Cramer-Rao Bound for Source Localization of Ingested Sources in the Human Intestine Using Finite-Element Method

In this paper we propose a computational framework using bioelectromagnetic equations for a general electromagnetic source that can account for both RF and microwave sources. We then calculate corresponding EM scatter field using realistic, fully segmented geometry of the human tract and finite-element model. We derive the corresponding inverse model for WEC localization and estimate the location and orientation of the WEC. In order to evaluate the performance of the proposed algorithm we also derive Cramer-Rao bound which is a commonly used tool in statistical signal processing used to evaluate performance of the unbiased estimators. Using our previous work we also account for the gastric pacemaker activity and evaluate its effect on the source localization accuracy and Cramer-Rao bound. In order to provide potentially useful guidelines we examine several different configurations using different source intensities, frequencies and coil orientations. As a result by calculating the lowest possible variance of the localization algorithms we expect to propose an efficient mathematical representation for the source that enables most accurate localization. We then demonstrate applicability of our results by performing numerical simulations and comparing the estimation accuracy for various configurations.