Biochemical Transport Modeling and Bayesian Source Estimation in Realistic Environments

Early detection and estimation of the spread of a biochemical contaminant are major issues in many applications, such as homeland security and pollution monitoring. We present an integrated approach combining the measurements given by an array of biochemical sensors with a physical model of the dispersion and statistical analysis to solve these problems and provide system performance measures. We approximate the dispersion model of a contaminant in a realistic environment through numerical simulations of reflected stochastic diffusions describing the microscopic transport phenomena due to wind and chemical diffusion and use the Feynmann-Kac formula. We consider arbitrary complex geometries and account for wind turbulence. Numerical examples are presented for two real-world scenarios: an urban area and an indoor ventilation duct. Localizing the dispersive sources is useful for decontamination purposes and estimation of the cloud evolution. To solve the associated inverse problem, we propose a Bayesian framework based on a random field that is particularly powerful for localizing multiple sources with small amounts of measurements