation; i.e., it is the problem of estimating random parameters when these parameters change from one time instant to the next. Consequently, the subject of state estimation flows quite naturally from the subject of parameter estimation.
There are four supplemental lessons. Lesson A is on sufficient statistics and statistical estimation of parameters and has been written by Professor Rama Chellappa. Lessons B and C are on higher-order statistics. These three lessons are on parameter estimation topics. Lesson D is a review of state-variable models. It has been included because I have found that some people who take a course on estimation theory are not as well versed as they need to be about state-variable models in order to understand state estimation.
This book is an outgrowth of a one-semester course on estimation theory taught at the University of Southern California since 1978, where we cover all its contents at the rate of two lessons a week. We have been doing this since 1978. I wish to thank Mostafa Shiva, Alan Laub, George Papavassilopoulos, and Rama Chellappa for encouraging me to convert the course lecture notes into a book. The result was the first version of this book, which was published in 1987 as {\it Lessons in Digital Estimation Theory}. Since that time the course has been taught many times and additional materials have been included. Very little has been deleted. The result is this new edition.
Most of the book's important results are summarized in theorems and corollaries. In order to guide the reader to these results, they have been summarized for easy reference in Appendix A.
Problems are included for all the lessons (except Lesson 1, which is the Introduction), because this is a textbook. The problems fall into three groups. The first group contains problems that ask the reader to fill in details, which have been ``left to the reader as an exercise.''
The second group contains problems that are related to the material in the lesson. They range from theoretical to easy computational problems, easy in the sense that the computations can be carried out by hand. The third group contains computational problems that can only be carried out using a computer. Many of the problems were developed by students in my Fall 1991 and Spring 1992 classes at USC on Estimation Theory. For these problems, the name(s) of the problem developer(s) appears in parentheses at the beginning of each problem. The author wishes to thank all the problem developers.
While writing the first edition of the book, the author had the benefit of comments and suggestions from many of his colleagues and students. I especially want to acknowledge the help of Georgios B. Giannakis, Guan-Zhong Dai, Chong-Yung Chi, Phil Burns, Youngby Kim, Chung-Chin Lu, and Tom Hebert. While writing the second edition of the book, the author had the benefit of comments and suggestions from Georgios B. Giannakis, Mithat C. Dogan, Don Specht, Tom Hebert, Ted Harris, and Egemen Gonen. Special thanks to Mitsuru Nakamura for writing the estimation algorithm M-files that appear in Appendix B; to Ananthram Swami for generating Figures B 4, B 5, and B 7; and to Gent Paparisto for helping with the editing of the galley proofs.
Additionally, the author wishes to thank Marcel Dekker, Inc., for permitting him to include material from J. M. Mendel, Discrete Techniques of Parameter Estimation: The Equation Error Formulation}, 1973, in Lessons 1--3, 5--9, 11, 18, and 23; Academic Press, Inc., for permitting him to include material from J. M. Mendel, Optimal Seismic Deconvolution: An Estimation-based Approach}, copyright\,\copyright\,1983 by Academic Press, Inc., in Lessons 11--17, 19--21, and 25; and the Institute of Electrical and Electronic Engineers (IEEE) for permitting him to include material from J. M. Mendel, Kalman Filtering and Other Digital Estimation Techniques: Study Guide}, copyright, 1987 IEEE, in Lessons 1--3, 5--26, and D. I hope that the readers do not find it too distracting when I reference myself for an item such as a proof (e.g., the proof of Theorem 17-1). This is done only when I have taken material from one of my former publications (e.g., any one of the preceding three), to comply with copyright law, and is in no way meant to imply that a particular result is necessarily my own.
I am very grateful to my editor Karen Gettman and to Jane Bonnell and other staff members at Prentice Hall for their help in the production of this book.
Finally, I want to thank my wife, Letty, to whom this book is dedicated, for providing me, for more than 30 years, with a wonderful environment that has made this book possible.
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3 of 3 people found the following review helpful:
4.0 out of 5 stars
Not for the mathematically faint of heart,
This review is from: Lessons in Estimation Theory for Signal Processing, Communications, and Control (2nd Edition) (Paperback)
I used this book for a class during my PhD in Elec Engr. This book is best read with a second book in statistics and a third on signals close at hand. The concepts are complex and presented in a reasonably brief manner. It packs a lot of punch in a relatively small space. If graduate classes in signal processing and control systems are your bag, this may be the book for you.
