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 position 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.