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Explicit Solution of the Generalized Kolmogorov Equation in Brockett-Mitter Program
Explicit Solution of the Generalized Kolmogorov Equation in Brockett-Mitter Program
组织者
演讲者
时间
2023年07月03日 15:00 至 15:30
地点
数学系理科楼A-304
摘要
Ever since the technique of the Kalman-Bucy filter was popularized, there has been an intense interest in finding new classes of finite-dimensional recursive filters. In the late 1970s the concept of the estimation algebra of a filtering system was introduced. In 1990, Tam, Wong, and Yau presented a rigorous proof of the Brocket-Mitter program which allows one to construct finite-dimensional recursive filters from finite-dimensional estimation algebras. Later Yau wrote down explicitly a system of ordinary differential equations and generalized Kolmogorov equation to which the robust DMZ equation can be reduced. Thus there remains three fundamental problems in Brockett-Mitter program, first of which is the problem of finding explicit solution to the generalized Kolmogorov equation. We will share these results in the presentation.