Thank you to the following supporters of ICASSP 2007
Prof. Harry L. Van Trees, George Mason University and University of Hawaii. and Prof. Kristine Bell George Mason University
Bayesian estimation plays a central role in many signal processing problems. These are often highly nonlinear problems for which evaluation of the exact performance is intractable. A widely used technique is to find a bound on the performance of any estimator, or some class of estimators, and compare the performance of various sub-optimal estimators to the bounds. Of particular interest is performance in the asymptotic and threshold regions. The most common of these bounds is the Bayesian Cramer-Rao bound (BCRB), which was originally developed for static parameter estimation problems and then extended to nonlinear dynamic systems. The BCRB is a small error bound useful for predicting performance in the asymptotic region. More sophisticated Bayesian bounds developed to analyze threshold region behavior for static parameters include the Weiss-Weinstein and Ziv-Zakai families of bounds. These have only recently begun to be investigated for dynamic nonlinear filtering and tracking systems. This course will provide a comprehensive discussion of Bayesian bounds from the original BCRB to the current state-of-the art, with a series of examples to demonstrate their application to static parameter estimation and nonlinear filtering/tracking problems of general interest.
1. Bayesian Estimation: static parameters (Van Trees & Bell) 1.1. Maximum Likelihood and Maximum a Posteriori estimation; nonrandom, random, and hybrid parameter models 1.2. Covariance inequality bounds; Bayesian Cramer-Rao Bound, Bayesian Bhattacharyya Bound, Bobrovsky-Zakai bound, Weiss-Weinstein bound. Application to range, frequency, and DOA estimation. 1.3. Ziv-Zakai family bounds; Ziv-Zakai bound, Bellini-Tartara bound, extended Ziv-Zakai bound. Comparison with covariance inequality family. 1.4. Method of interval estimation; two-step estimators and outlier probabilities. 2. Bayesian Estimation: nonlinear stochastic dynamic systems (Van Trees & Bell) 2.1. Sequential Bayesian estimation; brief treatment of extended Kalman filters, particle filters 2.2. Recursive Bayesian Cramer-Rao bound. Application to tracking and frequency estimation problems. 2.3. Recursive Weiss-Weinstein bound; application to bearing estimation and tracking. 3. Summary (Van Trees)A course in Estimation Theory is necessary to fully understand the material. Typical courses would use Van Trees, “Detection, Estimation and Modulation Theory, Part I or Kay, “Fundamentals of Statistical Signal Processing, Estimation Theory”. A course in Random Processes will enable one to follow the lectures but will require additional work to fully understand the results.
H. L. Van Trees and K. L. Bell, Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking, IEEE Press and Wiley Interscience, 2007.
This book will be published in July 2007. It is a collection of reprints of fundamental papers dealing with Bayesian bounds, with an introductory chapter of original material providing an overview of the topic and a series of examples.
This tutorial is excerpted from the introductory chapter. The book will not be available in time for the tutorial, however participants will find the book a useful companion to the course.
Dr. Van Trees joined the faculty at the University of Hawaii at Manoa as a Professor of Electrical Engineering in January of 2006. He teaches courses in the area of detection and estimation theory, array processing, and radar and sonar tracking systems. He is also a Distinguished Research Professor at George Mason University
He received the B.S. from the U.S. Military Academy, West Point. He received the M.S.E.E. from the University of Maryland and the Sc.D.E.E. from the Massachusetts Institute of Technology.
Prior to joining the faculty of George Mason University in September, 1988 as a Distinguished Professor of Information Technology, and Electrical and Systems Engineering, Dr. Van Trees was President of M/A - COM Government Systems, a high technology company in the defense electronics area. Previously, Dr. Van Trees served as Principal Deputy Assistant Secretary of Defense (C3I) and as Acting Assistant Secretary of Defense; Command, Control, Communications and Intelligence. He also served as Chief Scientist of the United States Air Force and Chief Scientist and Associate Director for Technology of the Defense Communications Agency.
Prior to his government service, Dr. Van Trees was a Professor of Electrical Engineering at M.I.T. for 14 years. During that period, he published a three-volume set of books on Detection, Estimation, and Modulation Theory (DEMT), which are the classics in the area. He also made a two-semester video course on Probability and Random Processes which is available on DVDs.
His professional awards include: Fellow, Institute of Electrical and Electronic Engineers; Presidential Award for Meritorious Executive and Distinguished Civilian Service Award. Dr. Van Trees has been a member of the U.S. Air Force Scientific Advisory Board and the Communications Society Board of Governors.
Dr. Van Trees was Director of the Center of Excellence in C3I at the George Mason University and a University Professor associated with the Departments of Electrical and Computer Engineering from 1988 to 2006 .He is currently a University Professor Emeritus and a part-time Distinguished Research Professor.
In 2002, he published a book on Optimum Array Processing, the 4th volume in the DEMT series. It was well received and is currently in it’s 4th printing.
Books: http://ite.gmu.edu/DetectionandEstimationTheory/
Resume: http://c3i.gmu.edu/resumes/HLVanTrees.html
Prof. Bell received a B.S. in Electrical Engineering from Rice University, Houston, TX in 1985, and an M.S. in Electrical Engineering and Ph.D. in Information Technology from George Mason University, Fairfax, VA in 1990 and 1995, respectively.
She joined the department of Applied and Engineering Statistics at George Mason University in 1996, where she is currently an Associate Professor. Her research interests are in the areas of robust, adaptive signal processing techniques and performance bounds for source localization and tracking with applications in radar, sonar, aeroacoustics, and satellite communications.
She has held visiting researcher positions at the Naval Research Lab and the Army Research Lab and has worked as a consultant for SAIC, ArgonST, Lockheed-Martin, and Metron, Inc. Her research has been sponsored by the Office of Naval Research (ONR), the Army Research Laboratory (ARL), the Defense Advanced Research Projects Agency (DARPA), as well as Orincon and Lockheed-Martin.
Prof. Bell has served as General Co-Chair for the 2002 IEEE Sensor Array and Multichannel Signal Processing (SAM) Workshop and as an Associate Editor for the IEEE Transactions on Signal Processing.
Resume: http://gunston.gmu.edu/kbell/