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RESEARCH PAPERS: Additional Technical Papers

A Discrete-Time Adaptive Filter for Stochastic Distributed Parameter Systems

[+] Author and Article Information
K. Watanabe

Department of Aeronautical Engineering, Kyushu University, Fukuoka, Japan

T. Yoshimura, T. Soeda

Department of Mechanical Engineering, Tokushima University, Tokushima, Japan

J. Dyn. Sys., Meas., Control 103(3), 266-278 (Sep 01, 1981) (13 pages) doi:10.1115/1.3140638 History: Received June 23, 1980; Online July 21, 2009

Abstract

A discrete-time adaptive filter is derived for a distributed system described by a linear partial differential equation with some unknown random constants whose a priori probabilities are known. The system concerned contains the Gaussian white noise in time, and its measurement system is treated as a so-called pointwise observation in which the measurement is taken at the finite discrete subdomains in the coordinate spaces. The use is conceptually made of an adaptive technique based on the Bayesian method and it is shown that the optimal distributed filter proposed here can be partitioned into two parts, a linear nonadaptive part that consists of a bank of distributed Kalman-Bucy type filters and a nonlinear part that incorporates the learning nature of the estimator. For the derivation of each “elemental filter”, the discrete-time innovation theory is utilized. The eigenfunction expanding method in a complete orthonormal system is applied for the numerical procedure of the proposed filter. From the simulation of the estimation problem for the neutron flux distribution in a slab type nuclear reactor, the proposed adaptive filter is shown to have attractive characteristics and therefore can be recommended for practical online adaptive estimation of distributed parameter systems.

Copyright © 1981 by ASME
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