In this investigation, we propose several algorithms to recover the location and intensity of a radiation source located in a simulated 250 m × 180 m block in an urban center based on synthetic measurements. Radioactive decay and detection are Poisson random processes, so we employ likelihood functions based on this distribution. Due to the domain geometry and the proposed response model, the negative logarithm of the likelihood is only piecewise continuous differentiable, and it has multiple local minima. To address these difficulties, we investigate three hybrid algorithms comprised of mixed optimization techniques. For global optimization, we consider Simulated Annealing (SA), Particle Swarm (PS) and Genetic Algorithm (GA), which rely solely on objective function evaluations; i.e., they do not evaluate the gradient in the objective function. By employing early stopping criteria for the global optimization methods, a pseudo-optimum point is obtained. This is subsequently utilized as the initial value by the deterministic Implicit Filtering method (IF), which is able to find local extrema in non-smooth functions, to finish the search in a narrow domain. These new hybrid techniques combining global optimization and Implicit Filtering address difficulties associated with the non-smooth response, and their performances are shown to significantly decrease the computational time over the global optimization methods alone. To quantify uncertainties associated with the source location and intensity, we employ the Delayed Rejection Adaptive Metropolis (DRAM) and DiffeRential Evolution Adaptive Metropolis (DREAM) algorithms. Marginal densities of the source properties are obtained, and the means of the chains' compare accurately with the estimates produced by the hybrid algorithms.

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Source localization, such as detecting a nuclear source in an urban area or ascertaining the origin of a chemical plume, is generally regarded as a well-documented inverse problem; however, optimally placing sensors to collect data for such problems is a more challenging task. In particular, optimal sensor placement-that is, measurement locations resulting in the least uncertainty in the estimated source parameters-depends on the location of the source, which is typically unknown a priori. Mobile sensors are advantageous because they have the flexibility to adapt to any given source position. While most mobile sensor strategies designate a trajectory for sensor movement, we instead employ mutual information, based on Shannon entropy, to choose the next measurement location from a discrete set of design conditions. K E Y W O R D SBayesian inference, inverse problem, mutual information, sensor placement, source localization

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