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We consider the robust localization of radioactive sources by using their gamma-ray count at the smallest number of sensors needed to theoretically localize. We formulate a class of non-convex cost functions and consider their gradient descent optimization. We show that in -dimensions, if there are exactly sensors and the source lies in their open convex hull, then this convex hull is devoid of false stationary points. Thus we augment gradient descent with random projections into the convex hull, when an estimate leaves it. We argue that convergence in probability to the correct source location, will occur. Simulations demonstrate the efficacy of this algorithm.

We describe the key ideas behind our implementation of distributed beamforming on a GNU-radio based softwaredefined radio platform. Distributed beamforming is a cooperative transmission scheme whereby a number of nodes in a wireless network organize themselves into a virtual antenna array and focus their transmission in the direction of the intended receiver, potentially achieving orders of magnitude improvements in energy efficiency. This technique has been extensively studied over the past decade and its practical feasibility has been demonstrated in multiple experimental prototypes. Our contributions in the work reported in this paper are three-fold: (a) the first ever all-wireless implementation of distributed beamforming without any secondary wired channels for clock distribution or channel feedback, (b) a novel digital baseband approach to synchronization of high frequency RF signals that requires no hardware modifications, and (c) an implementation of distributed beamforming on a standard, open platform that allows easy reuse and extension. We describe the design of our system in detail, present some initial results and discuss future directions for this work.

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.

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