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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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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Abstract 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.
AbstractList 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.
Author Oxley, Mark E
Sallberg, Scott A
Maybeck, Peter S
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  givenname: Peter S
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  givenname: Mark E
  surname: Oxley
  fullname: Oxley, Mark E
  email: Mark.Oxley@afit.edu
  organization: Dept. of Math. & Stat., Air Force Inst. of Technol., Wright-Patterson AFB, OH, USA
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Snippet 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...
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StartPage 5062
SubjectTerms Adaptation model
Approximation methods
Heating
Kalman filters
Mathematical model
Noise
Stochastic processes
Title Infinite-dimensional sampled-data Kalman filtering and the stochastic heat equation
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