State estimation with fluid dynamical evolution models in process tomography - an application to impedance tomography

In this paper we consider the reconstruction of rapidly varying objects in process tomography. The evolution of the physical parameters can often be a pproximated with stochastic convection-diffusion and fluid dynamics models. We use the state estimation approach to obtain the tomographic reconstruct ions and show how these flow models can be exploited with the actual observ ation models that by themselves induce ill-posed problems. The state estima tion problem can be stated in different ways based on the available tempora l information. We concentrate on such cases in which continuous monitoring is essential but a small delay for the reconstructions is allowable. The st ate estimation problem is solved with the fixed-lag Kalman smoother algorit hm. As the boundary observations we use the voltage data of electrical impe dance tomography, We also give a numerical illustration of the approach in a case in which we track a bolus that moves rapidly through a pipeline.