Localization of chemical sources using stochastic differential equations

Localization of chemical sources and prediction of their spread is an important issue in many applications. We propose computationally efficient framework for localizing low-intensity chemical sources using stochastic differential equations. The main advantage of this technique lies in the fact that it accounts for random effects such as Brownian motion which are not accounted for in commonly used classical techniques based on Fick’s law of diffusion. We model the dispersion using Fokker-Planck equation and derive corresponding inverse model. We then derive maximum likelihood estimator of source intensity, location and release time. We demonstrate the applicability of our results using numerical examples.