Adaptive Kalman filter-based information fusion in electrical impedance tomography for a two-phase flow

Abstract

Electrical impedance tomography (EIT) is a severely ill-posed nonlinear inverse problem. In order to obtain solutions with physical meaning, the inverse of the model of measurements requires the combination of information from various sources. This paper proposes a new approach through Kalman filtering for adaptive integration of EIT measurements, Tikhonov regularization and evolution models for the characterization of a two-phase air–water fluid flow. The Tikhonov regularization factor is embedded into the observation error covariance matrix, thus allowing for individual adjustment for each of the regularization equations. The filter outputs for different evolution models—random walk, advective and advective–diffusive—are compared in terms of estimate convergence and physical meaning. With the random walk evolution model the analysis of experimental data shows that the proposed information fusion strategy provides fewer artifacts, enabling a more effective identification of the phase interfaces. When the other two evolution models are incorporated into the Kalman filter and compared with the random walk model, faster and more accurate estimates of the flow are obtained even away from the electrodes, as well as sharper phase interfaces are identified. The results suggest that the reason for this improved performance is the fused information from the upstream–downstream dynamics of the advective and advective–diffusive models with the outer-inner structure influence of measurements.