Localization of Electrodes based on Resistance Measurements

This paper considers the problem of the localization of electrodes in a distributed sensor system. Especially in impedance tomography the localization of the electrodes is of great importance, since deviations from nominal positions affect the result of the inverse problem. Conformal mapping allows to obtain analytical solutions of the resistances for complex geometries. By measuring the resistances between the electrodes, an estimation of the distance between each pair of electrodes is possible. In the case of non-adjacent electrodes this result is biased by the other electrodes. The mass-spring-relaxation algorithm offers a possibility of an error-tolerant localization by only using distances between neighboring electrodes. However, the robustness against attaining local minima depends on the initial guess of the arrangement. To overcome this, the classical multidimensional scaling algorithm was used to obtain an initial guess of the positions of all elements in the network. The combination of the two algorithms is analyzed. A verification on simulated results with cylindrical electrodes demonstrates the effectiveness of the approach.