Maximum Likelihood Localization of Radioactive Sources Against a Highly Fluctuating Background

This paper considers the use of maximum likelihood estimation to localize a stationary source from total gamma ray counts, in an open area setting with a highly fluctuating background. As this turns out to be a highly nonconcave maximization, convergence rates of global convergent algorithms, such as simulated annealing, can be very slow and iterative algorithms such an Newton´s method for maximization can be captured by local maxima while fast. Thus, the selection of the initial estimate is critical to how well they perform. This paper proposes a way to generate such an initial estimate using an averaging process that is shown to be asymptotically convergent to the maximum likelihood source estimate. This ensures that with a sufficiently large number of samples, the initial estimate is indeed within of the basin of attraction of such iterative algorithms. Analytical results are supported by numerical simulations based on a measured background data and synthetically injected source data.