Maximum Likelihood Localization of Radiation Sources with unknown Source Intensity

Abstract

In this paper, we consider a novel and robust maximum likelihood approach to localizing radiation sources with unknown statistics of the source signal strength. The result utilizes the smallest number of sensors required theoretically to localize the source. It is shown, that should the source lie in the open convex hull of the sensors, precisely $N+1$ are required in $\mathbb{R}^N, ~N \in \{1,\cdots,3\}$. It is further shown that the region of interest, the open convex hull of the sensors, is entirely devoid of false stationary points. An augmented gradient ascent algorithm with random projections should an estimate escape the convex hull is presented.