A Kalman Filter Approach for the Application of Electrical Capacitance Tomography in Dynamic Processes using a State Reduction

Electrical capacitance tomography (ECT) refers to an imaging technique, which provides information about the spatial material distribution within an object. Since the image reconstruction forms a non-linear ill-posed inverse problem, prior information about the occurring material distributions is required in order to obtain stable reconstruction results. For the monitoring of dynamic industrial processes by means of ECT, recursive Bayesian estimation such as the extended Kalman filter (EKF) were shown to be suitable reconstruction algorithms. Though due to the usually high dimension of the inverse problem, computational costs are an immanent issue for the tracking of fast changes in the material distribution. In this paper we present a sample based state reduction approach for the extended Kalman filter. This approach not only allows stable reconstruction results but also involves significantly decreased reconstruction times due to the reduced state space.

[1]  Jari P. Kaipio,et al.  A Kalman filter approach applied to the tracking of fast movements of organ boundaries , 1998, Proceedings of the 20th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. Vol.20 Biomedical Engineering Towards the Year 2000 and Beyond (Cat. No.98CH36286).

[2]  H.-C. Kim,et al.  Electrical impedance tomography reconstruction algorithm using extended Kalman filter , 2001, ISIE 2001. 2001 IEEE International Symposium on Industrial Electronics Proceedings (Cat. No.01TH8570).

[3]  Thomas Bretterklieber,et al.  PCA Based State Reduction for Inverse Problems Using Prior Information , 2017 .

[4]  W. Marsden.  I and J , 2012 .

[5]  Tomasz Dyakowski,et al.  Application of electrical capacitance tomography for measurement of gas-solids flow characteristics in a pneumatic conveying system , 2001 .

[6]  Huaxiang Wang,et al.  A review on image reconstruction algorithms for electrical capacitance/resistance tomography , 2016 .

[7]  Daniel Watzenig,et al.  Reconstruction of inhomogeneities in fluids by means of capacitance tomography , 2003 .

[8]  M. Neumayer,et al.  Current Reconstruction Algorithms in Electrical Capacitance Tomography , 2011 .

[9]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[10]  E. Somersalo,et al.  Statistical and computational inverse problems , 2004 .

[11]  Dan Simon,et al.  Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches , 2006 .

[12]  D. Simon,et al.  Kalman filtering with state equality constraints , 2002 .