Infinite-dimensional sampled-data Kalman filtering and the stochastic heat equation

In this paper we apply the infinite-dimensional sampled-data Kalman filter (ISKF) to a system characterized by the stochastic heat equation for the purpose of estimating the temperature distribution along a slender (one-dimensional) cylindrical rod using a simple linear measurement model. The key to...

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Bibliographic Details
Published in49th IEEE Conference on Decision and Control (CDC) pp. 5062 - 5067
Main Authors Sallberg, Scott A, Maybeck, Peter S, Oxley, Mark E
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.12.2010
Subjects
Adaptation model
Approximation methods
Heating
Kalman filters
Mathematical model
Noise
Stochastic processes
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Summary:In this paper we apply the infinite-dimensional sampled-data Kalman filter (ISKF) to a system characterized by the stochastic heat equation for the purpose of estimating the temperature distribution along a slender (one-dimensional) cylindrical rod using a simple linear measurement model. The key to applying the ISKF is the development of an essentially equivalent finite-dimensional discrete-time model from an infinite-dimensional continuous-time dynamics model. In addition to estimating the temperature of the rod, we employ a bank of elemental filters via the multiple model adaptive estimation (MMAE) technique to estimate unknown model parameters such as the thermal diffusivity constant of the slender cylindrical rod.
ISBN:142447745X
9781424477456
ISSN:0191-2216
DOI:10.1109/CDC.2010.5717157