State space models in process tomography — approximation of state noise covariance

Abstract

In this paper we consider process tomography in the case of time-varying objects. Especially, we concentrate on the case in which the indirect observations from the system are obtained via electrical impedance tomographic (EIT) measurements and in which the time-evolution of the target can be described by a stochastic convection-diffusion model. We use the state estimation approach to obtain the tomographic reconstructions. The state estimation problem is solved with the fixed-lag Kalman smoother algorithm that is a feasible approach for continuous observation with an insignificant delay in the reconstructions. In particular we focus on the covariance structures associated with state space model. The covariance structures determine the temporal and spatial regularization properties of the algorithm. It is shown that the adoption of nontrivial covariance structures in the evolution model yields good estimates for the time-varying object in such a situation in which stationary reconstructions are completely useless.