Name: Aku Seppänen

Email: Aku.Seppanen@uku.fi

CompanyName: University of Kuopio

Country: Finland

Abstract: In this paper we consider tomographic imaging of moving fluids with
electrical impedance tomography (EIT) in process industry.
We have recently applied the state estimation approach to imaging
nonstationary targets with EIT.
In state estimation approach the target is modeled as a stochastic
process.
This evolution model together with the observation model of EIT
constitute the state-space representation of EIT.
The estimate for the time-varying conductivity distribution is
computed from EIT measurements based on this state-space
representation.
In the case of moving fluids the evolution model for the target can be
for example the stochastic convection-diffusion model.
In our previous studies the velocity field was assumed to be known {\it
a priori}, when constructing the convection-diffusion model for the
target evolution.
The state estimation scheme has been shown to give excellent results in
comparison to the stationary reconstructions, especially in the case
that the target changes very rapidly in comparison to the rate
of measurements.

In this paper we consider the state estimation approach in the case
that the velocity field is unknow.
We parameterize the velocity field and estimate the velocity parameters
together with the conductivity distribution.
This new estimation problem with additional unknown variables is
a nonlinear state estimation problem.
The recursive algorithms used for solving this problem are of extended
Kalman filter (EKF) -type.
In our numerical studies we illustrate the estimation of different kinds of
stationary velocity profiles.
Furthermore, the estimation of time-varying velocity fields is
considered.

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