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.