Some theoretical limits on nuclear source localization and tracking

We consider the simple and general estimation problem of finding the location of a nuclear source from radiation measurements. Our objective is to study the effect of the inherent quantum randomness of radioactive emissions on the accuracy to which nuclear sources can be localized. To this end, we consider an ideal mobile detector making perfect, noiseless measurements and formulate a general problem of maximum likelihood estimation of source location using such measurements. For the case of a stationary source and a detector moving with uniform speed in a straight line, we derive solutions to the maximum likelihood location estimate as well as the corresponding Cramer-Rao lower bounds. We present a simple iterative procedure for calculating the ML estimate, and argue that in the asymptotic case of source strength becoming large, the procedure converges to the ML estimate with high probability and this estimate is unbiased. We also present simulations showing that the maximum likelihood estimates approach the Cramer-Rao bounds, and comment on the implications of these theoretical results with ideal detectors and perfect estimators to the problem of nuclear source localization.