Unscented Kalman filter approach to tracking a moving interfacial boundary in sedimentation processes using three-dimensional electrical impedance tomography

Abstract

The monitoring of solid-fluid suspensions under the influence of gravity is widely used in industrial processes. By considering sedimentation layers with different electrical properties, non-invasive methods such as electrical impedance tomography (EIT) can be used to estimate the settling curves and velocities. In recent EIT studies, the problem of estimating the locations of phase interfaces and phase conductivities has been treated as a nonlinear state estimation problem and the extended Kalman filter (EKF) has been successfully applied. However, the EKF is based on a Gaussian assumption and requires a linearized measurement model. The linearization (or derivation of the Jacobian) is possible when there are no discontinuities in the system. Furthermore, having a complex phase interface representation makes derivation of the Jacobian a tedious task. Therefore, in this paper, we explore the unscented Kalman filter (UKF) as an alternative approach for estimating phase interfaces and conductivities in sedimentation processes. The UKF uses a nonlinear measurement model and is therefore more accurate. In order to justify the proposed approach, extensive numerical experiments have been performed and a comparative analysis with the EKF is provided.

New and emerging tomographic imaging techniques in medical and industrial applications

“…For these reasons, dynamic imaging techniques are important for the successful use of these imaging techniques for process monitoring. Khambampati et al (2009) present various methods of dynamic image reconstruction in electrical impedance tomography, a key technique in industrial process monitoring, which have been studied and the results are compared.…”

Mathematical concepts for image reconstruction in tomography

“…For the dynamic imaging, the Kalman filter algorithm and its variants are plausible (Khambampati, Rashid, Kim, Soleimani, & Kim, 2009;Kim et al, 2001Kim et al, , 2006Trigo, Gonzalez-Lima, & Amato, 2004;Vauhkonen, Karjalainen, & Kaipio, 1998). The Kalman filter well known in the control theory was devised to estimate the state of a discrete-time-controlled process governed by the linear stochastic difference equation with measurements.…”

An EKF based estimation scheme for sedimentation processes in vessels using EIT-type measurement data

“…However, these techniques are complex, invasive in nature and often too expensive, making it impracticable to use them online. Electrical impedance tomography (EIT) is a fast and non-invasive measurement technique in which an internal image can be reconstructed by imposing an electrical current and measuring voltages across the electrodes attached to the walls of the sedimentation tank [21][22][23]. This approach is suitable for the online estimation of settling parameters (such as settling curves and settling velocities) without the need to use a transparent settling tank.…”