Lectures on Wiener and Kalman Filtering
Suppose we have two random variables X, Y with a known joint density function fx,y(.,.). Assume that in a particular experiment, the random variable Y can be measured and takes the value y. What can be said about the corresponding value, say x, of the uno
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by Thornas KAI LATH
Department of Electrical Engineering Stanford University Stanford, Califomia 94305
T. Kailath, Lectures on Wiener and Kalman Filtering © Springer-Verlag Wien 1981
PREFACE These notes were first prepared for use in a special ten-hour lecture course at the CISM (Centre International des Seiences Mecaniques), Udine, Italy, ]une 11-22, 1972. The material in the first nine chapters was covered to varying degrees in the lectures, but advantage has been taken of the intervening time to slightly modify the text, especially with a view to including more UJrto-date references. Though several interesting results have appeared since 1972, I have resisted the temptation to include them here, except for a partial outline in the concluding Chapter 10 and a few exercises added at various points. At the last minute, it was also decided to reprint a recent survey paper as an Appendix. Though no attempt has been made to prepare a comprehensive set of exercises, I may say that the notes in this form have been used as a text for a one-quarter course at Stanford. I am grateful to many people for helping to deepen my understanding of the remarkably broad field of least-squares theory and I should like to mention W. Root, R. Price, D. Slepian, L. Zadeh, E. Parzen, F. Beutler, A. Balakrishnan, ]. Clark, L. Shepp, R. Kalman, A. Shiryaev, R. Lip'ser, G. Kallianpur, P.A. Meyer, A. Yaglom, M. Zaka~ ]. Ziv, E. Wong, T. Kadota, T. Hida, H. Kunita, M. Hitsuda, H. Akaike, ]. Rissanen, A. Schumitzky, B. Anderson, L. Silverman, A. Bryson, R. Bucy, L.A. Zachrisson, D. Lainiotis, ]. Moore, G. Bierman, M. Davis, L. Ljung and several former students, especiaUy ]. Omura, P. Faurre, P. Frost, R. Geesey, T. Duncan, B. Gopinath, D. Duttweiler, H. Aasnaes, M. Gevers, H. Weinert, A. Segall, N. Krasner, M. Morf, G. Sidhu, B. Dickinson, B. Friedlander, A. Vieira, S. Y. Kung and B. Levy. The manuscript was typed by Barbara McKee with the same skiU, and the same cheerfulness and patience with Iast-minute changes and deadlines, as she has shown with essentiaUy all my published (and unpublished) work. It also gives me great pleasure to acknowledge the consistent and generous research support of the Applied Mathematics Division of the Air Force Office of Scientific Research, which since 1963 has enabled me, with a minimum of overhead and reporting requirements, to pursue the studies that have provided the background on which these notes are based. I am grateful to Professor Sandor Csibi of Budapest, Professor Giuseppe Longo of Trieste, and the CISM staff, for the invitation to present these lectures and especially for their patience with the long delay in my release of this still quite rough
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manuscript. The reasons for this behavior are weU-known to aU authors (and many more potential authors), but perhaps they were best put by a writer on a different subject: "What we do here is nothing to what we dream of doing" in ]ustine, by D.A.F. de Sade.
T. Kailath Stanford, California June 1975
SECOND EDITION
The increasing use of these shott
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