2003年度 第1回システム制御セミナー

「Progressive Bayes: A New Framework for Nonlinear State Estimation」

日時 平成15年8月1日(金) 10:30 〜 12:00
会場 金沢大学 工学部 第 1 会議室
(金沢市 小立野 2-40-20)

講演者 Prof. Dr. -Ing. Uwe D. Hanebeck
Institute for Computer Design and Fault Tolerance
University of Karlsruhe
講演題目 「Progressive Bayes: A New Framework for Nonlinear State Estimation」
This talk is concerned with estimating the internal state of a dynamic system by processing measurements taken from the system output. An exact analytic representation of the probability density functions characterizing the estimate may not be possible to obtain. Even when available, it may be too complex or not practical because, for example, recursive application is required. Hence, approximations are generally inevitable. Gaussian mixture approximations are convenient for a number of reasons. However, calculating appropriate mixture parameters that minimize a global measure of deviation from the true density is a tough optimization task. Here, we propose a new approximation method that minimizes the squared integral deviation between the the true density and its mixture approximation. Rather than trying to solve the original problem, it is converted into a corresponding system of explicit ordinary first-order differential equations. This system of differential equations is then solved over a finite "time" interval, which is an efficient way of calculating the desired optimal parameter values. For polynomial measurement nonlinearities, closed-form analytic expressions for the coefficients of the system of differential equations are derived.

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