Some theoretical limits on nuclear source localization and tracking

Abstract

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 estima tion 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.Index Terms-Nuclear source localization, maximum likeli hood estimation, inhomogenous Poisson process.

Poisson source localization on the plane: the smooth case

“…where τ j = τ j (ϑ) is of course smooth function of ϑ. Recall that if κ ∈ 0, 1 2 , then we have cusp case [2] and if κ > 1 2 , then we have the smooth case considered in this work. We start with the problem of estimation the parameter τ = (τ 1 , .…”

“…The smooth case a) is studied in this work. See as well the work [1], where the similar model was considered. The case b) is discussed below in the Section 4.…”

Autonomous Distributed 3D Radiation Field Estimation for Nuclear Environment Characterization

“…The area of radiation field mapping and source localization has been studied through a set of contributions such as [2][3][4][5][6]. Among them, maximum likelihood estimation is utilized in [4,6], numerical adjoints in conjuction to a bayesian formulation are used in [2], while a particle filter is employed in [3].…”

Poisson Source Localization on the Plane. Change-Point Case

“…The detection of hidden nuclear material by means of sensors is an active area of research as part of defensive strategies. One can consult the work of Baidoo [1], Liu [16] and Rao [23] for details and references on this topic. Nuclear radiations are a probabilistic physical process consisting of discrete emissions of particles that can be recorded by radiation sensors.…”

“…An iterative procedure for calculating MLEs of a single nuclear source from radiation measurements as well as corresponding Cramer-Rao bounds for localization accuracy was given by Baidoo [1]. Concerning Bayesian statistics Liu [16] presented a technique to locate a source according to Bayesian update methods.…”