1 of 1 people found the following review helpful:
5.0 out of 5 stars
Lessons in Estimation Theory is an Excellent Text Book,
This review is from: Lessons in Estimation Theory for Signal Processing, Communications, and Control (2nd Edition) (Paperback)
I first used this text book in 1980 at USC. At that time, it was only in the form of prepared lecture notes. The current organization of this book is the same as before. New material has been added. I purchased this book because of the new revised material. I find the book to be very systematic. It is an excellent book for personal study of the subject or as a graduate text book. Since 1980, there are some other books that are now available on the subject. But this book stays very relevant and useful as ever. I recommend it highly.
5.0 out of 5 stars
A well organized, useful book on estimation theory,
This review is from: Lessons in Estimation Theory for Signal Processing, Communications, and Control (2nd Edition) (Paperback)
I am a student of the author and I really enjoyed this book along with his lectures. I may not enjoy reading this book without going through the lectures of the author (This is the scenario with many subjects to most students). The book is well written well organized and I benefited a lot from this book.
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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estimation errors act, state augmentation procedure, generic linear model, formal limiting procedure, filter tuning parameter, perturbation state equation, recursive predictor, iterated least squares, smoother formulas, vector random sequence, correlated noise case, convolutional model, linear perturbation equations, deconvolution filter, corrector equation, immediate past value, colored noise processes, covariance form, smoothed estimator, additive measurement noise, prediction error filter, linear prediction problem, artificial measurements, orthogonality principle, state estimation Key Phrases - Capitalized Phrases (CAPs): (learn more)
Supplementary Material, Least-squares Estimation, General Results, Steady-state Kalman Filter Lesson, Higher-order Statistics Lesson, Kalman-Bucy Filtering Lesson, Filtering Examples Lesson, Posteriori Estimation of Random Parameters Lesson, The Linear Model Lesson, Mean-squared Estimation of Random Parameters Lesson, Large-sample Properties of Estimators Lesson, Derive Equation, Best Linear Unbiased Estimation Lesson, Maximum-likelihood Estimation Lesson, Small-sample Properties of Estimators Lesson, Prediction Lesson, Batch Processing Lesson, Recursive Processing Lesson, Singular-value Decomposition Lesson, Computational Problem, Properties of Least-squares Estimators Lesson, Smoothing Lesson, Definitions of Higher-order Statistics, Prove Theorem, Brad Verona Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
estimation errors act, state augmentation procedure, generic linear model, formal limiting procedure, filter tuning parameter, perturbation state equation, recursive predictor, iterated least squares, smoother formulas, vector random sequence, correlated noise case, convolutional model, linear perturbation equations, deconvolution filter, corrector equation, immediate past value, colored noise processes, covariance form, smoothed estimator, additive measurement noise, prediction error filter, linear prediction problem, artificial measurements, orthogonality principle, state estimation Key Phrases - Capitalized Phrases (CAPs): (learn more)
Supplementary Material, Least-squares Estimation, General Results, Steady-state Kalman Filter Lesson, Higher-order Statistics Lesson, Kalman-Bucy Filtering Lesson, Filtering Examples Lesson, Posteriori Estimation of Random Parameters Lesson, The Linear Model Lesson, Mean-squared Estimation of Random Parameters Lesson, Large-sample Properties of Estimators Lesson, Derive Equation, Best Linear Unbiased Estimation Lesson, Maximum-likelihood Estimation Lesson, Small-sample Properties of Estimators Lesson, Prediction Lesson, Batch Processing Lesson, Recursive Processing Lesson, Singular-value Decomposition Lesson, Computational Problem, Properties of Least-squares Estimators Lesson, Smoothing Lesson, Definitions of Higher-order Statistics, Prove Theorem, Brad Verona Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
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- Model-Based Signal Processing (Adaptive and Learning Systems for Signal Processing, Communications and Control Series) by James V. Candy in Front Matter, page 17, and page 168
- Blind Equalization and System Identification: Batch Processing Algorithms, Performance and Applications (Advanced Textbooks in Control and Signal Processing) by Chong-Yung Chi on page 81
- Signal and Image Processing in Navigational Systems (Electrical Engineering & Applied Signal Processing Series) by Vyacheslav Tuzlukov on page 215
- Microphone Arrays: Signal Processing Techniques and Applications (Digital Signal Processing) by Michael Brandstein on page 225
- Cooperation in Wireless Networks: Principles and Applications: Real Egoistic Behavior is to Cooperate! by Frank H. P. Fitzek on page 125
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