The effect of data collection geometry on radiological source localisation

This paper examines how different data collection geometries influence the topography of objective function surfaces in radiological source localisation. It is shown that data gathered along the circumference of a circle around a point radiation source has an associated mirror image source of a different strength that exists outside the circle. When the radius of the circle becomes infinity, then the path becomes a straight line, and it results in a mirror image source of identical strength to the original source. These image sources cause the objective function surfaces to have global optima that are identical to the true source optima making source localisation algorithms to sometimes converge to image solutions and return unacceptable parameter estimates. Cramer-Rao bounds computed for the parameter estimators do not reflect this geometry-dependent uncertainty. It appears that data acquired along an irregular path generated using a random walk eliminate the image sources making source parameter estimation easier.