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 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.