9802423 Rozovskii Each time an outfielder tracks and catches a fly ball, he intuitively solves a problem of target tracking. That problem has stymied engineers, mathematicians, and computer scientists for years. Two great mathematicians, American, Norbert Wiener and Russian, Andrey Kolmogorov, first approached the problem during World War II. Rather than catching fly balls, Kolmogorov and Wiener were trying, in the days before computers, to develop mathematical algorithms that would help to track enemy aircraft by radar. The research started by Kolmogorov and Wiener has developed into a thriving area of applied mathematics known as Filtering Theory. Filtering, estimation of a signal or an image from noisy data, is the basic component of the data assimilation in target tracking. It is of central importance in navigation, image and signal processing, control theory, automatic tracking systems and other areas of engineering and science. This research is a joint collaborative effort between researchers at the Institute of Mathematics and Informatics, Vilnius, Lithuania, and researchers at the University of Southern California. The project is devoted to applications of stochastic partial differential equations to nonlinear filtering. The focus of the research is twofold: (1) Cauchy- boundary problems for parabolic partial differential equations arising in nonlinear filtering of stochastic processes evolving under some constraints; and (2) nonlinear filtering with distributed observation and applications to tracking of low-observable targets in images. The research will also consider the numerical aspects of nonlinear filtering. It is expected that relatively simple nonlinear filtering algorithms which are not too demanding in computational and memory requirements for on-line implementation and yet are nearly optimal from a statistical viewpoint will be developed for a wide variety of applications. The applications include air traffic control, human-computer interfaces based on motion- capture, and advanced optical and magnetic registration systems.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Keith Crank
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University of Southern California
Los Angeles
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