Fixed-lag smoothing and state estimation in dynamic electrical impedance tomography

In electrical impedance tomography (EIT), an approximation for the internal resistivity distribution is computed based on the knowledge of the injected currents and measured voltages on the surface of the body. The conventional approach is to inject several di erent current patterns and use the associated data for the reconstruction of a single distribution. This is an ill-posed inverse problem. In some applications the resistivity changes may be so fast that the target changes between the injection of the current patterns and thus the data do not correspond to the same target distribution. In these cases traditional reconstruction methods yield severely blurred resistivity estimates. We have earlier proposed to formulate the EIT problem as an augmented system theoretical state estimation problem. The reconstruction problem can then be solved with Kalman lter and Kalman smoother algorithms. In this paper, we use the so-called xed-lag smoother to solve the dynamic EIT reconstruction problem. We show that data storage di culties that are associated with the previously used xed-interval smoother can be avoided using the xed-lag smoother. The proposed methods are compared with simulated measurements and real data.