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nwrk - Boston University Department of Electrical and...

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Boston University Department of Electrical and Computer Engineering EC505 STOCHASTIC PROCESSES Norbert Wiener and Rudolf Kalman Norbert Wiener Rudolf Kalman Born: 1894, Columbia Missouri 1905: Entered Tufts college (age 11) 1909: Harvard graduate student in zoology (age 15) 1912: Harvard Ph.D. in Mathematical Logic (age 18) 1919: Position in MIT Math Department (age 25) 1932: Worked on: f ( x ) = Z 0 K ( x - y ) f ( y ) dy 1963: Winner National Medal of Science Worked on problems of fire control for WWII Father of “Cybernetics” Wiener Filter is a closed form, analytic solution Born: 1930, Budapest Hungary 1953: S.B. from MIT 1954: S.M. from MIT 1957: Sc.D. from Columbia 1958-59: DT LLSE “Kalman Filter” developed 1960-61: CT LLSE “Kalman Filter” developed with Bucy 1964-1971: Stanford University 1971-: Swiss Federal Institute of Technology (ETH) Motivated by control problems Showed duality between filtering and control problems Kalman Filter is an algorithm that needs a computer 1
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Engineers Look to Kalman Filtering for Guidance Barry Cipra SIAM News, Vol. 26, No. 5, August 1993 The American Society of Mechanical Engineers is probably not the first source you’d consult for a funda- mental paper in applied mathematics. Nonetheless, in 1960 and 1961, ASME’s Journal of Basic Engineering published not one, but two highly influential mathematics papers–papers that helped man set foot on the moon in the late 1960s and that today help commercial airline pilots get from New York to Seattle without winding up in, say, San Diego. Titled “A New Approach to Linear Filtering and Prediction Problems” and “New Results in Linear Filtering and Prediction Theory,” the two papers–the first by Rudolf Kalman, then of the Research Institute for Advanced Studies in Baltimore, the second by Kalman and Richard Bucy, then of the Johns Hopkins Applied Physics Laboratory–introduced a technique now widely known as Kalman filtering. In the past 30 years, Kalman filtering (often also called Kalman-Bucy filtering) has established itself as a workhorse among techniques in signal processing and control theory. Kalman filtering addresses an age-old question: How do you get accurate information out of inaccurate data? More pressingly, How do you update a “best” estimate for the state of a system as new, but still inaccurate, data pour in? Much as a coffee filter serves to keep undesirable grounds out of your morning mug, the Kalman filter is designed to strip unwanted noise out of a stream of data. The applications are endless. Kalman filtering has proved useful in navigational and guidance systems, radar tracking, sonar ranging, and satellite orbit determination, to name just a few areas. Kalman and Bucy’s original papers have generated thousands of other papers on aspects and applications of filtering.
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