The maximum likelihood estimate for radiation source localization: Initializing an iterative search

The maximum likelihood estimate approach is adopted in this paper for finding the unknown radiation source location and strength. The problem is nonlinear and has to rely on iterative numerical algorithms. Since the problem has possibly multiple local maxima, the initial estimate in those iterative algorithms plays a critical role in guaranteeing the global optimum. This paper proposes a way to generate such an initial estimate which is easy to calculate. Besides some insights that justifies the proposed approach, it is shown that the proposed initial estimate actually converges to the true but unknown maximum likelihood estimate asymptotically thus ensuring that the initial estimate is indeed in a neighborhood of the maximum likelihood estimate and consequently the convergence to the global optimum by local iterative numerical algorithms.