Kailath is Hitachi America Professor of Engineering emeritus at Stanford University. Here he has supervised about 80 Ph.D. theses. Kailath's research work has encompassed linear systems, estimation and control theory, signal processing, information theory and semiconductor device fabrication.[5][6][7]

This original work offers the most comprehensive and up-to-date treatment of the important subject of optimal linear estimation, which is encountered in many areas of engineering such as communications, control, and signal processing, and also in several other fields, e.g., econometrics and statistics. The book not only highlights the most significant contributions to this field during the 20th century, including the works of Wiener and Kalman, but it does so in an original and novel manner that paves the way for further developments. This book contains a large collection of problems that complement it and are an important part of piece, in addition to numerous sections that offer interesting historical accounts and insights. The book also includes several results that appear in print for the first time.


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After his studies at the Massachusetts Institute of Technology (Sc.D., 1961), Thomas Kailath was invited by S. Golomb to join the Communications Research Group at the Jet Propulsion Laboratory in Pasadena, CA, in a section led by A. Viterbi. He also held a visiting appointment at Caltech, which perhaps had a role in his move in 1963 to Stanford University, where he is now Hitachi America Professor of Engineering, Emeritus. Over the years, aided by a stellar array of over a hundred doctoral and postdoctoral scholars, his research has ranged over several fields, including information theory, linear systems, estimation and control, signal processing, semiconductor manufacturing, probability and statistics, and matrix and operator theory. Major honors include the IEEE Education and Signal Processing Medals and the IEEE Medal of Honor in 2007. He has also held Guggenheim and Churchill Fellowships, received several honorary degrees, co-founded companies with his students, and been elected to the U.S. National Academy of Engineering, the U.S. National Academy of Sciences, the American Academy of Arts and Sciences, the Silicon Valley Engineering Hall of Fame and several foreign academies. In 2009, he received a Padma Bhushan national award from the President of India, the Blaise Pascal Medal from the European Academy of Sciences, and was elected as a Foreign Member of the Royal Society of London.

It must be with some trepidation that one ventures to speak about the problems of linear estimation to an audience already well familiar with the overwhelmingly more difficult nonlinear filtering problem. However, perhaps to compensate for this spectacle, the organizers have given me the opportunity to speak first, with considerable latitude in the choice of my topics.

Much of the research I have performed has been carried out with some 100 doctoral and postdoctoral scholars over the last four decades and has ranged over many areas of electrical engineering (information and communication theory, statistical signal detection and estimation, linear system theory, control theory, inverse scattering, sensor array processing, VLSI design, and computation) and mathematics (stochastic processes, operator theory, linear algebra, and interpolation theory). I have particularly enjoyed working at the interfaces of these fields, carrying tools and insights across various disciplinary boundaries. My current major interests are in the area of semiconductor manufacturing and in developing fast algorithms for many applications by identifying and exploiting we have called "displacement structure" in the problem. In the first area I have introduced multi-variable system identification and control techniques to generate (essentially) arbitrary temperature profiles across a wafer, a possibility that can significantly increase the yield of thermal processing operations in many fields. So also in optical lithography, concepts of signal processing have been successfully introduced to break the "0.1 um barrier" in optical lithography.

Dr. Thomas Kailath was born on June 7, 1935, in Poona, India. Dating back to his early writings in the late 1950s, Dr. Kailath recognized that engineering theory would play a critical role in meeting technological challenges in the disciplines of communication, computation, control and signal processing. Since then, his theoretical work has led to fundamental breakthroughs in communications, information theory, signal detection and estimation, sensor array signal processing, VLSI architectures for signal processing and semiconductor manufacturing. He also contributed to probability and statistics, linear algebra, and matrix and operator theory.

He has written several books, authored or co-authored over 300 journal articles and papers, and shared in the development of 13 patents. Specific contributions by him and his over ninety Ph.D. students and postdoctoral scholars include algorithms for feedback communications, universal estimator-correlator detector structures for random signals in noise and the concept of displacement structure leading to fast algorithms in many fields, such as estimation, control, direction of arrival estimation, adaptive filtering, channel identification and equalization, VLSI systems for signal processing, matrix theory and linear algebra. Much of his early work outpaced what could be implemented at the time. As technology advanced, Dr. Kailath and his students were able to successfully address industrial issues in areas such as optical lithography and multiple antenna wireless communications.

His research and teaching have ranged over several fields of engineering and mathematics: information theory, communications, linear systems, estimation and control, signal processing, semiconductor manufacturing, probability and statistics, and matrix and operator theory. He has also co-founded and served as a director of several high-technology companies. He has mentored an outstanding array of over a hundred doctoral and postdoctoral scholars. Their joint efforts have led to over 300 journal papers, a dozen patents and several books and monographs, including the major textbooks: Linear Systems (1980) and Linear Estimation (2000).

Spline functions, which are solutions to certain deterministic optimization problems, can also be regarded as solutions to certain stochastic optimization problems; in particular, certain linear least-squares estimation problems. Such an interpretation leads to simple recursive algorithms for interpolating and smoothing splines. These algorithms compute the spline using one data point at a time, and are useful in real-time calculations when data are acquired sequentially.

The two-dimensional tracking problem in a clutter environment is solved in the discrete-time Bayes optimal (nonlinear, and non-Gaussian) estimation framework. The proposed method recursively finds the probability density functions of the target position and velocity. With our approach, the nonlinear estimation problem is converted into simpler linear convolution operations that can be implemented with optical devices efficiently. We present a possible optical implementation architecture, and its functionality is verified through computer simulation.

State-space modelling, solution and analysis of state-space equations. Control systems aspects include state feedback and pole placement, state estimation and optimal control. System identification, which is complementarily related to control systems design/analysis will develop and solve linear methods of model identification and creation from data. be457b7860

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