Morning Tutorial 5

• Summary and Purpose:

  Traditional methods in estimation theory (such as least-mean-squares, maximum-likelihood, and maximum entropy) assume perfect models and require a priori knowledge of the statistical properties of the exogenous signals. In many applications, however, one is faced with model uncertainties and lack of statistical information, so that traditional methods are not directly applicable.

  The objective of robust estimation, on the other hand, is to design estimators that have acceptable performance in the face of the aforementioned deficiencies. In this tutorial, we will describe the H-infinity approach to robust estimation, emphasizing both the physical, as well as the computational, aspects of the theory, and highlighting the differences and similarities that exist with conventional statistical techniques.

  Although originally conceived as a method for dealing with plant uncertainty in control systems, H-infinity theory has ramifications for problems well beyond those of control, and its power and applicability is largely underappreciated in the signal processing and communications communities. The goal of this tutorial therefore is to present some of the basic and newer results of H-infinity theory to researchers in these fields, and to describe a host of problems where the theory applies and where it can lead to significant new results.

• Outline:
  
  
  1. Theory:
     • Robust estimation:
       Worst-case vs. average and deterministic vs. stochastic performance.
     • H-infinity estimation:
       Relations to risk-sensitivity.
       Noncausal solutions.
       Optimal causal solutions.
     • Suboptimal H-infinity solutions.
     
     
  2. Computational Aspects:
     • State-space techniques. Riccati equations, LMI's, etc.
     
     
  3. Applications:
     • Adaptive filtering:
       The LMS algorithm.
     • Active noise cancellation.
     • Equalization:
       Linear and decision-feedback.
     • Filtering signals in additive noise.
     • Prediction.
     • Multirate signal processing:
       Design of synthesis filters.
     • Others.
  
  
  
• About the Tutorial Speakers:
  
  
  • Babak Hassibi was born in Tehran, Iran, in 1967. He received the B.S. degree from the University of Tehran in 1989, and the M.S. and Ph.D. degrees from Stanford University in 1993 and 1996, respectively, all in electrical engineering.

    From June 1992 to September 1992 he was with Ricoh California Research Center, Menlo Park, CA, and from August 1994 to December 1994 he was a short-term Research Fellow at the Indian Institute of Science, Bangalore India. Since September 1996 he has been a research associate at the Information Systems Laboratory, Stanford University, and starting November 1998 will be a Member of the Technical Staff at Bell Laboratories, Murray Hill, NJ. His research interests include robust estimation and control, equalization of communication channels, adaptive signal processing and neural networks, and linear algebra. He is the coauthor of the forthcoming books Indefinite Quadratic Estimation and Control: A Unified Approach to $H2$ and Theories (New York: SIAM, 1998) and State Space Estimation (Englewood Cliffs, NJ: Prentice Hall, 1998).

  • Thomas Kailath received the S.M. degree in 1959 and the Sc.D. degree in 1961 from the Massachussetts Institute of Technology.

    From October 1961 to December 1961, he worked at the Jet Propulsion Laboratories, Pasadena, CA, where he also taught part-time at the California Institute of Technology. He then went to Stanford University, where he served as Director of the Information Systems Laboratory from 1971 through 1980, as Associate Department Chairman from 1981 to 1987, and currently holds the Hitachi America Professorship in Engineering. He has held short-term appointments at several institutions around the world. His recent research interests include applications of signal processing, computation and control to problems in semiconductor manufacturing and wireless communications. He is the author of Linear Systems (Englewood Cliffs, NJ: Prentice Hall, 1980) and Lectures on Wiener and Kalman Filtering (New York: Springer-Verlag, 1981) and the coauthor of Indefinite Quadratic Estimation and Control: A Unified Approach to $H2$ and Theories (New York: SIAM, 1998) and State Space Estimation (Englewood Cliffs, NJ: Prentice Hall, 1998).

    Dr. Kailath is a fellow of the IEEE, the Institute of Mathematical Statistics, and is a member of the National Academy of Engineering and the American Academy of Arts and Sciences. He has held Guggenheim, Churchill and Royal Society fellowships, among others, and received awards from the IEEE Information Theory Society and the American Control Council, in addition to the Technical Achievement and Society Awards of the IEEE Signal Processing Society. He served as the President of the IEEE Information Theory Society in 1975.

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Last Update:  February 4, 1999         Ingo Höntsch